CERN-PH-TH-2014-069MCNET-14-08OUTP-14-05P

Tuning PYTHIA 81 the Monash 2013 Tune

P Skands1 S Carrazza2 J Rojo13

1 Theoretical Physics CERN CH-1211 Geneva 23 Switzerland2 Dipartimento di Fisica Universita di Milano and INFN Sezione di Milano Via Celoria 16 I-20133

Milano Italy3 Rudolf Peierls Centre for Theoretical Physics 1 Keble Road University of Oxford UK

Abstract

We present an updated set of parameters for the PYTHIA 8 event generator We reevaluate theconstraints imposed by LEP and SLD on hadronization in particular with regard to heavy-quarkfragmentation and strangeness production For hadron collisions we combine the updated frag-mentation parameters with the new NNPDF23 LO PDF set We use minimum-bias Drell-Yanand underlying-event data from the LHC to constrain the initial-state-radiation and multi-parton-interaction parameters combined with data from SPS and the Tevatron to constrain the energyscaling Several distributions show significant improvements with respect to the current defaultsfor both ee and pp collisions though we emphasize that interesting discrepancies remain in partic-ular for strange particles and baryons The updated parameters are available as an option startingfrom PYTHIA 8185 by setting Tuneee = 7 and Tunepp = 14

1 Introduction

A truly impressive amount of results on QCD has been produced by the first run of the LHC Mostof these are already available publicly eg via the data preservation site HEPDATA [1] A largefraction has also been encoded in the analysis preservation tool RIVET1 [2] Especially in the areaof soft QCD many of the experimental results have spurred further modelling efforts in the theorycommunity (nice summaries of some of the current challenges can be found in [3 4]) while there isalso significant activity dedicated to improving (ldquotuningrdquo) the parameters of the existing models tobetter describe some or all of the available new data (see eg the recent review in [5])

The PYTHIA event generator [6 7] has been extensively compared to LHC data and severaltuning efforts have already incorporated data from Run 1 [5 8ndash16] However in particular for thenewest version of the model PYTHIA 8 [7] it has been some time since the constraints imposedby ee colliders were revised (in 2009) and then only via an undocumented tuning effort (using thePROFESSOR tool [17]) One of the main aims of this paper is therefore first to take a critical lookat the constraints arising from LEP SLD and other e+eminus experiments reoptimize the final-stateradiation and hadronization parameters and document our findings We do this manually rather thanin an automated setup in order to better explain the reasoning behind each parameter adjustment

1In particular RIVET ensures that any (current or future) Monte Carlo event-generator codes can be compared consis-tently to the data with exactly the same cuts definitions etc as the original analysis

1

arX

iv1

404

5630

v1 [

hep-

ph]

22

Apr

201

4

This writeup is thus also intended to function as an aid to others wishing to explore the PYTHIA 8parameter space

We then consider the corresponding case for hadron colliders and use the opportunity to try outa new PDF set an LO fit produced by the NNPDF collaboration [18ndash20] which has recently beenintroduced in PYTHIA 8 (NLO and NNLO sets are also available for people that want to check theimpact of using LO vs (N)NLO PDFs in hard-scattering events) In a spirit similar to that of theso-called ldquoPerugia tunesrdquo of PYTHIA 6 [8 21] we choose the same value of αs(MZ) = 01365for both initial- and final-state radiation (Though we do regard this choice as somewhat arbitraryit may facilitate matching applications [21]) Again we adjust parameters manually and attempt togive brief explanations for each modification We also choose the αs(MZ) value for hard-scatteringmatrix elements to be the same as that in the PDFs here αs(MZ) = 013 (The difference betweenthe value used for radiation and that used for hard-scattering MEs may be interpreted as an artifact oftranslations between the CMW and MS schemes see section 33)

Below in Section 11 we begin by giving a brief general explanation of the plots and χ2 values thatare used throughout the paper Next in section 2 we describe the physics parameters and constraintsgoverning fragmentation in hadronic Z decays (final-state radiation and string fragmentation) Weturn to hadron colliders in section 3 (PDFs initial-state radiation and multi-parton interactions) Wethen focus on the energy scaling between different ee and pp (pp) collider energies in section 4including in particular the recently published high-statistics data from the Tevatron energy scan from300 to 1960 GeV [22 23] We round off with conclusions and a summary of recommendations forfuture efforts in section 5

A complete listing of the Monash 2013 tune parameters is given in appendix A Appendix Bcontains a few sets of additional plots complementing those presented in the main body of the paper

11 Plot Legends and χ2 Values

In several places we have chosen to use data sets constraints that differ from the standard onesavailable eg through RIVET (as documented below) Since our tuning setup is furthermore manualrather than automated we have in fact not relied on RIVET in this work (though we have madeextensive use of HEPDATA [1]) Instead we use the VINCIAROOT plotting tool [24] which wehave here upgraded to include a simple χ2 calculation the result of which is shown on each plot

Note that we include a blanket 5 ldquotheory uncertaintyrdquo in the definition of the χ2 value repre-senting a baseline sanity limit for the achievable accuracy of the modeling2 that also gives a basicprotection against overfitting Note also that rather than letting the MC uncertainty enter in the defi-nition of the χ2 value (and thereby risking that low statistics generate artificially low χ2 values) weuse the generated MC statistics to compute a plusmn uncertainty on the calculated χ2 value which is alsoshown on the plots Our definition of χ2 is thus

langχ2

5

rang=

1

Nbins

Nbinssumi=1

(MCi minusDatai)2

σ2Datai + (005MCi)2

(1)

with the corresponding MC uncertainty σMCi used to compute the statistical uncertainty on the χ2

computation as mentioned above As is shown here the normalization is always 1Nbins regardlessof whether the distributions are normalized to a fixed number or not and we do not attempt to takeinto account correlations between the different observables Since our tuning is not directly driven by

2We note that a similar convention is used on the MCPLOTS validation web site [25]

2

0 01 02 03 04

d(1

-T)

σ d

σ1

-310

-210

-110

1

10

2101-Thrust (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn03

01plusmn04

02plusmn05

V I

N C

I A

R O

O T

1-T (udsc)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

Figure 1 Hadronic Z decays atradics = 912 GeV The Thrust distribution in light-flavour tagged

events compared with L3 data [26]

a χ2 minimization we regard this as acceptable the χ25 values are intended merely to give an overall

indication of the level of agreement or disagreement for each observableThe resulting plots look as illustrated in fig 1 with a main pane (top) showing the distribution

itself and a bottom pane showing ratios In the top pane experimental data is always shown withfilled black square symbols with vertical black lines indicating the one-sigma uncertainties (with twoseparate black crossbars if separate statistical and systematic uncertainties are given) Lighter (grey)extensions of the vertical lines are used to indicate two-sigma uncertainties In the ratio pane the greenshaded region indicates the one-sigma uncertainty region while yellow is used to denote the two-sigma one An internal lighterdarker shading variation in each band is used to denote the breakdowninto statistical-only (inner) and statistical+systematic uncertainties (outer) whenever separate valuesfor each of these are given Finally next to each MC legend the χ2

5 value defined above is printedalong with its MC uncertainty A colour-coded box next to the χ2 value is shaded green (χ2 lt 1)yellow (1 lt χ2 lt 4) orange (4 lt χ2 lt 9) or red (9 lt χ2) depending on the level of agreement ordisagreement This functionality will be included in a forthcoming update of the VINCIA plug-in toPYTHIA 8

2 Final-State Radiation and Hadronization

The main parameter governing final-state radiation is the effective value of the strong coupling whichin PYTHIA 8 is specified by giving the value of αs(MZ) We follow the strategy of [24] and use aset of light-flavour (udsc) tagged e+eminus event shapes provided by the L3 experiment [26] to extracta best-fit value for αs(MZ) (This prevents B decays from contaminating this step of the analysisHeavy-quark fragmentation will be treated separately below) The renormalization scale for final-state shower emissions in PYTHIA is fixed to be [27]

FSR micro2R = p2

perpevol = z(1minus z)Q2 (2)

3

with Q2 = p2 minusm20 the offshellness of the emitting parton (with on-shell mass m0) and z the energy

fraction appearing in the DGLAP splitting kernels P (z) (To estimate the shower uncertainties asso-ciated with this choice of renormalization scale we recommend using ln(micro2

R)plusmn ln(2) correspondingto a factor

radic2 variation of microR)

Theoretically a set of formally subleading terms can be resummed by using 2-loop running of αsin the so-called MC (aka CMW) scheme [28] However in a leading-order code like PYTHIA thisproduces too little hard radiation in practice due to missing NLO ldquoKrdquo factors for hard emissions (seeeg the study of NLO corrections in [29]) Empirically we find that a better overall description isachieved with one-loop running which for a fixed value of ΛQCD can effectively mimic the effect ofmissing K factors via its relatively slower pace of running leading to values of αs(MZ) in the range0135minus 0140 consistent with other LO extractions of the same quantity (See [29] for an equivalentextraction at NLO)

For this study we did not find any significant advantage in reinterpreting this value in the CMWscheme3 and hence merely settled on an effective αs(MZ) = 01365 (to be compared with the currentdefault value of 01383)

For the infrared shower cutoff we choose a value close to4 ΛQCD in order to have a smoothtransition between low-pperp perturbative emissions and non-perturbative string breaks the latter ofwhich involve pperp kicks of order ΛQCD (In principle the perturbative evolution could be continuedto even lower scales if combined with a non-perturbative regularization of αs but such low cutoffvalues could risk generating problems at the fragmentation stage since the technical implementationof the string model becomes complicated if there are too many small gluon ldquokinksrdquo spaced closelyalong the strings) The set of relevant parameters in the code is

FSR Strong CouplingTimeShoweralphaSvalue = 01365TimeShoweralphaSorder = 1TimeShoweralphaSuseCMW = off

FSR IR cutoffTimeShowerpTmin = 050 for QCD radiationTimeShowerpTminChgQ = 050 for QED radiation off quarks

FSR Spin CorrelationsTimeShowerphiPolAsym = on approximate FSR polarization effects

The resulting distribution of the Thrust event-shape variable was shown in fig 1 comparing theMonash 2013 tune to the current default tune and to an alternative contemporary tune by N Fi-scher [30] To avoid clutter the other event-shape variables (C D BW and BT ) are collected inappendix B1 There are no significant changes to any of the light-flavour tagged event shapes in ourtune as compared to the current default one

21 Light-Flavour Fragmentation

Given a set of post-shower partons resolved at a scale ofQhad sim 1 GeV the non-perturbative stage ofthe fragmentation modeling now takes over to convert the partonic state into a set of on-shell hadrons

3One slight disadvantage is that the CMW scheme produces somewhat larger ΛQCD values Since the current formu-lation of the shower algorithm does not include a non-perturbative regularization of αs a higher ΛQCD value necessitatesa larger IR cutoff in the shower which can leave an undesirable gap between the transverse kicks generated by showeremissions and those generated by non-perturbative string splittings

4The IR shower cutoff must still remain somewhat above the Landau pole of αs a lower cutoff scale would activate ahardcoded protection mechanism implemented in the PYTHIA shower forcing it to be higher than ΛQCD

4

In the leading-colour approximation each perturbative dipole is dual to a non-perturbative stringpiece [31] Quarks thus become string endpoints while gluons become transverse kinks connectingtwo string pieces [32] The Lund string fragmentation model [33] describes the fragmentation of suchstring systems into on-shell hadrons

Since the shower has already resolved all the (perturbative) physics down to a transverse-momentumscale of pTmin = 05 GeV (for the Monash 2013 tune) we find it reasonable that the pperp kicks in-volved in string breaking should effectively average over dynamics in roughly the range 250 MeV =radicκπ lt σperp lt pTmin with the lower bound given by Fermi motion (with κ the string tension

see [34]) Further since we here choose pTmin to be only slightly greater than ΛQCD the size of thenon-perturbative corrections is naturally limited to kickscorrections appropriate for non-perturbativedynamics (in contrast eg to the cluster model [35] which can generate substantially larger kicks oforder the largest allowed cluster mass which can be several GeV [30]) For the Monash 2013 tunewe have settled on a value of σperp = 0335 GeV with a small (1) tail of breaks involving higher pperpvalues carried over from the default settings

StringPTsigma = 0335StringPTenhancedFraction = 001StringPTenhancedWidth = 20

This value is obtained essentially from the first two bins of the Thrust distribution fig 1 and from thebins near zero of the other event shapes see appendix B1 Note that the σperp value is interpreted as thewidth of a Gaussian distribution in the total pperp (measured transversely to the local string directionwhich may differ from the global event axis) such that each of the px and py components have aslightly smaller average value σ2

xy = 12σ

2perp = (0237 GeV)2 Also note that each non-leading hadron

will receive two pperp kicks one from each of the breaks surrounding it hencelangp2perphad

rang= 2σ2

perp =(0474 GeV)2

For massless quarks the longitudinal component of the energy carried by a hadron formed in thestring-breaking process stringrarr hadron+stringprime is governed by the Lund symmetric fragmentationfunction

f(z) prop z(aiminusaj)(1minus z)ajz

exp

(minusbm2

perpz

) (3)

where z is the energy carried by the newly formed (ij) hadron expressed as a fraction of the (light-cone) energy of the quark (or antiquark) endpoint i of the fragmenting string (The remaining energyfraction (1 minus z) goes to the new stringprime system from which another hadron can be split off in thesame manner etc until all the energy is used up) The transverse mass of the produced (ij) hadronis defined by m2

perp = m2had + p2

perphad hence heavier hadrons have harder spectra The proportionalitysign in eq (3) indicates that the function is to be normalized to unity

The a and b parameters govern the shape of the fragmentation function and must be constrainedby fits to data Eq (3) expresses the most general form of the fragmentation function for which the aparameters of the original string-endpoint quark ai and that of the (anti-)quark produced in the stringbreak aj can in principle be different while the b parameter is universal Within the Lund model thea value is normally also taken to be universal the same for all quarks with the only freedom beingthat a larger a parameter can be assigned to diquarks [36] from which baryons are formed and hencemeson and baryon spectra can be decoupled somewhat (See StringZaExtraDiquark below)

Roughly speaking large a parameters suppress the hard region z rarr 1 while a large b parametersuppresses the soft region z rarr 0 By adjusting them independently both the average hardness andthe width of the resulting fragmentation spectra can be modified For example increasing both a andb yields a narrower distribution while changing them in opposite directions moves the average An

5

The a parameter The b parameter

a = 09 a = 01 b = 05 b = 20

02 04 06 08 10

05

10

15

02 04 06 08 10

05

10

15

20

b = 1 GeVminus2 mperp = 1 GeV a = 05 mperp = 1 GeV

Figure 2 Illustration of the Lund symmetric fragmentation function (normalized to unity) for ai =aj equiv a Left variation of the a parameter from 01 (blue) to 09 (red) with fixed b Right variationof the b parameter from 05 (red) to 2 (blue) GeVminus2 with fixed a

illustration of the effect of varying the a and b parameters for ai = aj equiv a is given in fig 2 see alsothe lecture notes in [37] Note that the σperp parameter also affects the hardness with larger σperp valuesgenerating harder hadrons the difference being that the σperp parameter acts mainly in the directiontransverse to the string5 (and is an absolute scale expressed in GeV) while the a and b parameters actlongitudinally (with z a relative scale expressed as a fraction of the endpointrsquos energy)

In the context of this work we included the possibility of letting the a parameter for strangequarks be slightly different from that of u and d quarks but did not find any significant advantagesThe relevant parameters in the code we settled on for the Monash tune are

StringZaLund = 068StringZbLund = 098StringZaExtraDiquark = 097StringZaExtraSquark = 000

The average hardness of the produced hadrons is tightly (anti-)correlated with the average multi-plicity via momentum conservation if each hadron takes a lot of energy then fewer hadrons must bemade and vice versa Thus the σperp value and the a and b parameters of the fragmentation functioncan be well constrained by simultaneously considering both momentum and multiplicity spectra Inorder to be as universal as possible one normally uses the inclusive charged-particle spectra for thispurpose These are shown in fig 3 (Note the Fischer tune only included the average particle mul-tiplicity as a constraint so the full nch distribution is not expected to be reproduced perfectly [30])The momentum fraction in the right-hand plot is defined by

xp =2|p|Ecm

(4)

As above the experimental data come from a measurement by L3 [26] which only includes the fourlightest flavours thus excluding b quarks (which will be treated separately below)

Both of the earlier tunes exhibit a somewhat too broad multiplicity distribution in comparisonwith the L3 data The relatively large Lund a and b values used for the Monash tune combined with

5Explicitly σperp expresses the pperp broadening transverse to the string direction but implicitly its size also enters inthe logitudinal fragmentation function via the m2

perp term in eq (3) causing higher-pperp hadrons to have relatively harderlongitudinal spectra as well

6

0 20 40 60

)ch

Pro

babi

lity(

n

-610

-510

-410

-310

-210

-110

1

10

210 Charged Multiplicity (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn05

01plusmn07

02plusmn21

V I

N C

I A

R O

O T

chn0 20 40 60

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

chgt

dn

ch1

ltn

-310

-210

-110

1

10Charged Momentum Fraction (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn09

00plusmn05

00plusmn05

V I

N C

I A

R O

O T

)|p

|Ln(x0 2 4 6 8

The

ory

Dat

a06

08

1

12

14

Figure 3 Hadronic Z decays atradics = 912 GeV Charged-particle multiplicity (left) and momentum-

fraction (right) spectra

its large σperp value produce a narrower nCh spectrum with in particular a smaller tail towards largemultiplicities All the tunes produce a sensible momentum spectrum The dip around |ln(x)| sim 55corresponds to the extreme soft-pion tail with momenta at or below ΛQCD We did not find it possibleto remove it by retuning since a smaller b parameter would generate significantly too high particlemultiplicities and a smaller σperp would lead to conflict with the event-shape distributions

A zoom on the high-momentum tail is provided by the left-hand plot in fig 4 which shows acomparison on a linear momentum scale to a measurement by ALEPH [38] (now including Z rarr bbevents as well as light-flavour ones) All the tunes exhibit a mild overshooting of the data in the region05 lt xp lt 08 corresponding to 015 lt | ln(x)| lt 07 in which no similar excess was present inthe L3 comparison We therefore do not regard this as a significant issue6 but note that the excess issomewhat milder in the Fischer and Monash tunes

Further information to elucidate the structure of the momentum distribution is provided by theplot in the right-hand pane of fig 4 which uses the same |ln(x)| axis as the right-hand plot in fig 3and shows the relative particle composition in the Monash tune for each histogram bin (The categoryldquoOtherrdquo contains electrons and muons from weak decays) An interesting observation is that therelatively harder spectrum of Kaons implies that for the highest-momentum bins the charged tracksare made up of an almost exactly equal mixture of Kaons and pions despite Kaons on average onlymaking up about 10 of the charged multiplicity

6One might worry whether the effect could be due solely to the Z rarr bb events which are only present in the ALEPHmeasurement and if so whether this could indicate a significant mismodeling of the momentum distribution in b eventsHowever as we show below in the section on b fragmentation the charged-particle momentum distribution in b-taggedevents shows no excess in that region (in fact it shows an undershooting)

7

0 02 04 06 08 1

pd

xch

gt d

nch

1lt

n

-410

-310

-210

-110

1

10Charged Momentum Fraction

Pythia 8183Data from Barate et al Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn14

01plusmn08

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

IDgt

dn

ch1

ltn

0

02

04

06

08

1

12 Particle Composition vs Lnx (udsc)

Pythia 8183

plusmnπplusmnKplusmnp

Other

V I

N C

I A

R O

O T

)|p

|Ln(x0 2 4 6 8

Rat

io06

08

1

12

14

Figure 4 Hadronic Z decays atradics = 912 GeV Charged-particle momentum fraction xp on a linear

scale (left) and relative particle composition (right) for the log-scale distribution shown in fig 3

22 Identified Particles

Continuing on the topic of identified particles we note that the extraction of the a and b parametersfrom the inclusive charged-particle distributions is made slightly more complicated by the fact thatnot all observed particles are ldquoprimaryrdquo (originating directly from string breaks) many lower-massparticles are ldquosecondariesrdquo produced by prompt decays of more massive states (eg ρrarr ππ) whoserelative rates and decay kinematics therefore influence the spectra In the e+eminus measurements weinclude here particles with cτ lt 100 mm were treated as unstable hence leading to secondaries (Forcompleteness we note that the equivalent standard cut at the LHC is normally 10 mm)

The particle composition in PYTHIA 8 was already tuned to a set of reference values provided bythe PDG [39] and the default parameters do reasonably well certainly for the most copiously pro-duced sources of secondaries Nonetheless we have here reoptimized the flavour-selection parametersof the string-fragmentation model using a slightly different set of reference data combining the PDGtables with information provided directly by the LEP experiments via HEPDATA [1] Based on thelevel of agreement or disagreement between different measurements of the same particles we havemade our own judgement as to the level of uncertainty for a few of the particles as follows (Unlessotherwise stated we use the value from the PDG Particles and antiparticles are implicitly summedover and secondaries from particles with cτ lt 100 mm are included)

bull The various LEP and SLD measurements of the φ meson rate on HEPDATA are barely com-patible Eg OPAL [40] reports 〈nφ〉 = 0091 plusmn 0002 plusmn 0003 while ALEPH [38] quotes〈nφ〉 = 0122 plusmn 0004 plusmn 0008 a difference of 30 with uncertainties supposedly less than10 DELPHI [41] and SLD [42] fall in between The PDG value is 〈nφ〉 = 00963 plusmn 0003ie with a combined uncertainty of just 3 We choose to inflate the systematic uncertaintiesand arrive at 〈nφ〉 = 0101plusmn 0007

8

bull For Λ production we use the most precise of the LEP measurements by OPAL7 [43] 〈nΛ〉 =0374plusmn 0002plusmn 0010 about 5 lower than the corresponding PDG value

bull For Σplusmn baryons we use a combination of the two most recent LEP measurements by L3 [44]for Σ+ + Σ

minus and by DELPHI [45] for Σminus + Σ+ for an estimated 〈nΣplusmn〉 = 0195 plusmn 0018

which is roughly 10 higher than the PDG value

bull For Σ0 baryons we use the most recent measurement by L3 [44] 〈nΣ0〉 = 0095 plusmn 0015 plusmn0013 this is about 20 larger than the PDG value The L3 paper comments on their relativelyhigh value by noting that L3 had the best coverage for low-momentum baryons hence smallermodel-dependent correction factors

bull For ∆++ baryons there are only two measurements in HEPDATA [4647] which are mutuallydiscrepant by about 2σ The DELPHI measurement is nominally the most precise but OPALgives a much more serious discussion of systematic uncertainties We choose to increase theestimated extrapolation errors of the DELPHI measurement by 50 and obtain a weighted av-erage8 of 〈n∆++〉 = 009plusmn0017 5 larger than the PDG value with a 20 larger uncertainty

bull For Σlowast the three measurements on HEPDATA [38 43 48] are likewise discrepant by 2σ minus 3σWe inflate the systematic uncertainties and arrive at 〈nΣlowastplusmn〉 = 0050 plusmn 0006 which is again5 higher than the PDG value with twice as much uncertainty

bull The measurements for Ξplusmn are in good agreement [38 43 48] with a weighted average of〈nΞplusmn〉 = 00266plusmn 00012 slightly larger than the PDG value

bull For Ξlowast0 however the DELPHI measurement [48] gives a far lower number than the OPAL [43]and ALEPH [38] ones and the weighted average differs by more than 10 from the PDGvalue despite the latter claiming an uncertainty smaller than 10 Our weighted average is〈nΞlowast0〉 = 00059plusmn 00012

bull Finally for the Ω baryon the DELPHI [49] and OPAL [43] measurements are in agreementand we use the PDG value 〈nΩ〉 = 00016plusmn 00003

We summarize the constraints on the light-meson and baryon rates used here in tab 1 Note that weexpress them as percentages of the average charged multiplicity

〈nCh〉 = 207 (5)

obtained as a weighted average over MARK-II [50] ALEPH [38] DELPHI [51] OPAL [52] andL3 [53] measurements

The light-flavour-selection parameters for the Monash tune are (see appendix A for a comparisonof these values to the current default ones)

Light-Meson SectorStringFlavProbStoUD = 0217StringFlavmesonUDvector = 05StringFlavmesonSvector = 055

7We note that HEPDATA incorrectly gives the systematic error as 0002 while the value in the OPAL paper is 0010 [43]This has been communicated to the HEPDATA maintainers

8Even with the inflated error the uncertainty on the DELPHI measurement is still less than a third that of the OPAL oneDELPHI therefore still dominates the average

9

Mesons Our Reference Our〈n〉 〈nCh〉 Value (in ) Source

π+ + πminus 822 plusmn09 Pπ0 455 plusmn15 PK+ +Kminus 108 plusmn03 Pη 506 plusmn038 Pηprime 073 plusmn009 Pρ+ + ρminus 116 plusmn21 Pρ0 595 plusmn047 PKlowast+ +Klowastminus 345 plusmn028 Pω 490 plusmn031 Pφ 049 plusmn0035 ADOS

Baryons Our Reference Our〈n〉 〈nCh〉 Value (in ) Source

p+ p 507 plusmn016 PΛ + Λ 181 plusmn032 OΣ+ + Σminus + Σ+ + Σminus 0942 plusmn0087 DLΣ0 + Σ0 0459 plusmn0096 L∆++ + ∆minusminus 0434 plusmn0082 DOΣlowast+ + Σlowastminus + Σlowast+ + Σlowastminus 0242 plusmn0029 ADOΞ+ + Ξminus 0125 plusmn00050 ADOΞlowast0 + Ξlowast0 00285 plusmn00058 ADOΩminus + Ω+ 00077 plusmn00015 P

Table 1 Hadronic Z decays atradics = 912 GeV Measured rates of light-flavour mesons and baryons

expressed as percentages of the average charged-particle multiplicity as used in this work Multiplythe numbers by 207100 to translate the percentages to corresponding production rates Source labelsindicate A (ALEPH) D (DELPHI) L (L3) O (OPAL) S (SLD) P (PDG)

StringFlavetaSup = 060StringFlavetaPrimeSup = 012

Baryon SectorStringFlavprobQQtoQ = 0081StringFlavprobSQtoQQ = 0915StringFlavprobQQ1toQQ0 = 00275StringFlavsuppressLeadingB = offStringFlavpopcornSpair = 09StringFlavpopcornSmeson = 05

Since strange-particle and baryon spectra at the LHC exhibit interesting differences with respectto existing models (see below) we paid particular attention to first obtaining a good description ofthese sectors in e+eminus collisions Specifically we have increased the overall amount of strangenessby about 10 while decreasing the rate of vector mesons by a similar amount9 (these two effectslargely cancel for Klowast) This improves the total Kplusmn ρ0 ω Λ Ξlowast and Ω yields on our combined LEPestimates discussed above The price is that we now overshoot the measured rate of Ξplusmn baryons by10 The resulting identified-meson and -baryon rates expressed as fractions of the average charged-particle multiplicity are plotted in fig 5 Note that the last four bins of the meson plot and the thirdand fourth bins of the baryon plot are not 〈n〉 〈nCh〉 fractions but rather the KlowastK φKlowast φKφπ Λp and ΛK ratios respectively Note also that section 4 on energy scaling below includes acomparison to the average Kaon and Lambda rates as a function of ee CM energy (fig 25)

To provide further information on identified particles we include a limited comparison to momen-tum spectra of Kplusmn p Λ and Ξplusmn which are the states of most immediate interest in the context ofsimilar comparisons now being made at LHC The spectra of Kplusmn mesons and Λ baryons are shownin fig 6 while the pplusmn and Ξplusmn spectra are relegated to appendix B2 The modified parameters of theMonash tune have virtually no effect on the Kaon distribution which still exhibits too many very softKaons (with ln(x) lt minus4 corresponding to x lt 0018 so momentum scales below sim 1 GeV) while

9For reference the current default value of ProbStoUD is 019 while ours is 0217 The increased value also improvesthe agreement with the Ds and Bs rates see section 23 The default values of mesonUDvector and mesonSvectorare 062 and 0725 respectively while ours are 05 and 055

10

plusmnπ 0π plusmnK η η plusmnρ 0ρ plusmnK ω φKK-

RKφ

RK-φ

R-πφ

R

gtch

ltnltngt

-310

-210

-110

1

10Meson Fractions

Pythia 8183Data from PDGHEPDATA

LEP + SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn06

00plusmn12

00plusmn12

V I

N C

I A

R O

O T

plusmnπ 0π plusmnK η η plusmnρ 0ρ plusmnK ω φKK-

RKφ

RK-φ

R-πφ

R

The

ory

Dat

a

06

08

1

12

14

p ΛpΛ

RKΛ

R plusmnΣ 0Σ ++∆ Σ plusmnΞ 0Ξ Ω

gtch

ltnltngt

-410

-310

-210

-110

1Baryon Fractions

Pythia 8183Data from PDGHEPDATA

LEP PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn11

00plusmn22

00plusmn22

V I

N C

I A

R O

O T

p ΛpΛ

RKΛ

R plusmnΣ 0Σ ++∆ Σ plusmnΞ 0Ξ Ω

The

ory

Dat

a

06

08

1

12

14

Figure 5 Hadronic Z decays atradics = 912 GeV Identified-meson and -baryon rates expressed as

fractions of the average charged-particle multiplicity

-4 -2 0

dln

(x)

Kgt

dn

K1

ltn

-310

-210

-110

1

10

) (Combined)plusmnx(K

Pythia 8183Data from ZPC66(1995)355 ZPC63(1994)181 EPJC5(1998)585

LEP (A+D+O)PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn16

00plusmn14

01plusmn19

V I

N C

I A

R O

O T

)p

ln(x-4 -2 0

The

ory

Dat

a

06

08

1

12

14

0 1 2 3 4 5

ξd

Λgt

dn

Λ1

ltn

0

02

04

06)]|0Λ|Ln[x(

Pythia 8183Data from EPJ C16 (2000) 613

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn08

01plusmn15

01plusmn12

V I

N C

I A

R O

O T

pξ

0 1 2 3 4 5

The

ory

Dat

a

06

08

1

12

14

Figure 6 Hadronic Z decays atradics = 912 GeV Kplusmn and Λ momentum-fraction spectra

11

the significant increase in the value of aExtraDiquark from 05 (Default) to 097 (Monash cf sec-tion 21) produces a desirable suppression of very hard Λ baryons The corresponding change in themeasured parts of the p and Ξplusmn spectra (cf appendix B2) are small compared with the experimentaluncertainties

It is interesting however to note that all of these spectra indicate or are at least consistent with amodelling excess of soft identified-particle production below ln(x) sim minus45 corresponding to absolutemomentum scales around 500 MeV while we recall that the inclusive ln(x) spectrum above showedan underproduction around ln(x) sim minus55 Within the constraints of the current theory model wehave not managed to find a way to mitigate these features while remaining consistent with the rest ofthe data Nonetheless it should be mentioned that these observations could have relevance also in thecontext of understanding identified-particle spectra at LHC a possibility which to our knowledge hasso far been ignored

23 Heavy-Quark Fragmentation

Similarly to above we first discuss the inclusive rates of hadrons containing heavy quarks before wediscuss their spectra Unfortunately there are also here substantial disagreements between differentpieces of information We have made the following choices

bull ForD mesons the average Dplusmn rate given in sec 46 of the PDG (0175) is equal to the inclusivebranching fraction for Z rarr DplusmnX given in the Z boson summary table in the same Review(after normalizing the latter to the hadronic Z fraction of 6991 [39]) However the formerought to be substantially larger given that some Z rarr cc events will contain two Dplusmn mesons(counting once in the Z rarr DplusmnX branching fraction but twice in the average Dplusmn multiplicity)We therefore here use a measurement by ALEPH [54] to fix the Dplusmn and D0 rates resulting ina reference value for the average Dplusmn multiplicity almost twice as large as that given by sec 46in the PDG

bull For Λ+c the average multiplicity given in sec 46 of the PDG is twice as large as that indicated

by the branching fraction BR(Z rarr Λ+c X) in the Z boson summary table in the same Review

We here use the branching from the Z boson summary table as our constraint on the Λ+c rate

normalized to the total branching fraction BR(Z rarr hadrons)

bull We also include the average rate of g rarr cc splittings obtained by combining an ALEPH [55]and an OPAL measurement [56] but with an additional 10 systematic uncertainty added toboth measurements to account for possibly larger mismodeling effects in the correction fac-tors [57 58]

bull For B particles we use the quite precise inclusive Z rarr B+X branching fraction from the Zboson summary in the PDG

bull We also use the sum of Bplusmn and B0(B0) in sec 46 of the PDG10

bull TheB0s multiplicity given in sec 46 of the PDG (0057plusmn0013) is more than twice the inclusive

BR(Z rarr B0sX)BR(Z rarr hadrons) branching fraction (00227 plusmn 00019) quoted in the Z

10Note that we have a factor 2 relative to the PDG since it appears the PDG quotes the average rather than the sum Notealso that all the average B meson multiplicities in sec 46 of the PDG are accompanied by a note ldquo(d)rdquo stating that the SMB(Z rarr bb) = 0217 was used for the normalization For completeness the reader should be aware that this is the fractionnormalized to hadronic Z decays the branching fraction relative to all Z decays is 0151 [39]

12

Charm Our Reference Our〈n〉 or BR Value Source

D+ +Dminus 0251 plusmn0047 AD0 + D0 0518 plusmn0063 ADlowast+ +Dlowastminus 0194 plusmn00057 PD+

s +Dminuss 0131 plusmn0021 PBR(Z rarr Λ+

c X) 00220 plusmn00047 ZBR(Z rarr X + cc) 00306 plusmn00047 AOJψ 00052 plusmn00004 Pχc1 00041 plusmn00011 Pψprime 00023 plusmn00004 P

Beauty Our Reference Our〈n〉 or BR Value Source

BR(Z rarr B+X) 0087 plusmn0002 ZB+ +B0 + B0 +Bminus 0330 plusmn0052 PBlowastu +Blowastd +Blowasts 0288 plusmn0026 PBR(Z rarr B0

sX) 00227 plusmn00019 ZBR(Z rarr BbaryonX) 00197 plusmn00032 ZBR(Z rarr X + bb) 000288 plusmn000061 ADSBR(Z rarr bbbbX) 000051 plusmn000019 ZΥ (times10) 00014 plusmn00007 P

Table 2 Hadronic Z decays atradics = MZ Measured rates and inclusive branching fractions of

particles containing c and b quarks as used in this work Note the branching fractions are normalizedto Z rarr hadrons and hence should be interpreted as eg BR(Z rarr B+X)BR(Z rarr hadrons)Note 2 the sum over Blowast states includes both particles and anti-particles Note 3 the Υ rate ismultiplied by a factor 10 Source labels indicate A (ALEPH) D (DELPHI) O (OPAL) P (PDGsection 46) S (SLD) Z (PDG Z Boson Summary Table)

boson summary table We find these two numbers difficult to reconcile and choose to use theinclusive BR(Z rarr B0

sX)BR(Z rarr hadrons) branching fraction as our main constraint

bull We also include the inclusive branching fractions for B-baryons (summed over baryons andantibaryons) the rate of g rarr bb splittings obtained by combining ALEPH [59] DELPHI [60]and SLD [61] measurements (including an additional 10 systematic to account for largerpossible mismodeling effects in the correction factors [57 58]) and the rate of Z rarr bbbb fromthe PDG Z boson summary table [39]

Our constraints on the heavy-quark particle rates are summarized in tab 2 Comparisons to these ratesare shown in fig 7 now without normalizing to the average charged-particle multiplicity Given thatmost of the c and b quarks come directly from Z rarr cc and Z rarr bb decays there is not a lot of roomfor tuning to these numbers apart from the relative rates of vector mesons vs pseudoscalars which iscontrolled by the parameters

Heavy MesonsStringFlavmesonCvector = 088StringFlavmesonBvector = 22

Our parameters are slightly smaller than the current default values leading to slightly smaller Dlowast

and Blowast rates as can be seen from the plots in fig 7 Note also that the increased overall amount ofstrangeness in the fragmentation leads to slightly higherDs andBs fractions in better agreement withthe data Uncertainties are however large and some exotic onium states like χc1 ψprime and Υ are notwell described by the default modeling (It is encouraging that at least the multiplicity of Jψ mesonsis well described though a substantial fraction of this likely owes to the feed-down from B decaysand hence does not depend directly on the string-fragmentation model itself)

We also note that it would be desirable to reduce the rate of g rarr bb and Z rarr bbbb events whilethe g rarr cc one appears consistent with the LEP constraints We suspect that this issue may be tiedto the fixed choice of using pperp as the renormalization scale for both gluon emissions and for g rarr qq

13

plusmnD 0D plusmnD plusmns

D X+

cΛ

ccrarrg ψJ c1χ

3685

ψ

X)

rarrlt

ngt o

r B

R(Z

-410

-310

-210

-110

1

10Charm Rates

Pythia 8185Data from HEPDATAPDG

LEP

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn15

00plusmn18

00plusmn17

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

plusmnD 0Dplusmn

D plusmnsD X+

cΛ ccrarrg ψJ c1χ

3685ψ

The

ory

Dat

a

0

05

1

15

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

X)

rarrlt

ngt o

r B

R(Z

-510

-410

-310

-210

-110

1

10Beauty Rates

Pythia 8185Data from HEPDATAPDG

LEP+SLD

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn17

00plusmn23

00plusmn23

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

The

ory

Dat

a0

05

1

15

Figure 7 Hadronic Z decays atradics = 912 GeV Rates and inclusive Z rarr X branching fractions

(normalized to Z rarr hadrons) of particles containing c and b quarks

splittings in the current version of PYTHIA A more natural choice for g rarr qq could be microR prop mqqas used eg in the VINCIA shower model [29]

We now turn to the dynamics of heavy-quark fragmentation focusing mainly on the b quarkFor heavy quarks the Lund fragmentation function is modified due to the (massive) endpoints not

moving along straight lightcones as the string pulls on them they slow down resulting in the stringtracing out a smaller space-time area than it would for massless quarks This modifies the implicationsof the string area law in a manner captured by the so-called Bowler modification of the fragmentationfunction [62]

fmassive(zmQ) prop f(z)

zbrQm2Q

(6)

with mQ the heavy-quark mass b the same universal parameter that appears in the massless fragmen-tation function eq (3) and rQ a tuning parameter which is unity in the original derivation of Bowlerbut can be assigned values different from unity to reduce (rQ rarr 0) or emphasize (rQ gt 1) the effectSince rQ multiplies the heavy-quark mass (squared) it can also be viewed as an effective rescalingof the mass value The net result is a suppression of the region z rarr 1 hence a relative softening ofthe fragmentation spectrum for heavy flavours (relative since the presence of m2

perp in the exponent ofeq (3) still implies an overall harder fragmentation for higher hadron masses)

We emphasize that this is the only fragmentation function that is self-consistent within the string-fragmentation model [33 62] Although a few alternative forms of the fragmentation functions formassive quarks are available in the code we therefore here work only with the Bowler type As forthe massless function the proportionality sign in eq (6) indicates that the function is normalized tounity

In PYTHIA separate rQ parameters are provided for c and b quarks We consider the one for bquarks first Its default value is rb = 067 but this appears to give too hard b fragmentation spectrawhen compared to LEP and SLD data see below For the Monash tune we instead use

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (DELPHI)weak

Bx

Pythia 8181Data from EurPhysJ C71 (2011) 1557

DELPHI PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn16

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (SLD)weak

Bx

Pythia 8181HepData5111d1-x1-y1

SLDPY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn07

00plusmn15

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a06

08

1

12

14

Figure 8 Hadronic Z decays atradics = 912 GeV Momentum (xB) spectra of weakly decaying B

hadrons compared to data from DELPHI [63] (left) and SLD [64] (right)

StringZrFactB = 0855

which produces softer B spectra and simultaneously agrees better with the theoretically preferredvalue (rb = 1)

A comparison to the scaled-momentum spectra (xB = 2|pB|Ecm) of weakly decayingB hadronsfrom both DELPHI [63] and SLD [64] is given in fig 8 (due to small differences between the twomeasured results we choose to show both) The dampening of the hardest part of the spectrum causedby the increase in the rb parameter is visible in the right-most two bins of the distributions and in thesmaller χ2

5 values for the Monash tune The effects of the modification can be further emphasizedby an analysis of the moments of the distribution in which the higher moments are increasinglydominated by the region xB rarr 1 A comparison to a combined LEP analysis of the moments of thexB distribution [63] is given in fig 9 further emphasizing that the high-xB part of the distribution isnow under better control

The reason we have not increased the rb parameter further is that it comes at a price If theB hadrons are taking less energy then there is more energy left over to produce other particlesand the generated multiplicity distribution in b events already exhibits a slightly high tail towardslarge multiplicities Nonetheless since the revised light-flavour fragmentation parameters produce anoverall narrower fragmentation function the end result is still a slight improvement in the multiplicitydistribution also for b events This is illustrated together with the inclusive momentum distributionfor b-tagged events in fig 10 compared to measurements by L3 [26] Interestingly the multiplicitydistribution still appears to be too wide but within the constraints of the present study we were unableto obtain further improvements As a point of speculation we note that the distribution of the numberof partons before hadronization is also quite wide in PYTHIA and this may be playing a role ineffectively setting a lower limit on the width that can be achieved for the hadron-level distribution

Comparisons to L3 event shapes in b-tagged events are collected in appendix B1 (the left columnof plots contains light-flavour tagged event shapes the right column b-tagged ones) In particular the

15

0 10 20 30 40

Mom

ent

0

02

04

06

08 (moments)weakBx

Pythia 8181Data from Eur Phys J C71 (2011) 1557

LEP (combined)PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn10

00plusmn103

00plusmn129

V I

N C

I A

R O

O T

N0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

Figure 9 Hadronic Z decays atradics = 912 GeV Moments of the B fragmentation function com-

pared to a combined analysis of LEP+SLD data by DELPHI [63]

0 20 40

)ch

Pro

babi

lity(

n

-610

-510

-410

-310

-210

-110

1

10

210 Charged Multiplicity (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

06plusmn45

08plusmn64

13plusmn110

V I

N C

I A

R O

O T

(b)chn0 20 40

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

ch d

nch

1n

-510

-410

-310

-210

-110

1

10

210 Charged Momentum Fraction (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn08

00plusmn06 V

I N

C I

A R

O O

T

)| (b)p

|Ln(x0 2 4 6 8

The

ory

Dat

a

06

08

1

12

14

Figure 10 HadronicZ decays atradics = 912 GeV Charged-hadron multiplicity (left) and momentum-

fraction (right) spectra in b-tagged events

16

0 02 04 06 08 1

dx

Dgt

dn

D1

ltn

0

05

1

15

2

25gt01)

E) (x

plusmnx(D

Pythia 8183Data from EurPhysJ C16 (2000) 597

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn14

02plusmn28

02plusmn32

V I

N C

I A

R O

O T

Ex0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

EX02 04 06 08 1

E)

dX

dN

(DZ

had

1N

0

0002

0004

0006

0008

001

0012

0014

0016

ALEPHHerwig++Sherpa

91 GeV ee Z (hadronic)

mcp

lots

cer

nch

41

M e

vent

sge

Riv

et 1

82

Herwig++ 261a Sherpa 141

ALEPH_1999_S4193598

spectrum (particle-level)+-D

02 04 06 08 105

1

15Ratio to ALEPH

Figure 11 The inclusive Dlowast spectrum in hadronic Z decays [55] Left Monash 2013 tune com-pared with default PYTHIA 8 and the Fischer tune Right comparison with HERWIG (dashed) andSHERPA (dotted) from MCPLOTS [25] Note that the plot in the left-hand pane is normalized tounity while the one in the right-hand pane is normalized to the number of hadronic Z decays

Monash tune gives a significant improvement in the soft region of the jet-broadening parameters inb-tagged events while no significant changes are observed for the other event shapes These smallimprovements are presumably a direct consequence of the softening of the b fragmentation functionit is now less likely to find an isolated ultra-hard B hadron

We round off the discussion of heavy-quark fragmentation by noting that a similarly comprehen-sive study of charm-quark fragmentation would be desirable However charm-quark tagged multi-plicity and event-shape data is not available to our knowledge and most of the D meson spectra onHEPDATA concern only specific decay chains (hence depend on the decay modeling) andor are lim-ited to restricted fiducial regions (limiting their generality) Experimentally the cleanest measurementis obtained from Dlowast decays and an inclusive momentum spectrum for Dlowast mesons has been measuredby ALEPH [55] From this distribution shown in fig 11 we determine a value for rc of

StringZrFactC = 132

We note that the low-x part of the Dlowast spectrum originates from g rarr cc shower splittings whilethe high-x tail represents prompt Dlowast production from leading charm in Z rarr cc (see [55] for a nicefigure illustrating this) The intermediate range contains a large component of feed-down from brarr cdecays hence this distribution is also indirectly sensitive to the b-quark sector The previous defaulttune had a harder spectrum for both b- and c-fragmentation leading to an overestimate of the high-xpart of the Dlowast distribution The undershooting at low xDlowast values which remains unchanged in theMonash tune most likely indicates an underproduction of g rarr cc branchings in the shower We notethat such an underproduction may also be reflected in the LHC data on Dlowast production see eg [65]We return to this issue in the discussion of identified particles at LHC section 35

17

This writeup is thus also intended to function as an aid to others wishing to explore the PYTHIA 8parameter space

We then consider the corresponding case for hadron colliders and use the opportunity to try outa new PDF set an LO fit produced by the NNPDF collaboration [18ndash20] which has recently beenintroduced in PYTHIA 8 (NLO and NNLO sets are also available for people that want to check theimpact of using LO vs (N)NLO PDFs in hard-scattering events) In a spirit similar to that of theso-called ldquoPerugia tunesrdquo of PYTHIA 6 [8 21] we choose the same value of αs(MZ) = 01365for both initial- and final-state radiation (Though we do regard this choice as somewhat arbitraryit may facilitate matching applications [21]) Again we adjust parameters manually and attempt togive brief explanations for each modification We also choose the αs(MZ) value for hard-scatteringmatrix elements to be the same as that in the PDFs here αs(MZ) = 013 (The difference betweenthe value used for radiation and that used for hard-scattering MEs may be interpreted as an artifact oftranslations between the CMW and MS schemes see section 33)

Below in Section 11 we begin by giving a brief general explanation of the plots and χ2 values thatare used throughout the paper Next in section 2 we describe the physics parameters and constraintsgoverning fragmentation in hadronic Z decays (final-state radiation and string fragmentation) Weturn to hadron colliders in section 3 (PDFs initial-state radiation and multi-parton interactions) Wethen focus on the energy scaling between different ee and pp (pp) collider energies in section 4including in particular the recently published high-statistics data from the Tevatron energy scan from300 to 1960 GeV [22 23] We round off with conclusions and a summary of recommendations forfuture efforts in section 5

A complete listing of the Monash 2013 tune parameters is given in appendix A Appendix Bcontains a few sets of additional plots complementing those presented in the main body of the paper

11 Plot Legends and χ2 Values

In several places we have chosen to use data sets constraints that differ from the standard onesavailable eg through RIVET (as documented below) Since our tuning setup is furthermore manualrather than automated we have in fact not relied on RIVET in this work (though we have madeextensive use of HEPDATA [1]) Instead we use the VINCIAROOT plotting tool [24] which wehave here upgraded to include a simple χ2 calculation the result of which is shown on each plot

Note that we include a blanket 5 ldquotheory uncertaintyrdquo in the definition of the χ2 value repre-senting a baseline sanity limit for the achievable accuracy of the modeling2 that also gives a basicprotection against overfitting Note also that rather than letting the MC uncertainty enter in the defi-nition of the χ2 value (and thereby risking that low statistics generate artificially low χ2 values) weuse the generated MC statistics to compute a plusmn uncertainty on the calculated χ2 value which is alsoshown on the plots Our definition of χ2 is thus

langχ2

5

rang=

1

Nbins

Nbinssumi=1

(MCi minusDatai)2

σ2Datai + (005MCi)2

(1)

with the corresponding MC uncertainty σMCi used to compute the statistical uncertainty on the χ2

computation as mentioned above As is shown here the normalization is always 1Nbins regardlessof whether the distributions are normalized to a fixed number or not and we do not attempt to takeinto account correlations between the different observables Since our tuning is not directly driven by

2We note that a similar convention is used on the MCPLOTS validation web site [25]

2

0 01 02 03 04

d(1

-T)

σ d

σ1

-310

-210

-110

1

10

2101-Thrust (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn03

01plusmn04

02plusmn05

V I

N C

I A

R O

O T

1-T (udsc)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

Figure 1 Hadronic Z decays atradics = 912 GeV The Thrust distribution in light-flavour tagged

events compared with L3 data [26]

a χ2 minimization we regard this as acceptable the χ25 values are intended merely to give an overall

indication of the level of agreement or disagreement for each observableThe resulting plots look as illustrated in fig 1 with a main pane (top) showing the distribution

itself and a bottom pane showing ratios In the top pane experimental data is always shown withfilled black square symbols with vertical black lines indicating the one-sigma uncertainties (with twoseparate black crossbars if separate statistical and systematic uncertainties are given) Lighter (grey)extensions of the vertical lines are used to indicate two-sigma uncertainties In the ratio pane the greenshaded region indicates the one-sigma uncertainty region while yellow is used to denote the two-sigma one An internal lighterdarker shading variation in each band is used to denote the breakdowninto statistical-only (inner) and statistical+systematic uncertainties (outer) whenever separate valuesfor each of these are given Finally next to each MC legend the χ2

5 value defined above is printedalong with its MC uncertainty A colour-coded box next to the χ2 value is shaded green (χ2 lt 1)yellow (1 lt χ2 lt 4) orange (4 lt χ2 lt 9) or red (9 lt χ2) depending on the level of agreement ordisagreement This functionality will be included in a forthcoming update of the VINCIA plug-in toPYTHIA 8

2 Final-State Radiation and Hadronization

The main parameter governing final-state radiation is the effective value of the strong coupling whichin PYTHIA 8 is specified by giving the value of αs(MZ) We follow the strategy of [24] and use aset of light-flavour (udsc) tagged e+eminus event shapes provided by the L3 experiment [26] to extracta best-fit value for αs(MZ) (This prevents B decays from contaminating this step of the analysisHeavy-quark fragmentation will be treated separately below) The renormalization scale for final-state shower emissions in PYTHIA is fixed to be [27]

FSR micro2R = p2

perpevol = z(1minus z)Q2 (2)

3

with Q2 = p2 minusm20 the offshellness of the emitting parton (with on-shell mass m0) and z the energy

fraction appearing in the DGLAP splitting kernels P (z) (To estimate the shower uncertainties asso-ciated with this choice of renormalization scale we recommend using ln(micro2

R)plusmn ln(2) correspondingto a factor

radic2 variation of microR)

Theoretically a set of formally subleading terms can be resummed by using 2-loop running of αsin the so-called MC (aka CMW) scheme [28] However in a leading-order code like PYTHIA thisproduces too little hard radiation in practice due to missing NLO ldquoKrdquo factors for hard emissions (seeeg the study of NLO corrections in [29]) Empirically we find that a better overall description isachieved with one-loop running which for a fixed value of ΛQCD can effectively mimic the effect ofmissing K factors via its relatively slower pace of running leading to values of αs(MZ) in the range0135minus 0140 consistent with other LO extractions of the same quantity (See [29] for an equivalentextraction at NLO)

For this study we did not find any significant advantage in reinterpreting this value in the CMWscheme3 and hence merely settled on an effective αs(MZ) = 01365 (to be compared with the currentdefault value of 01383)

For the infrared shower cutoff we choose a value close to4 ΛQCD in order to have a smoothtransition between low-pperp perturbative emissions and non-perturbative string breaks the latter ofwhich involve pperp kicks of order ΛQCD (In principle the perturbative evolution could be continuedto even lower scales if combined with a non-perturbative regularization of αs but such low cutoffvalues could risk generating problems at the fragmentation stage since the technical implementationof the string model becomes complicated if there are too many small gluon ldquokinksrdquo spaced closelyalong the strings) The set of relevant parameters in the code is

FSR Strong CouplingTimeShoweralphaSvalue = 01365TimeShoweralphaSorder = 1TimeShoweralphaSuseCMW = off

FSR IR cutoffTimeShowerpTmin = 050 for QCD radiationTimeShowerpTminChgQ = 050 for QED radiation off quarks

FSR Spin CorrelationsTimeShowerphiPolAsym = on approximate FSR polarization effects

The resulting distribution of the Thrust event-shape variable was shown in fig 1 comparing theMonash 2013 tune to the current default tune and to an alternative contemporary tune by N Fi-scher [30] To avoid clutter the other event-shape variables (C D BW and BT ) are collected inappendix B1 There are no significant changes to any of the light-flavour tagged event shapes in ourtune as compared to the current default one

21 Light-Flavour Fragmentation

Given a set of post-shower partons resolved at a scale ofQhad sim 1 GeV the non-perturbative stage ofthe fragmentation modeling now takes over to convert the partonic state into a set of on-shell hadrons

3One slight disadvantage is that the CMW scheme produces somewhat larger ΛQCD values Since the current formu-lation of the shower algorithm does not include a non-perturbative regularization of αs a higher ΛQCD value necessitatesa larger IR cutoff in the shower which can leave an undesirable gap between the transverse kicks generated by showeremissions and those generated by non-perturbative string splittings

4The IR shower cutoff must still remain somewhat above the Landau pole of αs a lower cutoff scale would activate ahardcoded protection mechanism implemented in the PYTHIA shower forcing it to be higher than ΛQCD

4

In the leading-colour approximation each perturbative dipole is dual to a non-perturbative stringpiece [31] Quarks thus become string endpoints while gluons become transverse kinks connectingtwo string pieces [32] The Lund string fragmentation model [33] describes the fragmentation of suchstring systems into on-shell hadrons

Since the shower has already resolved all the (perturbative) physics down to a transverse-momentumscale of pTmin = 05 GeV (for the Monash 2013 tune) we find it reasonable that the pperp kicks in-volved in string breaking should effectively average over dynamics in roughly the range 250 MeV =radicκπ lt σperp lt pTmin with the lower bound given by Fermi motion (with κ the string tension

see [34]) Further since we here choose pTmin to be only slightly greater than ΛQCD the size of thenon-perturbative corrections is naturally limited to kickscorrections appropriate for non-perturbativedynamics (in contrast eg to the cluster model [35] which can generate substantially larger kicks oforder the largest allowed cluster mass which can be several GeV [30]) For the Monash 2013 tunewe have settled on a value of σperp = 0335 GeV with a small (1) tail of breaks involving higher pperpvalues carried over from the default settings

StringPTsigma = 0335StringPTenhancedFraction = 001StringPTenhancedWidth = 20

This value is obtained essentially from the first two bins of the Thrust distribution fig 1 and from thebins near zero of the other event shapes see appendix B1 Note that the σperp value is interpreted as thewidth of a Gaussian distribution in the total pperp (measured transversely to the local string directionwhich may differ from the global event axis) such that each of the px and py components have aslightly smaller average value σ2

xy = 12σ

2perp = (0237 GeV)2 Also note that each non-leading hadron

will receive two pperp kicks one from each of the breaks surrounding it hencelangp2perphad

rang= 2σ2

perp =(0474 GeV)2

For massless quarks the longitudinal component of the energy carried by a hadron formed in thestring-breaking process stringrarr hadron+stringprime is governed by the Lund symmetric fragmentationfunction

f(z) prop z(aiminusaj)(1minus z)ajz

exp

(minusbm2

perpz

) (3)

where z is the energy carried by the newly formed (ij) hadron expressed as a fraction of the (light-cone) energy of the quark (or antiquark) endpoint i of the fragmenting string (The remaining energyfraction (1 minus z) goes to the new stringprime system from which another hadron can be split off in thesame manner etc until all the energy is used up) The transverse mass of the produced (ij) hadronis defined by m2

perp = m2had + p2

perphad hence heavier hadrons have harder spectra The proportionalitysign in eq (3) indicates that the function is to be normalized to unity

The a and b parameters govern the shape of the fragmentation function and must be constrainedby fits to data Eq (3) expresses the most general form of the fragmentation function for which the aparameters of the original string-endpoint quark ai and that of the (anti-)quark produced in the stringbreak aj can in principle be different while the b parameter is universal Within the Lund model thea value is normally also taken to be universal the same for all quarks with the only freedom beingthat a larger a parameter can be assigned to diquarks [36] from which baryons are formed and hencemeson and baryon spectra can be decoupled somewhat (See StringZaExtraDiquark below)

Roughly speaking large a parameters suppress the hard region z rarr 1 while a large b parametersuppresses the soft region z rarr 0 By adjusting them independently both the average hardness andthe width of the resulting fragmentation spectra can be modified For example increasing both a andb yields a narrower distribution while changing them in opposite directions moves the average An

5

The a parameter The b parameter

a = 09 a = 01 b = 05 b = 20

02 04 06 08 10

05

10

15

02 04 06 08 10

05

10

15

20

b = 1 GeVminus2 mperp = 1 GeV a = 05 mperp = 1 GeV

Figure 2 Illustration of the Lund symmetric fragmentation function (normalized to unity) for ai =aj equiv a Left variation of the a parameter from 01 (blue) to 09 (red) with fixed b Right variationof the b parameter from 05 (red) to 2 (blue) GeVminus2 with fixed a

illustration of the effect of varying the a and b parameters for ai = aj equiv a is given in fig 2 see alsothe lecture notes in [37] Note that the σperp parameter also affects the hardness with larger σperp valuesgenerating harder hadrons the difference being that the σperp parameter acts mainly in the directiontransverse to the string5 (and is an absolute scale expressed in GeV) while the a and b parameters actlongitudinally (with z a relative scale expressed as a fraction of the endpointrsquos energy)

In the context of this work we included the possibility of letting the a parameter for strangequarks be slightly different from that of u and d quarks but did not find any significant advantagesThe relevant parameters in the code we settled on for the Monash tune are

StringZaLund = 068StringZbLund = 098StringZaExtraDiquark = 097StringZaExtraSquark = 000

The average hardness of the produced hadrons is tightly (anti-)correlated with the average multi-plicity via momentum conservation if each hadron takes a lot of energy then fewer hadrons must bemade and vice versa Thus the σperp value and the a and b parameters of the fragmentation functioncan be well constrained by simultaneously considering both momentum and multiplicity spectra Inorder to be as universal as possible one normally uses the inclusive charged-particle spectra for thispurpose These are shown in fig 3 (Note the Fischer tune only included the average particle mul-tiplicity as a constraint so the full nch distribution is not expected to be reproduced perfectly [30])The momentum fraction in the right-hand plot is defined by

xp =2|p|Ecm

(4)

As above the experimental data come from a measurement by L3 [26] which only includes the fourlightest flavours thus excluding b quarks (which will be treated separately below)

Both of the earlier tunes exhibit a somewhat too broad multiplicity distribution in comparisonwith the L3 data The relatively large Lund a and b values used for the Monash tune combined with

5Explicitly σperp expresses the pperp broadening transverse to the string direction but implicitly its size also enters inthe logitudinal fragmentation function via the m2

perp term in eq (3) causing higher-pperp hadrons to have relatively harderlongitudinal spectra as well

6

0 20 40 60

)ch

Pro

babi

lity(

n

-610

-510

-410

-310

-210

-110

1

10

210 Charged Multiplicity (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn05

01plusmn07

02plusmn21

V I

N C

I A

R O

O T

chn0 20 40 60

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

chgt

dn

ch1

ltn

-310

-210

-110

1

10Charged Momentum Fraction (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn09

00plusmn05

00plusmn05

V I

N C

I A

R O

O T

)|p

|Ln(x0 2 4 6 8

The

ory

Dat

a06

08

1

12

14

Figure 3 Hadronic Z decays atradics = 912 GeV Charged-particle multiplicity (left) and momentum-

fraction (right) spectra

its large σperp value produce a narrower nCh spectrum with in particular a smaller tail towards largemultiplicities All the tunes produce a sensible momentum spectrum The dip around |ln(x)| sim 55corresponds to the extreme soft-pion tail with momenta at or below ΛQCD We did not find it possibleto remove it by retuning since a smaller b parameter would generate significantly too high particlemultiplicities and a smaller σperp would lead to conflict with the event-shape distributions

A zoom on the high-momentum tail is provided by the left-hand plot in fig 4 which shows acomparison on a linear momentum scale to a measurement by ALEPH [38] (now including Z rarr bbevents as well as light-flavour ones) All the tunes exhibit a mild overshooting of the data in the region05 lt xp lt 08 corresponding to 015 lt | ln(x)| lt 07 in which no similar excess was present inthe L3 comparison We therefore do not regard this as a significant issue6 but note that the excess issomewhat milder in the Fischer and Monash tunes

Further information to elucidate the structure of the momentum distribution is provided by theplot in the right-hand pane of fig 4 which uses the same |ln(x)| axis as the right-hand plot in fig 3and shows the relative particle composition in the Monash tune for each histogram bin (The categoryldquoOtherrdquo contains electrons and muons from weak decays) An interesting observation is that therelatively harder spectrum of Kaons implies that for the highest-momentum bins the charged tracksare made up of an almost exactly equal mixture of Kaons and pions despite Kaons on average onlymaking up about 10 of the charged multiplicity

6One might worry whether the effect could be due solely to the Z rarr bb events which are only present in the ALEPHmeasurement and if so whether this could indicate a significant mismodeling of the momentum distribution in b eventsHowever as we show below in the section on b fragmentation the charged-particle momentum distribution in b-taggedevents shows no excess in that region (in fact it shows an undershooting)

7

0 02 04 06 08 1

pd

xch

gt d

nch

1lt

n

-410

-310

-210

-110

1

10Charged Momentum Fraction

Pythia 8183Data from Barate et al Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn14

01plusmn08

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

IDgt

dn

ch1

ltn

0

02

04

06

08

1

12 Particle Composition vs Lnx (udsc)

Pythia 8183

plusmnπplusmnKplusmnp

Other

V I

N C

I A

R O

O T

)|p

|Ln(x0 2 4 6 8

Rat

io06

08

1

12

14

Figure 4 Hadronic Z decays atradics = 912 GeV Charged-particle momentum fraction xp on a linear

scale (left) and relative particle composition (right) for the log-scale distribution shown in fig 3

22 Identified Particles

Continuing on the topic of identified particles we note that the extraction of the a and b parametersfrom the inclusive charged-particle distributions is made slightly more complicated by the fact thatnot all observed particles are ldquoprimaryrdquo (originating directly from string breaks) many lower-massparticles are ldquosecondariesrdquo produced by prompt decays of more massive states (eg ρrarr ππ) whoserelative rates and decay kinematics therefore influence the spectra In the e+eminus measurements weinclude here particles with cτ lt 100 mm were treated as unstable hence leading to secondaries (Forcompleteness we note that the equivalent standard cut at the LHC is normally 10 mm)

The particle composition in PYTHIA 8 was already tuned to a set of reference values provided bythe PDG [39] and the default parameters do reasonably well certainly for the most copiously pro-duced sources of secondaries Nonetheless we have here reoptimized the flavour-selection parametersof the string-fragmentation model using a slightly different set of reference data combining the PDGtables with information provided directly by the LEP experiments via HEPDATA [1] Based on thelevel of agreement or disagreement between different measurements of the same particles we havemade our own judgement as to the level of uncertainty for a few of the particles as follows (Unlessotherwise stated we use the value from the PDG Particles and antiparticles are implicitly summedover and secondaries from particles with cτ lt 100 mm are included)

bull The various LEP and SLD measurements of the φ meson rate on HEPDATA are barely com-patible Eg OPAL [40] reports 〈nφ〉 = 0091 plusmn 0002 plusmn 0003 while ALEPH [38] quotes〈nφ〉 = 0122 plusmn 0004 plusmn 0008 a difference of 30 with uncertainties supposedly less than10 DELPHI [41] and SLD [42] fall in between The PDG value is 〈nφ〉 = 00963 plusmn 0003ie with a combined uncertainty of just 3 We choose to inflate the systematic uncertaintiesand arrive at 〈nφ〉 = 0101plusmn 0007

8

bull For Λ production we use the most precise of the LEP measurements by OPAL7 [43] 〈nΛ〉 =0374plusmn 0002plusmn 0010 about 5 lower than the corresponding PDG value

bull For Σplusmn baryons we use a combination of the two most recent LEP measurements by L3 [44]for Σ+ + Σ

minus and by DELPHI [45] for Σminus + Σ+ for an estimated 〈nΣplusmn〉 = 0195 plusmn 0018

which is roughly 10 higher than the PDG value

bull For Σ0 baryons we use the most recent measurement by L3 [44] 〈nΣ0〉 = 0095 plusmn 0015 plusmn0013 this is about 20 larger than the PDG value The L3 paper comments on their relativelyhigh value by noting that L3 had the best coverage for low-momentum baryons hence smallermodel-dependent correction factors

bull For ∆++ baryons there are only two measurements in HEPDATA [4647] which are mutuallydiscrepant by about 2σ The DELPHI measurement is nominally the most precise but OPALgives a much more serious discussion of systematic uncertainties We choose to increase theestimated extrapolation errors of the DELPHI measurement by 50 and obtain a weighted av-erage8 of 〈n∆++〉 = 009plusmn0017 5 larger than the PDG value with a 20 larger uncertainty

bull For Σlowast the three measurements on HEPDATA [38 43 48] are likewise discrepant by 2σ minus 3σWe inflate the systematic uncertainties and arrive at 〈nΣlowastplusmn〉 = 0050 plusmn 0006 which is again5 higher than the PDG value with twice as much uncertainty

bull The measurements for Ξplusmn are in good agreement [38 43 48] with a weighted average of〈nΞplusmn〉 = 00266plusmn 00012 slightly larger than the PDG value

bull For Ξlowast0 however the DELPHI measurement [48] gives a far lower number than the OPAL [43]and ALEPH [38] ones and the weighted average differs by more than 10 from the PDGvalue despite the latter claiming an uncertainty smaller than 10 Our weighted average is〈nΞlowast0〉 = 00059plusmn 00012

bull Finally for the Ω baryon the DELPHI [49] and OPAL [43] measurements are in agreementand we use the PDG value 〈nΩ〉 = 00016plusmn 00003

We summarize the constraints on the light-meson and baryon rates used here in tab 1 Note that weexpress them as percentages of the average charged multiplicity

〈nCh〉 = 207 (5)

obtained as a weighted average over MARK-II [50] ALEPH [38] DELPHI [51] OPAL [52] andL3 [53] measurements

The light-flavour-selection parameters for the Monash tune are (see appendix A for a comparisonof these values to the current default ones)

Light-Meson SectorStringFlavProbStoUD = 0217StringFlavmesonUDvector = 05StringFlavmesonSvector = 055

7We note that HEPDATA incorrectly gives the systematic error as 0002 while the value in the OPAL paper is 0010 [43]This has been communicated to the HEPDATA maintainers

8Even with the inflated error the uncertainty on the DELPHI measurement is still less than a third that of the OPAL oneDELPHI therefore still dominates the average

9

Mesons Our Reference Our〈n〉 〈nCh〉 Value (in ) Source

π+ + πminus 822 plusmn09 Pπ0 455 plusmn15 PK+ +Kminus 108 plusmn03 Pη 506 plusmn038 Pηprime 073 plusmn009 Pρ+ + ρminus 116 plusmn21 Pρ0 595 plusmn047 PKlowast+ +Klowastminus 345 plusmn028 Pω 490 plusmn031 Pφ 049 plusmn0035 ADOS

Baryons Our Reference Our〈n〉 〈nCh〉 Value (in ) Source

p+ p 507 plusmn016 PΛ + Λ 181 plusmn032 OΣ+ + Σminus + Σ+ + Σminus 0942 plusmn0087 DLΣ0 + Σ0 0459 plusmn0096 L∆++ + ∆minusminus 0434 plusmn0082 DOΣlowast+ + Σlowastminus + Σlowast+ + Σlowastminus 0242 plusmn0029 ADOΞ+ + Ξminus 0125 plusmn00050 ADOΞlowast0 + Ξlowast0 00285 plusmn00058 ADOΩminus + Ω+ 00077 plusmn00015 P

Table 1 Hadronic Z decays atradics = 912 GeV Measured rates of light-flavour mesons and baryons

expressed as percentages of the average charged-particle multiplicity as used in this work Multiplythe numbers by 207100 to translate the percentages to corresponding production rates Source labelsindicate A (ALEPH) D (DELPHI) L (L3) O (OPAL) S (SLD) P (PDG)

StringFlavetaSup = 060StringFlavetaPrimeSup = 012

Baryon SectorStringFlavprobQQtoQ = 0081StringFlavprobSQtoQQ = 0915StringFlavprobQQ1toQQ0 = 00275StringFlavsuppressLeadingB = offStringFlavpopcornSpair = 09StringFlavpopcornSmeson = 05

Since strange-particle and baryon spectra at the LHC exhibit interesting differences with respectto existing models (see below) we paid particular attention to first obtaining a good description ofthese sectors in e+eminus collisions Specifically we have increased the overall amount of strangenessby about 10 while decreasing the rate of vector mesons by a similar amount9 (these two effectslargely cancel for Klowast) This improves the total Kplusmn ρ0 ω Λ Ξlowast and Ω yields on our combined LEPestimates discussed above The price is that we now overshoot the measured rate of Ξplusmn baryons by10 The resulting identified-meson and -baryon rates expressed as fractions of the average charged-particle multiplicity are plotted in fig 5 Note that the last four bins of the meson plot and the thirdand fourth bins of the baryon plot are not 〈n〉 〈nCh〉 fractions but rather the KlowastK φKlowast φKφπ Λp and ΛK ratios respectively Note also that section 4 on energy scaling below includes acomparison to the average Kaon and Lambda rates as a function of ee CM energy (fig 25)

To provide further information on identified particles we include a limited comparison to momen-tum spectra of Kplusmn p Λ and Ξplusmn which are the states of most immediate interest in the context ofsimilar comparisons now being made at LHC The spectra of Kplusmn mesons and Λ baryons are shownin fig 6 while the pplusmn and Ξplusmn spectra are relegated to appendix B2 The modified parameters of theMonash tune have virtually no effect on the Kaon distribution which still exhibits too many very softKaons (with ln(x) lt minus4 corresponding to x lt 0018 so momentum scales below sim 1 GeV) while

9For reference the current default value of ProbStoUD is 019 while ours is 0217 The increased value also improvesthe agreement with the Ds and Bs rates see section 23 The default values of mesonUDvector and mesonSvectorare 062 and 0725 respectively while ours are 05 and 055

10

plusmnπ 0π plusmnK η η plusmnρ 0ρ plusmnK ω φKK-

RKφ

RK-φ

R-πφ

R

gtch

ltnltngt

-310

-210

-110

1

10Meson Fractions

Pythia 8183Data from PDGHEPDATA

LEP + SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn06

00plusmn12

00plusmn12

V I

N C

I A

R O

O T

plusmnπ 0π plusmnK η η plusmnρ 0ρ plusmnK ω φKK-

RKφ

RK-φ

R-πφ

R

The

ory

Dat

a

06

08

1

12

14

p ΛpΛ

RKΛ

R plusmnΣ 0Σ ++∆ Σ plusmnΞ 0Ξ Ω

gtch

ltnltngt

-410

-310

-210

-110

1Baryon Fractions

Pythia 8183Data from PDGHEPDATA

LEP PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn11

00plusmn22

00plusmn22

V I

N C

I A

R O

O T

p ΛpΛ

RKΛ

R plusmnΣ 0Σ ++∆ Σ plusmnΞ 0Ξ Ω

The

ory

Dat

a

06

08

1

12

14

Figure 5 Hadronic Z decays atradics = 912 GeV Identified-meson and -baryon rates expressed as

fractions of the average charged-particle multiplicity

-4 -2 0

dln

(x)

Kgt

dn

K1

ltn

-310

-210

-110

1

10

) (Combined)plusmnx(K

Pythia 8183Data from ZPC66(1995)355 ZPC63(1994)181 EPJC5(1998)585

LEP (A+D+O)PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn16

00plusmn14

01plusmn19

V I

N C

I A

R O

O T

)p

ln(x-4 -2 0

The

ory

Dat

a

06

08

1

12

14

0 1 2 3 4 5

ξd

Λgt

dn

Λ1

ltn

0

02

04

06)]|0Λ|Ln[x(

Pythia 8183Data from EPJ C16 (2000) 613

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn08

01plusmn15

01plusmn12

V I

N C

I A

R O

O T

pξ

0 1 2 3 4 5

The

ory

Dat

a

06

08

1

12

14

Figure 6 Hadronic Z decays atradics = 912 GeV Kplusmn and Λ momentum-fraction spectra

11

the significant increase in the value of aExtraDiquark from 05 (Default) to 097 (Monash cf sec-tion 21) produces a desirable suppression of very hard Λ baryons The corresponding change in themeasured parts of the p and Ξplusmn spectra (cf appendix B2) are small compared with the experimentaluncertainties

It is interesting however to note that all of these spectra indicate or are at least consistent with amodelling excess of soft identified-particle production below ln(x) sim minus45 corresponding to absolutemomentum scales around 500 MeV while we recall that the inclusive ln(x) spectrum above showedan underproduction around ln(x) sim minus55 Within the constraints of the current theory model wehave not managed to find a way to mitigate these features while remaining consistent with the rest ofthe data Nonetheless it should be mentioned that these observations could have relevance also in thecontext of understanding identified-particle spectra at LHC a possibility which to our knowledge hasso far been ignored

23 Heavy-Quark Fragmentation

Similarly to above we first discuss the inclusive rates of hadrons containing heavy quarks before wediscuss their spectra Unfortunately there are also here substantial disagreements between differentpieces of information We have made the following choices

bull ForD mesons the average Dplusmn rate given in sec 46 of the PDG (0175) is equal to the inclusivebranching fraction for Z rarr DplusmnX given in the Z boson summary table in the same Review(after normalizing the latter to the hadronic Z fraction of 6991 [39]) However the formerought to be substantially larger given that some Z rarr cc events will contain two Dplusmn mesons(counting once in the Z rarr DplusmnX branching fraction but twice in the average Dplusmn multiplicity)We therefore here use a measurement by ALEPH [54] to fix the Dplusmn and D0 rates resulting ina reference value for the average Dplusmn multiplicity almost twice as large as that given by sec 46in the PDG

bull For Λ+c the average multiplicity given in sec 46 of the PDG is twice as large as that indicated

by the branching fraction BR(Z rarr Λ+c X) in the Z boson summary table in the same Review

We here use the branching from the Z boson summary table as our constraint on the Λ+c rate

normalized to the total branching fraction BR(Z rarr hadrons)

bull We also include the average rate of g rarr cc splittings obtained by combining an ALEPH [55]and an OPAL measurement [56] but with an additional 10 systematic uncertainty added toboth measurements to account for possibly larger mismodeling effects in the correction fac-tors [57 58]

bull For B particles we use the quite precise inclusive Z rarr B+X branching fraction from the Zboson summary in the PDG

bull We also use the sum of Bplusmn and B0(B0) in sec 46 of the PDG10

bull TheB0s multiplicity given in sec 46 of the PDG (0057plusmn0013) is more than twice the inclusive

BR(Z rarr B0sX)BR(Z rarr hadrons) branching fraction (00227 plusmn 00019) quoted in the Z

10Note that we have a factor 2 relative to the PDG since it appears the PDG quotes the average rather than the sum Notealso that all the average B meson multiplicities in sec 46 of the PDG are accompanied by a note ldquo(d)rdquo stating that the SMB(Z rarr bb) = 0217 was used for the normalization For completeness the reader should be aware that this is the fractionnormalized to hadronic Z decays the branching fraction relative to all Z decays is 0151 [39]

12

Charm Our Reference Our〈n〉 or BR Value Source

D+ +Dminus 0251 plusmn0047 AD0 + D0 0518 plusmn0063 ADlowast+ +Dlowastminus 0194 plusmn00057 PD+

s +Dminuss 0131 plusmn0021 PBR(Z rarr Λ+

c X) 00220 plusmn00047 ZBR(Z rarr X + cc) 00306 plusmn00047 AOJψ 00052 plusmn00004 Pχc1 00041 plusmn00011 Pψprime 00023 plusmn00004 P

Beauty Our Reference Our〈n〉 or BR Value Source

BR(Z rarr B+X) 0087 plusmn0002 ZB+ +B0 + B0 +Bminus 0330 plusmn0052 PBlowastu +Blowastd +Blowasts 0288 plusmn0026 PBR(Z rarr B0

sX) 00227 plusmn00019 ZBR(Z rarr BbaryonX) 00197 plusmn00032 ZBR(Z rarr X + bb) 000288 plusmn000061 ADSBR(Z rarr bbbbX) 000051 plusmn000019 ZΥ (times10) 00014 plusmn00007 P

Table 2 Hadronic Z decays atradics = MZ Measured rates and inclusive branching fractions of

particles containing c and b quarks as used in this work Note the branching fractions are normalizedto Z rarr hadrons and hence should be interpreted as eg BR(Z rarr B+X)BR(Z rarr hadrons)Note 2 the sum over Blowast states includes both particles and anti-particles Note 3 the Υ rate ismultiplied by a factor 10 Source labels indicate A (ALEPH) D (DELPHI) O (OPAL) P (PDGsection 46) S (SLD) Z (PDG Z Boson Summary Table)

boson summary table We find these two numbers difficult to reconcile and choose to use theinclusive BR(Z rarr B0

sX)BR(Z rarr hadrons) branching fraction as our main constraint

bull We also include the inclusive branching fractions for B-baryons (summed over baryons andantibaryons) the rate of g rarr bb splittings obtained by combining ALEPH [59] DELPHI [60]and SLD [61] measurements (including an additional 10 systematic to account for largerpossible mismodeling effects in the correction factors [57 58]) and the rate of Z rarr bbbb fromthe PDG Z boson summary table [39]

Our constraints on the heavy-quark particle rates are summarized in tab 2 Comparisons to these ratesare shown in fig 7 now without normalizing to the average charged-particle multiplicity Given thatmost of the c and b quarks come directly from Z rarr cc and Z rarr bb decays there is not a lot of roomfor tuning to these numbers apart from the relative rates of vector mesons vs pseudoscalars which iscontrolled by the parameters

Heavy MesonsStringFlavmesonCvector = 088StringFlavmesonBvector = 22

Our parameters are slightly smaller than the current default values leading to slightly smaller Dlowast

and Blowast rates as can be seen from the plots in fig 7 Note also that the increased overall amount ofstrangeness in the fragmentation leads to slightly higherDs andBs fractions in better agreement withthe data Uncertainties are however large and some exotic onium states like χc1 ψprime and Υ are notwell described by the default modeling (It is encouraging that at least the multiplicity of Jψ mesonsis well described though a substantial fraction of this likely owes to the feed-down from B decaysand hence does not depend directly on the string-fragmentation model itself)

We also note that it would be desirable to reduce the rate of g rarr bb and Z rarr bbbb events whilethe g rarr cc one appears consistent with the LEP constraints We suspect that this issue may be tiedto the fixed choice of using pperp as the renormalization scale for both gluon emissions and for g rarr qq

13

plusmnD 0D plusmnD plusmns

D X+

cΛ

ccrarrg ψJ c1χ

3685

ψ

X)

rarrlt

ngt o

r B

R(Z

-410

-310

-210

-110

1

10Charm Rates

Pythia 8185Data from HEPDATAPDG

LEP

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn15

00plusmn18

00plusmn17

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

plusmnD 0Dplusmn

D plusmnsD X+

cΛ ccrarrg ψJ c1χ

3685ψ

The

ory

Dat

a

0

05

1

15

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

X)

rarrlt

ngt o

r B

R(Z

-510

-410

-310

-210

-110

1

10Beauty Rates

Pythia 8185Data from HEPDATAPDG

LEP+SLD

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn17

00plusmn23

00plusmn23

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

The

ory

Dat

a0

05

1

15

Figure 7 Hadronic Z decays atradics = 912 GeV Rates and inclusive Z rarr X branching fractions

(normalized to Z rarr hadrons) of particles containing c and b quarks

splittings in the current version of PYTHIA A more natural choice for g rarr qq could be microR prop mqqas used eg in the VINCIA shower model [29]

We now turn to the dynamics of heavy-quark fragmentation focusing mainly on the b quarkFor heavy quarks the Lund fragmentation function is modified due to the (massive) endpoints not

moving along straight lightcones as the string pulls on them they slow down resulting in the stringtracing out a smaller space-time area than it would for massless quarks This modifies the implicationsof the string area law in a manner captured by the so-called Bowler modification of the fragmentationfunction [62]

fmassive(zmQ) prop f(z)

zbrQm2Q

(6)

with mQ the heavy-quark mass b the same universal parameter that appears in the massless fragmen-tation function eq (3) and rQ a tuning parameter which is unity in the original derivation of Bowlerbut can be assigned values different from unity to reduce (rQ rarr 0) or emphasize (rQ gt 1) the effectSince rQ multiplies the heavy-quark mass (squared) it can also be viewed as an effective rescalingof the mass value The net result is a suppression of the region z rarr 1 hence a relative softening ofthe fragmentation spectrum for heavy flavours (relative since the presence of m2

perp in the exponent ofeq (3) still implies an overall harder fragmentation for higher hadron masses)

We emphasize that this is the only fragmentation function that is self-consistent within the string-fragmentation model [33 62] Although a few alternative forms of the fragmentation functions formassive quarks are available in the code we therefore here work only with the Bowler type As forthe massless function the proportionality sign in eq (6) indicates that the function is normalized tounity

In PYTHIA separate rQ parameters are provided for c and b quarks We consider the one for bquarks first Its default value is rb = 067 but this appears to give too hard b fragmentation spectrawhen compared to LEP and SLD data see below For the Monash tune we instead use

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (DELPHI)weak

Bx

Pythia 8181Data from EurPhysJ C71 (2011) 1557

DELPHI PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn16

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (SLD)weak

Bx

Pythia 8181HepData5111d1-x1-y1

SLDPY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn07

00plusmn15

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a06

08

1

12

14

Figure 8 Hadronic Z decays atradics = 912 GeV Momentum (xB) spectra of weakly decaying B

hadrons compared to data from DELPHI [63] (left) and SLD [64] (right)

StringZrFactB = 0855

which produces softer B spectra and simultaneously agrees better with the theoretically preferredvalue (rb = 1)

A comparison to the scaled-momentum spectra (xB = 2|pB|Ecm) of weakly decayingB hadronsfrom both DELPHI [63] and SLD [64] is given in fig 8 (due to small differences between the twomeasured results we choose to show both) The dampening of the hardest part of the spectrum causedby the increase in the rb parameter is visible in the right-most two bins of the distributions and in thesmaller χ2

5 values for the Monash tune The effects of the modification can be further emphasizedby an analysis of the moments of the distribution in which the higher moments are increasinglydominated by the region xB rarr 1 A comparison to a combined LEP analysis of the moments of thexB distribution [63] is given in fig 9 further emphasizing that the high-xB part of the distribution isnow under better control

The reason we have not increased the rb parameter further is that it comes at a price If theB hadrons are taking less energy then there is more energy left over to produce other particlesand the generated multiplicity distribution in b events already exhibits a slightly high tail towardslarge multiplicities Nonetheless since the revised light-flavour fragmentation parameters produce anoverall narrower fragmentation function the end result is still a slight improvement in the multiplicitydistribution also for b events This is illustrated together with the inclusive momentum distributionfor b-tagged events in fig 10 compared to measurements by L3 [26] Interestingly the multiplicitydistribution still appears to be too wide but within the constraints of the present study we were unableto obtain further improvements As a point of speculation we note that the distribution of the numberof partons before hadronization is also quite wide in PYTHIA and this may be playing a role ineffectively setting a lower limit on the width that can be achieved for the hadron-level distribution

Comparisons to L3 event shapes in b-tagged events are collected in appendix B1 (the left columnof plots contains light-flavour tagged event shapes the right column b-tagged ones) In particular the

15

0 10 20 30 40

Mom

ent

0

02

04

06

08 (moments)weakBx

Pythia 8181Data from Eur Phys J C71 (2011) 1557

LEP (combined)PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn10

00plusmn103

00plusmn129

V I

N C

I A

R O

O T

N0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

Figure 9 Hadronic Z decays atradics = 912 GeV Moments of the B fragmentation function com-

pared to a combined analysis of LEP+SLD data by DELPHI [63]

0 20 40

)ch

Pro

babi

lity(

n

-610

-510

-410

-310

-210

-110

1

10

210 Charged Multiplicity (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

06plusmn45

08plusmn64

13plusmn110

V I

N C

I A

R O

O T

(b)chn0 20 40

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

ch d

nch

1n

-510

-410

-310

-210

-110

1

10

210 Charged Momentum Fraction (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn08

00plusmn06 V

I N

C I

A R

O O

T

)| (b)p

|Ln(x0 2 4 6 8

The

ory

Dat

a

06

08

1

12

14

Figure 10 HadronicZ decays atradics = 912 GeV Charged-hadron multiplicity (left) and momentum-

fraction (right) spectra in b-tagged events

16

0 02 04 06 08 1

dx

Dgt

dn

D1

ltn

0

05

1

15

2

25gt01)

E) (x

plusmnx(D

Pythia 8183Data from EurPhysJ C16 (2000) 597

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn14

02plusmn28

02plusmn32

V I

N C

I A

R O

O T

Ex0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

EX02 04 06 08 1

E)

dX

dN

(DZ

had

1N

0

0002

0004

0006

0008

001

0012

0014

0016

ALEPHHerwig++Sherpa

91 GeV ee Z (hadronic)

mcp

lots

cer

nch

41

M e

vent

sge

Riv

et 1

82

Herwig++ 261a Sherpa 141

ALEPH_1999_S4193598

spectrum (particle-level)+-D

02 04 06 08 105

1

15Ratio to ALEPH

Figure 11 The inclusive Dlowast spectrum in hadronic Z decays [55] Left Monash 2013 tune com-pared with default PYTHIA 8 and the Fischer tune Right comparison with HERWIG (dashed) andSHERPA (dotted) from MCPLOTS [25] Note that the plot in the left-hand pane is normalized tounity while the one in the right-hand pane is normalized to the number of hadronic Z decays

Monash tune gives a significant improvement in the soft region of the jet-broadening parameters inb-tagged events while no significant changes are observed for the other event shapes These smallimprovements are presumably a direct consequence of the softening of the b fragmentation functionit is now less likely to find an isolated ultra-hard B hadron

We round off the discussion of heavy-quark fragmentation by noting that a similarly comprehen-sive study of charm-quark fragmentation would be desirable However charm-quark tagged multi-plicity and event-shape data is not available to our knowledge and most of the D meson spectra onHEPDATA concern only specific decay chains (hence depend on the decay modeling) andor are lim-ited to restricted fiducial regions (limiting their generality) Experimentally the cleanest measurementis obtained from Dlowast decays and an inclusive momentum spectrum for Dlowast mesons has been measuredby ALEPH [55] From this distribution shown in fig 11 we determine a value for rc of

StringZrFactC = 132

We note that the low-x part of the Dlowast spectrum originates from g rarr cc shower splittings whilethe high-x tail represents prompt Dlowast production from leading charm in Z rarr cc (see [55] for a nicefigure illustrating this) The intermediate range contains a large component of feed-down from brarr cdecays hence this distribution is also indirectly sensitive to the b-quark sector The previous defaulttune had a harder spectrum for both b- and c-fragmentation leading to an overestimate of the high-xpart of the Dlowast distribution The undershooting at low xDlowast values which remains unchanged in theMonash tune most likely indicates an underproduction of g rarr cc branchings in the shower We notethat such an underproduction may also be reflected in the LHC data on Dlowast production see eg [65]We return to this issue in the discussion of identified particles at LHC section 35

17

0 01 02 03 04

d(1

-T)

σ d

σ1

-310

-210

-110

1

10

2101-Thrust (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn03

01plusmn04

02plusmn05

V I

N C

I A

R O

O T

1-T (udsc)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

Figure 1 Hadronic Z decays atradics = 912 GeV The Thrust distribution in light-flavour tagged

events compared with L3 data [26]

a χ2 minimization we regard this as acceptable the χ25 values are intended merely to give an overall

indication of the level of agreement or disagreement for each observableThe resulting plots look as illustrated in fig 1 with a main pane (top) showing the distribution

itself and a bottom pane showing ratios In the top pane experimental data is always shown withfilled black square symbols with vertical black lines indicating the one-sigma uncertainties (with twoseparate black crossbars if separate statistical and systematic uncertainties are given) Lighter (grey)extensions of the vertical lines are used to indicate two-sigma uncertainties In the ratio pane the greenshaded region indicates the one-sigma uncertainty region while yellow is used to denote the two-sigma one An internal lighterdarker shading variation in each band is used to denote the breakdowninto statistical-only (inner) and statistical+systematic uncertainties (outer) whenever separate valuesfor each of these are given Finally next to each MC legend the χ2

5 value defined above is printedalong with its MC uncertainty A colour-coded box next to the χ2 value is shaded green (χ2 lt 1)yellow (1 lt χ2 lt 4) orange (4 lt χ2 lt 9) or red (9 lt χ2) depending on the level of agreement ordisagreement This functionality will be included in a forthcoming update of the VINCIA plug-in toPYTHIA 8

2 Final-State Radiation and Hadronization

The main parameter governing final-state radiation is the effective value of the strong coupling whichin PYTHIA 8 is specified by giving the value of αs(MZ) We follow the strategy of [24] and use aset of light-flavour (udsc) tagged e+eminus event shapes provided by the L3 experiment [26] to extracta best-fit value for αs(MZ) (This prevents B decays from contaminating this step of the analysisHeavy-quark fragmentation will be treated separately below) The renormalization scale for final-state shower emissions in PYTHIA is fixed to be [27]

FSR micro2R = p2

perpevol = z(1minus z)Q2 (2)

3

with Q2 = p2 minusm20 the offshellness of the emitting parton (with on-shell mass m0) and z the energy

fraction appearing in the DGLAP splitting kernels P (z) (To estimate the shower uncertainties asso-ciated with this choice of renormalization scale we recommend using ln(micro2

R)plusmn ln(2) correspondingto a factor

radic2 variation of microR)

Theoretically a set of formally subleading terms can be resummed by using 2-loop running of αsin the so-called MC (aka CMW) scheme [28] However in a leading-order code like PYTHIA thisproduces too little hard radiation in practice due to missing NLO ldquoKrdquo factors for hard emissions (seeeg the study of NLO corrections in [29]) Empirically we find that a better overall description isachieved with one-loop running which for a fixed value of ΛQCD can effectively mimic the effect ofmissing K factors via its relatively slower pace of running leading to values of αs(MZ) in the range0135minus 0140 consistent with other LO extractions of the same quantity (See [29] for an equivalentextraction at NLO)

For this study we did not find any significant advantage in reinterpreting this value in the CMWscheme3 and hence merely settled on an effective αs(MZ) = 01365 (to be compared with the currentdefault value of 01383)

For the infrared shower cutoff we choose a value close to4 ΛQCD in order to have a smoothtransition between low-pperp perturbative emissions and non-perturbative string breaks the latter ofwhich involve pperp kicks of order ΛQCD (In principle the perturbative evolution could be continuedto even lower scales if combined with a non-perturbative regularization of αs but such low cutoffvalues could risk generating problems at the fragmentation stage since the technical implementationof the string model becomes complicated if there are too many small gluon ldquokinksrdquo spaced closelyalong the strings) The set of relevant parameters in the code is

FSR Strong CouplingTimeShoweralphaSvalue = 01365TimeShoweralphaSorder = 1TimeShoweralphaSuseCMW = off

FSR IR cutoffTimeShowerpTmin = 050 for QCD radiationTimeShowerpTminChgQ = 050 for QED radiation off quarks

FSR Spin CorrelationsTimeShowerphiPolAsym = on approximate FSR polarization effects

The resulting distribution of the Thrust event-shape variable was shown in fig 1 comparing theMonash 2013 tune to the current default tune and to an alternative contemporary tune by N Fi-scher [30] To avoid clutter the other event-shape variables (C D BW and BT ) are collected inappendix B1 There are no significant changes to any of the light-flavour tagged event shapes in ourtune as compared to the current default one

21 Light-Flavour Fragmentation

Given a set of post-shower partons resolved at a scale ofQhad sim 1 GeV the non-perturbative stage ofthe fragmentation modeling now takes over to convert the partonic state into a set of on-shell hadrons

3One slight disadvantage is that the CMW scheme produces somewhat larger ΛQCD values Since the current formu-lation of the shower algorithm does not include a non-perturbative regularization of αs a higher ΛQCD value necessitatesa larger IR cutoff in the shower which can leave an undesirable gap between the transverse kicks generated by showeremissions and those generated by non-perturbative string splittings

4The IR shower cutoff must still remain somewhat above the Landau pole of αs a lower cutoff scale would activate ahardcoded protection mechanism implemented in the PYTHIA shower forcing it to be higher than ΛQCD

4

In the leading-colour approximation each perturbative dipole is dual to a non-perturbative stringpiece [31] Quarks thus become string endpoints while gluons become transverse kinks connectingtwo string pieces [32] The Lund string fragmentation model [33] describes the fragmentation of suchstring systems into on-shell hadrons

Since the shower has already resolved all the (perturbative) physics down to a transverse-momentumscale of pTmin = 05 GeV (for the Monash 2013 tune) we find it reasonable that the pperp kicks in-volved in string breaking should effectively average over dynamics in roughly the range 250 MeV =radicκπ lt σperp lt pTmin with the lower bound given by Fermi motion (with κ the string tension

see [34]) Further since we here choose pTmin to be only slightly greater than ΛQCD the size of thenon-perturbative corrections is naturally limited to kickscorrections appropriate for non-perturbativedynamics (in contrast eg to the cluster model [35] which can generate substantially larger kicks oforder the largest allowed cluster mass which can be several GeV [30]) For the Monash 2013 tunewe have settled on a value of σperp = 0335 GeV with a small (1) tail of breaks involving higher pperpvalues carried over from the default settings

StringPTsigma = 0335StringPTenhancedFraction = 001StringPTenhancedWidth = 20

This value is obtained essentially from the first two bins of the Thrust distribution fig 1 and from thebins near zero of the other event shapes see appendix B1 Note that the σperp value is interpreted as thewidth of a Gaussian distribution in the total pperp (measured transversely to the local string directionwhich may differ from the global event axis) such that each of the px and py components have aslightly smaller average value σ2

xy = 12σ

2perp = (0237 GeV)2 Also note that each non-leading hadron

will receive two pperp kicks one from each of the breaks surrounding it hencelangp2perphad

rang= 2σ2

perp =(0474 GeV)2

For massless quarks the longitudinal component of the energy carried by a hadron formed in thestring-breaking process stringrarr hadron+stringprime is governed by the Lund symmetric fragmentationfunction

f(z) prop z(aiminusaj)(1minus z)ajz

exp

(minusbm2

perpz

) (3)

where z is the energy carried by the newly formed (ij) hadron expressed as a fraction of the (light-cone) energy of the quark (or antiquark) endpoint i of the fragmenting string (The remaining energyfraction (1 minus z) goes to the new stringprime system from which another hadron can be split off in thesame manner etc until all the energy is used up) The transverse mass of the produced (ij) hadronis defined by m2

perp = m2had + p2

perphad hence heavier hadrons have harder spectra The proportionalitysign in eq (3) indicates that the function is to be normalized to unity

The a and b parameters govern the shape of the fragmentation function and must be constrainedby fits to data Eq (3) expresses the most general form of the fragmentation function for which the aparameters of the original string-endpoint quark ai and that of the (anti-)quark produced in the stringbreak aj can in principle be different while the b parameter is universal Within the Lund model thea value is normally also taken to be universal the same for all quarks with the only freedom beingthat a larger a parameter can be assigned to diquarks [36] from which baryons are formed and hencemeson and baryon spectra can be decoupled somewhat (See StringZaExtraDiquark below)

Roughly speaking large a parameters suppress the hard region z rarr 1 while a large b parametersuppresses the soft region z rarr 0 By adjusting them independently both the average hardness andthe width of the resulting fragmentation spectra can be modified For example increasing both a andb yields a narrower distribution while changing them in opposite directions moves the average An

5

The a parameter The b parameter

a = 09 a = 01 b = 05 b = 20

02 04 06 08 10

05

10

15

02 04 06 08 10

05

10

15

20

b = 1 GeVminus2 mperp = 1 GeV a = 05 mperp = 1 GeV

Figure 2 Illustration of the Lund symmetric fragmentation function (normalized to unity) for ai =aj equiv a Left variation of the a parameter from 01 (blue) to 09 (red) with fixed b Right variationof the b parameter from 05 (red) to 2 (blue) GeVminus2 with fixed a

illustration of the effect of varying the a and b parameters for ai = aj equiv a is given in fig 2 see alsothe lecture notes in [37] Note that the σperp parameter also affects the hardness with larger σperp valuesgenerating harder hadrons the difference being that the σperp parameter acts mainly in the directiontransverse to the string5 (and is an absolute scale expressed in GeV) while the a and b parameters actlongitudinally (with z a relative scale expressed as a fraction of the endpointrsquos energy)

In the context of this work we included the possibility of letting the a parameter for strangequarks be slightly different from that of u and d quarks but did not find any significant advantagesThe relevant parameters in the code we settled on for the Monash tune are

StringZaLund = 068StringZbLund = 098StringZaExtraDiquark = 097StringZaExtraSquark = 000

The average hardness of the produced hadrons is tightly (anti-)correlated with the average multi-plicity via momentum conservation if each hadron takes a lot of energy then fewer hadrons must bemade and vice versa Thus the σperp value and the a and b parameters of the fragmentation functioncan be well constrained by simultaneously considering both momentum and multiplicity spectra Inorder to be as universal as possible one normally uses the inclusive charged-particle spectra for thispurpose These are shown in fig 3 (Note the Fischer tune only included the average particle mul-tiplicity as a constraint so the full nch distribution is not expected to be reproduced perfectly [30])The momentum fraction in the right-hand plot is defined by

xp =2|p|Ecm

(4)

As above the experimental data come from a measurement by L3 [26] which only includes the fourlightest flavours thus excluding b quarks (which will be treated separately below)

Both of the earlier tunes exhibit a somewhat too broad multiplicity distribution in comparisonwith the L3 data The relatively large Lund a and b values used for the Monash tune combined with

5Explicitly σperp expresses the pperp broadening transverse to the string direction but implicitly its size also enters inthe logitudinal fragmentation function via the m2

perp term in eq (3) causing higher-pperp hadrons to have relatively harderlongitudinal spectra as well

6

0 20 40 60

)ch

Pro

babi

lity(

n

-610

-510

-410

-310

-210

-110

1

10

210 Charged Multiplicity (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn05

01plusmn07

02plusmn21

V I

N C

I A

R O

O T

chn0 20 40 60

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

chgt

dn

ch1

ltn

-310

-210

-110

1

10Charged Momentum Fraction (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn09

00plusmn05

00plusmn05

V I

N C

I A

R O

O T

)|p

|Ln(x0 2 4 6 8

The

ory

Dat

a06

08

1

12

14

Figure 3 Hadronic Z decays atradics = 912 GeV Charged-particle multiplicity (left) and momentum-

fraction (right) spectra

its large σperp value produce a narrower nCh spectrum with in particular a smaller tail towards largemultiplicities All the tunes produce a sensible momentum spectrum The dip around |ln(x)| sim 55corresponds to the extreme soft-pion tail with momenta at or below ΛQCD We did not find it possibleto remove it by retuning since a smaller b parameter would generate significantly too high particlemultiplicities and a smaller σperp would lead to conflict with the event-shape distributions

A zoom on the high-momentum tail is provided by the left-hand plot in fig 4 which shows acomparison on a linear momentum scale to a measurement by ALEPH [38] (now including Z rarr bbevents as well as light-flavour ones) All the tunes exhibit a mild overshooting of the data in the region05 lt xp lt 08 corresponding to 015 lt | ln(x)| lt 07 in which no similar excess was present inthe L3 comparison We therefore do not regard this as a significant issue6 but note that the excess issomewhat milder in the Fischer and Monash tunes

Further information to elucidate the structure of the momentum distribution is provided by theplot in the right-hand pane of fig 4 which uses the same |ln(x)| axis as the right-hand plot in fig 3and shows the relative particle composition in the Monash tune for each histogram bin (The categoryldquoOtherrdquo contains electrons and muons from weak decays) An interesting observation is that therelatively harder spectrum of Kaons implies that for the highest-momentum bins the charged tracksare made up of an almost exactly equal mixture of Kaons and pions despite Kaons on average onlymaking up about 10 of the charged multiplicity

6One might worry whether the effect could be due solely to the Z rarr bb events which are only present in the ALEPHmeasurement and if so whether this could indicate a significant mismodeling of the momentum distribution in b eventsHowever as we show below in the section on b fragmentation the charged-particle momentum distribution in b-taggedevents shows no excess in that region (in fact it shows an undershooting)

7

0 02 04 06 08 1

pd

xch

gt d

nch

1lt

n

-410

-310

-210

-110

1

10Charged Momentum Fraction

Pythia 8183Data from Barate et al Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn14

01plusmn08

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

IDgt

dn

ch1

ltn

0

02

04

06

08

1

12 Particle Composition vs Lnx (udsc)

Pythia 8183

plusmnπplusmnKplusmnp

Other

V I

N C

I A

R O

O T

)|p

|Ln(x0 2 4 6 8

Rat

io06

08

1

12

14

Figure 4 Hadronic Z decays atradics = 912 GeV Charged-particle momentum fraction xp on a linear

scale (left) and relative particle composition (right) for the log-scale distribution shown in fig 3

22 Identified Particles

Continuing on the topic of identified particles we note that the extraction of the a and b parametersfrom the inclusive charged-particle distributions is made slightly more complicated by the fact thatnot all observed particles are ldquoprimaryrdquo (originating directly from string breaks) many lower-massparticles are ldquosecondariesrdquo produced by prompt decays of more massive states (eg ρrarr ππ) whoserelative rates and decay kinematics therefore influence the spectra In the e+eminus measurements weinclude here particles with cτ lt 100 mm were treated as unstable hence leading to secondaries (Forcompleteness we note that the equivalent standard cut at the LHC is normally 10 mm)

The particle composition in PYTHIA 8 was already tuned to a set of reference values provided bythe PDG [39] and the default parameters do reasonably well certainly for the most copiously pro-duced sources of secondaries Nonetheless we have here reoptimized the flavour-selection parametersof the string-fragmentation model using a slightly different set of reference data combining the PDGtables with information provided directly by the LEP experiments via HEPDATA [1] Based on thelevel of agreement or disagreement between different measurements of the same particles we havemade our own judgement as to the level of uncertainty for a few of the particles as follows (Unlessotherwise stated we use the value from the PDG Particles and antiparticles are implicitly summedover and secondaries from particles with cτ lt 100 mm are included)

bull The various LEP and SLD measurements of the φ meson rate on HEPDATA are barely com-patible Eg OPAL [40] reports 〈nφ〉 = 0091 plusmn 0002 plusmn 0003 while ALEPH [38] quotes〈nφ〉 = 0122 plusmn 0004 plusmn 0008 a difference of 30 with uncertainties supposedly less than10 DELPHI [41] and SLD [42] fall in between The PDG value is 〈nφ〉 = 00963 plusmn 0003ie with a combined uncertainty of just 3 We choose to inflate the systematic uncertaintiesand arrive at 〈nφ〉 = 0101plusmn 0007

8

bull For Λ production we use the most precise of the LEP measurements by OPAL7 [43] 〈nΛ〉 =0374plusmn 0002plusmn 0010 about 5 lower than the corresponding PDG value

bull For Σplusmn baryons we use a combination of the two most recent LEP measurements by L3 [44]for Σ+ + Σ

minus and by DELPHI [45] for Σminus + Σ+ for an estimated 〈nΣplusmn〉 = 0195 plusmn 0018

which is roughly 10 higher than the PDG value

bull For Σ0 baryons we use the most recent measurement by L3 [44] 〈nΣ0〉 = 0095 plusmn 0015 plusmn0013 this is about 20 larger than the PDG value The L3 paper comments on their relativelyhigh value by noting that L3 had the best coverage for low-momentum baryons hence smallermodel-dependent correction factors

bull For ∆++ baryons there are only two measurements in HEPDATA [4647] which are mutuallydiscrepant by about 2σ The DELPHI measurement is nominally the most precise but OPALgives a much more serious discussion of systematic uncertainties We choose to increase theestimated extrapolation errors of the DELPHI measurement by 50 and obtain a weighted av-erage8 of 〈n∆++〉 = 009plusmn0017 5 larger than the PDG value with a 20 larger uncertainty

bull For Σlowast the three measurements on HEPDATA [38 43 48] are likewise discrepant by 2σ minus 3σWe inflate the systematic uncertainties and arrive at 〈nΣlowastplusmn〉 = 0050 plusmn 0006 which is again5 higher than the PDG value with twice as much uncertainty

bull The measurements for Ξplusmn are in good agreement [38 43 48] with a weighted average of〈nΞplusmn〉 = 00266plusmn 00012 slightly larger than the PDG value

bull For Ξlowast0 however the DELPHI measurement [48] gives a far lower number than the OPAL [43]and ALEPH [38] ones and the weighted average differs by more than 10 from the PDGvalue despite the latter claiming an uncertainty smaller than 10 Our weighted average is〈nΞlowast0〉 = 00059plusmn 00012

bull Finally for the Ω baryon the DELPHI [49] and OPAL [43] measurements are in agreementand we use the PDG value 〈nΩ〉 = 00016plusmn 00003

We summarize the constraints on the light-meson and baryon rates used here in tab 1 Note that weexpress them as percentages of the average charged multiplicity

〈nCh〉 = 207 (5)

obtained as a weighted average over MARK-II [50] ALEPH [38] DELPHI [51] OPAL [52] andL3 [53] measurements

The light-flavour-selection parameters for the Monash tune are (see appendix A for a comparisonof these values to the current default ones)

Light-Meson SectorStringFlavProbStoUD = 0217StringFlavmesonUDvector = 05StringFlavmesonSvector = 055

7We note that HEPDATA incorrectly gives the systematic error as 0002 while the value in the OPAL paper is 0010 [43]This has been communicated to the HEPDATA maintainers

8Even with the inflated error the uncertainty on the DELPHI measurement is still less than a third that of the OPAL oneDELPHI therefore still dominates the average

9

Mesons Our Reference Our〈n〉 〈nCh〉 Value (in ) Source

π+ + πminus 822 plusmn09 Pπ0 455 plusmn15 PK+ +Kminus 108 plusmn03 Pη 506 plusmn038 Pηprime 073 plusmn009 Pρ+ + ρminus 116 plusmn21 Pρ0 595 plusmn047 PKlowast+ +Klowastminus 345 plusmn028 Pω 490 plusmn031 Pφ 049 plusmn0035 ADOS

Baryons Our Reference Our〈n〉 〈nCh〉 Value (in ) Source

p+ p 507 plusmn016 PΛ + Λ 181 plusmn032 OΣ+ + Σminus + Σ+ + Σminus 0942 plusmn0087 DLΣ0 + Σ0 0459 plusmn0096 L∆++ + ∆minusminus 0434 plusmn0082 DOΣlowast+ + Σlowastminus + Σlowast+ + Σlowastminus 0242 plusmn0029 ADOΞ+ + Ξminus 0125 plusmn00050 ADOΞlowast0 + Ξlowast0 00285 plusmn00058 ADOΩminus + Ω+ 00077 plusmn00015 P

Table 1 Hadronic Z decays atradics = 912 GeV Measured rates of light-flavour mesons and baryons

expressed as percentages of the average charged-particle multiplicity as used in this work Multiplythe numbers by 207100 to translate the percentages to corresponding production rates Source labelsindicate A (ALEPH) D (DELPHI) L (L3) O (OPAL) S (SLD) P (PDG)

StringFlavetaSup = 060StringFlavetaPrimeSup = 012

Baryon SectorStringFlavprobQQtoQ = 0081StringFlavprobSQtoQQ = 0915StringFlavprobQQ1toQQ0 = 00275StringFlavsuppressLeadingB = offStringFlavpopcornSpair = 09StringFlavpopcornSmeson = 05

Since strange-particle and baryon spectra at the LHC exhibit interesting differences with respectto existing models (see below) we paid particular attention to first obtaining a good description ofthese sectors in e+eminus collisions Specifically we have increased the overall amount of strangenessby about 10 while decreasing the rate of vector mesons by a similar amount9 (these two effectslargely cancel for Klowast) This improves the total Kplusmn ρ0 ω Λ Ξlowast and Ω yields on our combined LEPestimates discussed above The price is that we now overshoot the measured rate of Ξplusmn baryons by10 The resulting identified-meson and -baryon rates expressed as fractions of the average charged-particle multiplicity are plotted in fig 5 Note that the last four bins of the meson plot and the thirdand fourth bins of the baryon plot are not 〈n〉 〈nCh〉 fractions but rather the KlowastK φKlowast φKφπ Λp and ΛK ratios respectively Note also that section 4 on energy scaling below includes acomparison to the average Kaon and Lambda rates as a function of ee CM energy (fig 25)

To provide further information on identified particles we include a limited comparison to momen-tum spectra of Kplusmn p Λ and Ξplusmn which are the states of most immediate interest in the context ofsimilar comparisons now being made at LHC The spectra of Kplusmn mesons and Λ baryons are shownin fig 6 while the pplusmn and Ξplusmn spectra are relegated to appendix B2 The modified parameters of theMonash tune have virtually no effect on the Kaon distribution which still exhibits too many very softKaons (with ln(x) lt minus4 corresponding to x lt 0018 so momentum scales below sim 1 GeV) while

9For reference the current default value of ProbStoUD is 019 while ours is 0217 The increased value also improvesthe agreement with the Ds and Bs rates see section 23 The default values of mesonUDvector and mesonSvectorare 062 and 0725 respectively while ours are 05 and 055

10

plusmnπ 0π plusmnK η η plusmnρ 0ρ plusmnK ω φKK-

RKφ

RK-φ

R-πφ

R

gtch

ltnltngt

-310

-210

-110

1

10Meson Fractions

Pythia 8183Data from PDGHEPDATA

LEP + SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn06

00plusmn12

00plusmn12

V I

N C

I A

R O

O T

plusmnπ 0π plusmnK η η plusmnρ 0ρ plusmnK ω φKK-

RKφ

RK-φ

R-πφ

R

The

ory

Dat

a

06

08

1

12

14

p ΛpΛ

RKΛ

R plusmnΣ 0Σ ++∆ Σ plusmnΞ 0Ξ Ω

gtch

ltnltngt

-410

-310

-210

-110

1Baryon Fractions

Pythia 8183Data from PDGHEPDATA

LEP PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn11

00plusmn22

00plusmn22

V I

N C

I A

R O

O T

p ΛpΛ

RKΛ

R plusmnΣ 0Σ ++∆ Σ plusmnΞ 0Ξ Ω

The

ory

Dat

a

06

08

1

12

14

Figure 5 Hadronic Z decays atradics = 912 GeV Identified-meson and -baryon rates expressed as

fractions of the average charged-particle multiplicity

-4 -2 0

dln

(x)

Kgt

dn

K1

ltn

-310

-210

-110

1

10

) (Combined)plusmnx(K

Pythia 8183Data from ZPC66(1995)355 ZPC63(1994)181 EPJC5(1998)585

LEP (A+D+O)PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn16

00plusmn14

01plusmn19

V I

N C

I A

R O

O T

)p

ln(x-4 -2 0

The

ory

Dat

a

06

08

1

12

14

0 1 2 3 4 5

ξd

Λgt

dn

Λ1

ltn

0

02

04

06)]|0Λ|Ln[x(

Pythia 8183Data from EPJ C16 (2000) 613

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn08

01plusmn15

01plusmn12

V I

N C

I A

R O

O T

pξ

0 1 2 3 4 5

The

ory

Dat

a

06

08

1

12

14

Figure 6 Hadronic Z decays atradics = 912 GeV Kplusmn and Λ momentum-fraction spectra

11

the significant increase in the value of aExtraDiquark from 05 (Default) to 097 (Monash cf sec-tion 21) produces a desirable suppression of very hard Λ baryons The corresponding change in themeasured parts of the p and Ξplusmn spectra (cf appendix B2) are small compared with the experimentaluncertainties

It is interesting however to note that all of these spectra indicate or are at least consistent with amodelling excess of soft identified-particle production below ln(x) sim minus45 corresponding to absolutemomentum scales around 500 MeV while we recall that the inclusive ln(x) spectrum above showedan underproduction around ln(x) sim minus55 Within the constraints of the current theory model wehave not managed to find a way to mitigate these features while remaining consistent with the rest ofthe data Nonetheless it should be mentioned that these observations could have relevance also in thecontext of understanding identified-particle spectra at LHC a possibility which to our knowledge hasso far been ignored

23 Heavy-Quark Fragmentation

Similarly to above we first discuss the inclusive rates of hadrons containing heavy quarks before wediscuss their spectra Unfortunately there are also here substantial disagreements between differentpieces of information We have made the following choices

bull ForD mesons the average Dplusmn rate given in sec 46 of the PDG (0175) is equal to the inclusivebranching fraction for Z rarr DplusmnX given in the Z boson summary table in the same Review(after normalizing the latter to the hadronic Z fraction of 6991 [39]) However the formerought to be substantially larger given that some Z rarr cc events will contain two Dplusmn mesons(counting once in the Z rarr DplusmnX branching fraction but twice in the average Dplusmn multiplicity)We therefore here use a measurement by ALEPH [54] to fix the Dplusmn and D0 rates resulting ina reference value for the average Dplusmn multiplicity almost twice as large as that given by sec 46in the PDG

bull For Λ+c the average multiplicity given in sec 46 of the PDG is twice as large as that indicated

by the branching fraction BR(Z rarr Λ+c X) in the Z boson summary table in the same Review

We here use the branching from the Z boson summary table as our constraint on the Λ+c rate

normalized to the total branching fraction BR(Z rarr hadrons)

bull We also include the average rate of g rarr cc splittings obtained by combining an ALEPH [55]and an OPAL measurement [56] but with an additional 10 systematic uncertainty added toboth measurements to account for possibly larger mismodeling effects in the correction fac-tors [57 58]

bull For B particles we use the quite precise inclusive Z rarr B+X branching fraction from the Zboson summary in the PDG

bull We also use the sum of Bplusmn and B0(B0) in sec 46 of the PDG10

bull TheB0s multiplicity given in sec 46 of the PDG (0057plusmn0013) is more than twice the inclusive

BR(Z rarr B0sX)BR(Z rarr hadrons) branching fraction (00227 plusmn 00019) quoted in the Z

10Note that we have a factor 2 relative to the PDG since it appears the PDG quotes the average rather than the sum Notealso that all the average B meson multiplicities in sec 46 of the PDG are accompanied by a note ldquo(d)rdquo stating that the SMB(Z rarr bb) = 0217 was used for the normalization For completeness the reader should be aware that this is the fractionnormalized to hadronic Z decays the branching fraction relative to all Z decays is 0151 [39]

12

Charm Our Reference Our〈n〉 or BR Value Source

D+ +Dminus 0251 plusmn0047 AD0 + D0 0518 plusmn0063 ADlowast+ +Dlowastminus 0194 plusmn00057 PD+

s +Dminuss 0131 plusmn0021 PBR(Z rarr Λ+

c X) 00220 plusmn00047 ZBR(Z rarr X + cc) 00306 plusmn00047 AOJψ 00052 plusmn00004 Pχc1 00041 plusmn00011 Pψprime 00023 plusmn00004 P

Beauty Our Reference Our〈n〉 or BR Value Source

BR(Z rarr B+X) 0087 plusmn0002 ZB+ +B0 + B0 +Bminus 0330 plusmn0052 PBlowastu +Blowastd +Blowasts 0288 plusmn0026 PBR(Z rarr B0

sX) 00227 plusmn00019 ZBR(Z rarr BbaryonX) 00197 plusmn00032 ZBR(Z rarr X + bb) 000288 plusmn000061 ADSBR(Z rarr bbbbX) 000051 plusmn000019 ZΥ (times10) 00014 plusmn00007 P

Table 2 Hadronic Z decays atradics = MZ Measured rates and inclusive branching fractions of

particles containing c and b quarks as used in this work Note the branching fractions are normalizedto Z rarr hadrons and hence should be interpreted as eg BR(Z rarr B+X)BR(Z rarr hadrons)Note 2 the sum over Blowast states includes both particles and anti-particles Note 3 the Υ rate ismultiplied by a factor 10 Source labels indicate A (ALEPH) D (DELPHI) O (OPAL) P (PDGsection 46) S (SLD) Z (PDG Z Boson Summary Table)

boson summary table We find these two numbers difficult to reconcile and choose to use theinclusive BR(Z rarr B0

sX)BR(Z rarr hadrons) branching fraction as our main constraint

bull We also include the inclusive branching fractions for B-baryons (summed over baryons andantibaryons) the rate of g rarr bb splittings obtained by combining ALEPH [59] DELPHI [60]and SLD [61] measurements (including an additional 10 systematic to account for largerpossible mismodeling effects in the correction factors [57 58]) and the rate of Z rarr bbbb fromthe PDG Z boson summary table [39]

Our constraints on the heavy-quark particle rates are summarized in tab 2 Comparisons to these ratesare shown in fig 7 now without normalizing to the average charged-particle multiplicity Given thatmost of the c and b quarks come directly from Z rarr cc and Z rarr bb decays there is not a lot of roomfor tuning to these numbers apart from the relative rates of vector mesons vs pseudoscalars which iscontrolled by the parameters

Heavy MesonsStringFlavmesonCvector = 088StringFlavmesonBvector = 22

Our parameters are slightly smaller than the current default values leading to slightly smaller Dlowast

and Blowast rates as can be seen from the plots in fig 7 Note also that the increased overall amount ofstrangeness in the fragmentation leads to slightly higherDs andBs fractions in better agreement withthe data Uncertainties are however large and some exotic onium states like χc1 ψprime and Υ are notwell described by the default modeling (It is encouraging that at least the multiplicity of Jψ mesonsis well described though a substantial fraction of this likely owes to the feed-down from B decaysand hence does not depend directly on the string-fragmentation model itself)

We also note that it would be desirable to reduce the rate of g rarr bb and Z rarr bbbb events whilethe g rarr cc one appears consistent with the LEP constraints We suspect that this issue may be tiedto the fixed choice of using pperp as the renormalization scale for both gluon emissions and for g rarr qq

13

plusmnD 0D plusmnD plusmns

D X+

cΛ

ccrarrg ψJ c1χ

3685

ψ

X)

rarrlt

ngt o

r B

R(Z

-410

-310

-210

-110

1

10Charm Rates

Pythia 8185Data from HEPDATAPDG

LEP

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn15

00plusmn18

00plusmn17

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

plusmnD 0Dplusmn

D plusmnsD X+

cΛ ccrarrg ψJ c1χ

3685ψ

The

ory

Dat

a

0

05

1

15

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

X)

rarrlt

ngt o

r B

R(Z

-510

-410

-310

-210

-110

1

10Beauty Rates

Pythia 8185Data from HEPDATAPDG

LEP+SLD

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn17

00plusmn23

00plusmn23

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

The

ory

Dat

a0

05

1

15

Figure 7 Hadronic Z decays atradics = 912 GeV Rates and inclusive Z rarr X branching fractions

(normalized to Z rarr hadrons) of particles containing c and b quarks

splittings in the current version of PYTHIA A more natural choice for g rarr qq could be microR prop mqqas used eg in the VINCIA shower model [29]

We now turn to the dynamics of heavy-quark fragmentation focusing mainly on the b quarkFor heavy quarks the Lund fragmentation function is modified due to the (massive) endpoints not

moving along straight lightcones as the string pulls on them they slow down resulting in the stringtracing out a smaller space-time area than it would for massless quarks This modifies the implicationsof the string area law in a manner captured by the so-called Bowler modification of the fragmentationfunction [62]

fmassive(zmQ) prop f(z)

zbrQm2Q

(6)

with mQ the heavy-quark mass b the same universal parameter that appears in the massless fragmen-tation function eq (3) and rQ a tuning parameter which is unity in the original derivation of Bowlerbut can be assigned values different from unity to reduce (rQ rarr 0) or emphasize (rQ gt 1) the effectSince rQ multiplies the heavy-quark mass (squared) it can also be viewed as an effective rescalingof the mass value The net result is a suppression of the region z rarr 1 hence a relative softening ofthe fragmentation spectrum for heavy flavours (relative since the presence of m2

perp in the exponent ofeq (3) still implies an overall harder fragmentation for higher hadron masses)

We emphasize that this is the only fragmentation function that is self-consistent within the string-fragmentation model [33 62] Although a few alternative forms of the fragmentation functions formassive quarks are available in the code we therefore here work only with the Bowler type As forthe massless function the proportionality sign in eq (6) indicates that the function is normalized tounity

In PYTHIA separate rQ parameters are provided for c and b quarks We consider the one for bquarks first Its default value is rb = 067 but this appears to give too hard b fragmentation spectrawhen compared to LEP and SLD data see below For the Monash tune we instead use

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (DELPHI)weak

Bx

Pythia 8181Data from EurPhysJ C71 (2011) 1557

DELPHI PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn16

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (SLD)weak

Bx

Pythia 8181HepData5111d1-x1-y1

SLDPY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn07

00plusmn15

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a06

08

1

12

14

Figure 8 Hadronic Z decays atradics = 912 GeV Momentum (xB) spectra of weakly decaying B

hadrons compared to data from DELPHI [63] (left) and SLD [64] (right)

StringZrFactB = 0855

which produces softer B spectra and simultaneously agrees better with the theoretically preferredvalue (rb = 1)

A comparison to the scaled-momentum spectra (xB = 2|pB|Ecm) of weakly decayingB hadronsfrom both DELPHI [63] and SLD [64] is given in fig 8 (due to small differences between the twomeasured results we choose to show both) The dampening of the hardest part of the spectrum causedby the increase in the rb parameter is visible in the right-most two bins of the distributions and in thesmaller χ2

5 values for the Monash tune The effects of the modification can be further emphasizedby an analysis of the moments of the distribution in which the higher moments are increasinglydominated by the region xB rarr 1 A comparison to a combined LEP analysis of the moments of thexB distribution [63] is given in fig 9 further emphasizing that the high-xB part of the distribution isnow under better control

The reason we have not increased the rb parameter further is that it comes at a price If theB hadrons are taking less energy then there is more energy left over to produce other particlesand the generated multiplicity distribution in b events already exhibits a slightly high tail towardslarge multiplicities Nonetheless since the revised light-flavour fragmentation parameters produce anoverall narrower fragmentation function the end result is still a slight improvement in the multiplicitydistribution also for b events This is illustrated together with the inclusive momentum distributionfor b-tagged events in fig 10 compared to measurements by L3 [26] Interestingly the multiplicitydistribution still appears to be too wide but within the constraints of the present study we were unableto obtain further improvements As a point of speculation we note that the distribution of the numberof partons before hadronization is also quite wide in PYTHIA and this may be playing a role ineffectively setting a lower limit on the width that can be achieved for the hadron-level distribution

Comparisons to L3 event shapes in b-tagged events are collected in appendix B1 (the left columnof plots contains light-flavour tagged event shapes the right column b-tagged ones) In particular the

15

0 10 20 30 40

Mom

ent

0

02

04

06

08 (moments)weakBx

Pythia 8181Data from Eur Phys J C71 (2011) 1557

LEP (combined)PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn10

00plusmn103

00plusmn129

V I

N C

I A

R O

O T

N0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

Figure 9 Hadronic Z decays atradics = 912 GeV Moments of the B fragmentation function com-

pared to a combined analysis of LEP+SLD data by DELPHI [63]

0 20 40

)ch

Pro

babi

lity(

n

-610

-510

-410

-310

-210

-110

1

10

210 Charged Multiplicity (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

06plusmn45

08plusmn64

13plusmn110

V I

N C

I A

R O

O T

(b)chn0 20 40

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

ch d

nch

1n

-510

-410

-310

-210

-110

1

10

210 Charged Momentum Fraction (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn08

00plusmn06 V

I N

C I

A R

O O

T

)| (b)p

|Ln(x0 2 4 6 8

The

ory

Dat

a

06

08

1

12

14

Figure 10 HadronicZ decays atradics = 912 GeV Charged-hadron multiplicity (left) and momentum-

fraction (right) spectra in b-tagged events

16

0 02 04 06 08 1

dx

Dgt

dn

D1

ltn

0

05

1

15

2

25gt01)

E) (x

plusmnx(D

Pythia 8183Data from EurPhysJ C16 (2000) 597

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn14

02plusmn28

02plusmn32

V I

N C

I A

R O

O T

Ex0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

EX02 04 06 08 1

E)

dX

dN

(DZ

had

1N

0

0002

0004

0006

0008

001

0012

0014

0016

ALEPHHerwig++Sherpa

91 GeV ee Z (hadronic)

mcp

lots

cer

nch

41

M e

vent

sge

Riv

et 1

82

Herwig++ 261a Sherpa 141

ALEPH_1999_S4193598

spectrum (particle-level)+-D

02 04 06 08 105

1

15Ratio to ALEPH

Figure 11 The inclusive Dlowast spectrum in hadronic Z decays [55] Left Monash 2013 tune com-pared with default PYTHIA 8 and the Fischer tune Right comparison with HERWIG (dashed) andSHERPA (dotted) from MCPLOTS [25] Note that the plot in the left-hand pane is normalized tounity while the one in the right-hand pane is normalized to the number of hadronic Z decays

Monash tune gives a significant improvement in the soft region of the jet-broadening parameters inb-tagged events while no significant changes are observed for the other event shapes These smallimprovements are presumably a direct consequence of the softening of the b fragmentation functionit is now less likely to find an isolated ultra-hard B hadron

We round off the discussion of heavy-quark fragmentation by noting that a similarly comprehen-sive study of charm-quark fragmentation would be desirable However charm-quark tagged multi-plicity and event-shape data is not available to our knowledge and most of the D meson spectra onHEPDATA concern only specific decay chains (hence depend on the decay modeling) andor are lim-ited to restricted fiducial regions (limiting their generality) Experimentally the cleanest measurementis obtained from Dlowast decays and an inclusive momentum spectrum for Dlowast mesons has been measuredby ALEPH [55] From this distribution shown in fig 11 we determine a value for rc of

StringZrFactC = 132

We note that the low-x part of the Dlowast spectrum originates from g rarr cc shower splittings whilethe high-x tail represents prompt Dlowast production from leading charm in Z rarr cc (see [55] for a nicefigure illustrating this) The intermediate range contains a large component of feed-down from brarr cdecays hence this distribution is also indirectly sensitive to the b-quark sector The previous defaulttune had a harder spectrum for both b- and c-fragmentation leading to an overestimate of the high-xpart of the Dlowast distribution The undershooting at low xDlowast values which remains unchanged in theMonash tune most likely indicates an underproduction of g rarr cc branchings in the shower We notethat such an underproduction may also be reflected in the LHC data on Dlowast production see eg [65]We return to this issue in the discussion of identified particles at LHC section 35

17

with Q2 = p2 minusm20 the offshellness of the emitting parton (with on-shell mass m0) and z the energy

fraction appearing in the DGLAP splitting kernels P (z) (To estimate the shower uncertainties asso-ciated with this choice of renormalization scale we recommend using ln(micro2

R)plusmn ln(2) correspondingto a factor

radic2 variation of microR)

Theoretically a set of formally subleading terms can be resummed by using 2-loop running of αsin the so-called MC (aka CMW) scheme [28] However in a leading-order code like PYTHIA thisproduces too little hard radiation in practice due to missing NLO ldquoKrdquo factors for hard emissions (seeeg the study of NLO corrections in [29]) Empirically we find that a better overall description isachieved with one-loop running which for a fixed value of ΛQCD can effectively mimic the effect ofmissing K factors via its relatively slower pace of running leading to values of αs(MZ) in the range0135minus 0140 consistent with other LO extractions of the same quantity (See [29] for an equivalentextraction at NLO)

For this study we did not find any significant advantage in reinterpreting this value in the CMWscheme3 and hence merely settled on an effective αs(MZ) = 01365 (to be compared with the currentdefault value of 01383)

For the infrared shower cutoff we choose a value close to4 ΛQCD in order to have a smoothtransition between low-pperp perturbative emissions and non-perturbative string breaks the latter ofwhich involve pperp kicks of order ΛQCD (In principle the perturbative evolution could be continuedto even lower scales if combined with a non-perturbative regularization of αs but such low cutoffvalues could risk generating problems at the fragmentation stage since the technical implementationof the string model becomes complicated if there are too many small gluon ldquokinksrdquo spaced closelyalong the strings) The set of relevant parameters in the code is

FSR Strong CouplingTimeShoweralphaSvalue = 01365TimeShoweralphaSorder = 1TimeShoweralphaSuseCMW = off

FSR IR cutoffTimeShowerpTmin = 050 for QCD radiationTimeShowerpTminChgQ = 050 for QED radiation off quarks

FSR Spin CorrelationsTimeShowerphiPolAsym = on approximate FSR polarization effects

The resulting distribution of the Thrust event-shape variable was shown in fig 1 comparing theMonash 2013 tune to the current default tune and to an alternative contemporary tune by N Fi-scher [30] To avoid clutter the other event-shape variables (C D BW and BT ) are collected inappendix B1 There are no significant changes to any of the light-flavour tagged event shapes in ourtune as compared to the current default one

21 Light-Flavour Fragmentation

Given a set of post-shower partons resolved at a scale ofQhad sim 1 GeV the non-perturbative stage ofthe fragmentation modeling now takes over to convert the partonic state into a set of on-shell hadrons

3One slight disadvantage is that the CMW scheme produces somewhat larger ΛQCD values Since the current formu-lation of the shower algorithm does not include a non-perturbative regularization of αs a higher ΛQCD value necessitatesa larger IR cutoff in the shower which can leave an undesirable gap between the transverse kicks generated by showeremissions and those generated by non-perturbative string splittings

4The IR shower cutoff must still remain somewhat above the Landau pole of αs a lower cutoff scale would activate ahardcoded protection mechanism implemented in the PYTHIA shower forcing it to be higher than ΛQCD

4

In the leading-colour approximation each perturbative dipole is dual to a non-perturbative stringpiece [31] Quarks thus become string endpoints while gluons become transverse kinks connectingtwo string pieces [32] The Lund string fragmentation model [33] describes the fragmentation of suchstring systems into on-shell hadrons

Since the shower has already resolved all the (perturbative) physics down to a transverse-momentumscale of pTmin = 05 GeV (for the Monash 2013 tune) we find it reasonable that the pperp kicks in-volved in string breaking should effectively average over dynamics in roughly the range 250 MeV =radicκπ lt σperp lt pTmin with the lower bound given by Fermi motion (with κ the string tension

see [34]) Further since we here choose pTmin to be only slightly greater than ΛQCD the size of thenon-perturbative corrections is naturally limited to kickscorrections appropriate for non-perturbativedynamics (in contrast eg to the cluster model [35] which can generate substantially larger kicks oforder the largest allowed cluster mass which can be several GeV [30]) For the Monash 2013 tunewe have settled on a value of σperp = 0335 GeV with a small (1) tail of breaks involving higher pperpvalues carried over from the default settings

StringPTsigma = 0335StringPTenhancedFraction = 001StringPTenhancedWidth = 20

This value is obtained essentially from the first two bins of the Thrust distribution fig 1 and from thebins near zero of the other event shapes see appendix B1 Note that the σperp value is interpreted as thewidth of a Gaussian distribution in the total pperp (measured transversely to the local string directionwhich may differ from the global event axis) such that each of the px and py components have aslightly smaller average value σ2

xy = 12σ

2perp = (0237 GeV)2 Also note that each non-leading hadron

will receive two pperp kicks one from each of the breaks surrounding it hencelangp2perphad

rang= 2σ2

perp =(0474 GeV)2

For massless quarks the longitudinal component of the energy carried by a hadron formed in thestring-breaking process stringrarr hadron+stringprime is governed by the Lund symmetric fragmentationfunction

f(z) prop z(aiminusaj)(1minus z)ajz

exp

(minusbm2

perpz

) (3)

where z is the energy carried by the newly formed (ij) hadron expressed as a fraction of the (light-cone) energy of the quark (or antiquark) endpoint i of the fragmenting string (The remaining energyfraction (1 minus z) goes to the new stringprime system from which another hadron can be split off in thesame manner etc until all the energy is used up) The transverse mass of the produced (ij) hadronis defined by m2

perp = m2had + p2

perphad hence heavier hadrons have harder spectra The proportionalitysign in eq (3) indicates that the function is to be normalized to unity

The a and b parameters govern the shape of the fragmentation function and must be constrainedby fits to data Eq (3) expresses the most general form of the fragmentation function for which the aparameters of the original string-endpoint quark ai and that of the (anti-)quark produced in the stringbreak aj can in principle be different while the b parameter is universal Within the Lund model thea value is normally also taken to be universal the same for all quarks with the only freedom beingthat a larger a parameter can be assigned to diquarks [36] from which baryons are formed and hencemeson and baryon spectra can be decoupled somewhat (See StringZaExtraDiquark below)

Roughly speaking large a parameters suppress the hard region z rarr 1 while a large b parametersuppresses the soft region z rarr 0 By adjusting them independently both the average hardness andthe width of the resulting fragmentation spectra can be modified For example increasing both a andb yields a narrower distribution while changing them in opposite directions moves the average An

5

The a parameter The b parameter

a = 09 a = 01 b = 05 b = 20

02 04 06 08 10

05

10

15

02 04 06 08 10

05

10

15

20

b = 1 GeVminus2 mperp = 1 GeV a = 05 mperp = 1 GeV

Figure 2 Illustration of the Lund symmetric fragmentation function (normalized to unity) for ai =aj equiv a Left variation of the a parameter from 01 (blue) to 09 (red) with fixed b Right variationof the b parameter from 05 (red) to 2 (blue) GeVminus2 with fixed a

illustration of the effect of varying the a and b parameters for ai = aj equiv a is given in fig 2 see alsothe lecture notes in [37] Note that the σperp parameter also affects the hardness with larger σperp valuesgenerating harder hadrons the difference being that the σperp parameter acts mainly in the directiontransverse to the string5 (and is an absolute scale expressed in GeV) while the a and b parameters actlongitudinally (with z a relative scale expressed as a fraction of the endpointrsquos energy)

In the context of this work we included the possibility of letting the a parameter for strangequarks be slightly different from that of u and d quarks but did not find any significant advantagesThe relevant parameters in the code we settled on for the Monash tune are

StringZaLund = 068StringZbLund = 098StringZaExtraDiquark = 097StringZaExtraSquark = 000

The average hardness of the produced hadrons is tightly (anti-)correlated with the average multi-plicity via momentum conservation if each hadron takes a lot of energy then fewer hadrons must bemade and vice versa Thus the σperp value and the a and b parameters of the fragmentation functioncan be well constrained by simultaneously considering both momentum and multiplicity spectra Inorder to be as universal as possible one normally uses the inclusive charged-particle spectra for thispurpose These are shown in fig 3 (Note the Fischer tune only included the average particle mul-tiplicity as a constraint so the full nch distribution is not expected to be reproduced perfectly [30])The momentum fraction in the right-hand plot is defined by

xp =2|p|Ecm

(4)

As above the experimental data come from a measurement by L3 [26] which only includes the fourlightest flavours thus excluding b quarks (which will be treated separately below)

Both of the earlier tunes exhibit a somewhat too broad multiplicity distribution in comparisonwith the L3 data The relatively large Lund a and b values used for the Monash tune combined with

5Explicitly σperp expresses the pperp broadening transverse to the string direction but implicitly its size also enters inthe logitudinal fragmentation function via the m2

perp term in eq (3) causing higher-pperp hadrons to have relatively harderlongitudinal spectra as well

6

0 20 40 60

)ch

Pro

babi

lity(

n

-610

-510

-410

-310

-210

-110

1

10

210 Charged Multiplicity (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn05

01plusmn07

02plusmn21

V I

N C

I A

R O

O T

chn0 20 40 60

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

chgt

dn

ch1

ltn

-310

-210

-110

1

10Charged Momentum Fraction (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn09

00plusmn05

00plusmn05

V I

N C

I A

R O

O T

)|p

|Ln(x0 2 4 6 8

The

ory

Dat

a06

08

1

12

14

Figure 3 Hadronic Z decays atradics = 912 GeV Charged-particle multiplicity (left) and momentum-

fraction (right) spectra

its large σperp value produce a narrower nCh spectrum with in particular a smaller tail towards largemultiplicities All the tunes produce a sensible momentum spectrum The dip around |ln(x)| sim 55corresponds to the extreme soft-pion tail with momenta at or below ΛQCD We did not find it possibleto remove it by retuning since a smaller b parameter would generate significantly too high particlemultiplicities and a smaller σperp would lead to conflict with the event-shape distributions

A zoom on the high-momentum tail is provided by the left-hand plot in fig 4 which shows acomparison on a linear momentum scale to a measurement by ALEPH [38] (now including Z rarr bbevents as well as light-flavour ones) All the tunes exhibit a mild overshooting of the data in the region05 lt xp lt 08 corresponding to 015 lt | ln(x)| lt 07 in which no similar excess was present inthe L3 comparison We therefore do not regard this as a significant issue6 but note that the excess issomewhat milder in the Fischer and Monash tunes

Further information to elucidate the structure of the momentum distribution is provided by theplot in the right-hand pane of fig 4 which uses the same |ln(x)| axis as the right-hand plot in fig 3and shows the relative particle composition in the Monash tune for each histogram bin (The categoryldquoOtherrdquo contains electrons and muons from weak decays) An interesting observation is that therelatively harder spectrum of Kaons implies that for the highest-momentum bins the charged tracksare made up of an almost exactly equal mixture of Kaons and pions despite Kaons on average onlymaking up about 10 of the charged multiplicity

6One might worry whether the effect could be due solely to the Z rarr bb events which are only present in the ALEPHmeasurement and if so whether this could indicate a significant mismodeling of the momentum distribution in b eventsHowever as we show below in the section on b fragmentation the charged-particle momentum distribution in b-taggedevents shows no excess in that region (in fact it shows an undershooting)

7

0 02 04 06 08 1

pd

xch

gt d

nch

1lt

n

-410

-310

-210

-110

1

10Charged Momentum Fraction

Pythia 8183Data from Barate et al Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn14

01plusmn08

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

IDgt

dn

ch1

ltn

0

02

04

06

08

1

12 Particle Composition vs Lnx (udsc)

Pythia 8183

plusmnπplusmnKplusmnp

Other

V I

N C

I A

R O

O T

)|p

|Ln(x0 2 4 6 8

Rat

io06

08

1

12

14

Figure 4 Hadronic Z decays atradics = 912 GeV Charged-particle momentum fraction xp on a linear

scale (left) and relative particle composition (right) for the log-scale distribution shown in fig 3

22 Identified Particles

Continuing on the topic of identified particles we note that the extraction of the a and b parametersfrom the inclusive charged-particle distributions is made slightly more complicated by the fact thatnot all observed particles are ldquoprimaryrdquo (originating directly from string breaks) many lower-massparticles are ldquosecondariesrdquo produced by prompt decays of more massive states (eg ρrarr ππ) whoserelative rates and decay kinematics therefore influence the spectra In the e+eminus measurements weinclude here particles with cτ lt 100 mm were treated as unstable hence leading to secondaries (Forcompleteness we note that the equivalent standard cut at the LHC is normally 10 mm)

The particle composition in PYTHIA 8 was already tuned to a set of reference values provided bythe PDG [39] and the default parameters do reasonably well certainly for the most copiously pro-duced sources of secondaries Nonetheless we have here reoptimized the flavour-selection parametersof the string-fragmentation model using a slightly different set of reference data combining the PDGtables with information provided directly by the LEP experiments via HEPDATA [1] Based on thelevel of agreement or disagreement between different measurements of the same particles we havemade our own judgement as to the level of uncertainty for a few of the particles as follows (Unlessotherwise stated we use the value from the PDG Particles and antiparticles are implicitly summedover and secondaries from particles with cτ lt 100 mm are included)

bull The various LEP and SLD measurements of the φ meson rate on HEPDATA are barely com-patible Eg OPAL [40] reports 〈nφ〉 = 0091 plusmn 0002 plusmn 0003 while ALEPH [38] quotes〈nφ〉 = 0122 plusmn 0004 plusmn 0008 a difference of 30 with uncertainties supposedly less than10 DELPHI [41] and SLD [42] fall in between The PDG value is 〈nφ〉 = 00963 plusmn 0003ie with a combined uncertainty of just 3 We choose to inflate the systematic uncertaintiesand arrive at 〈nφ〉 = 0101plusmn 0007

8

bull For Λ production we use the most precise of the LEP measurements by OPAL7 [43] 〈nΛ〉 =0374plusmn 0002plusmn 0010 about 5 lower than the corresponding PDG value

bull For Σplusmn baryons we use a combination of the two most recent LEP measurements by L3 [44]for Σ+ + Σ

minus and by DELPHI [45] for Σminus + Σ+ for an estimated 〈nΣplusmn〉 = 0195 plusmn 0018

which is roughly 10 higher than the PDG value

bull For Σ0 baryons we use the most recent measurement by L3 [44] 〈nΣ0〉 = 0095 plusmn 0015 plusmn0013 this is about 20 larger than the PDG value The L3 paper comments on their relativelyhigh value by noting that L3 had the best coverage for low-momentum baryons hence smallermodel-dependent correction factors

bull For ∆++ baryons there are only two measurements in HEPDATA [4647] which are mutuallydiscrepant by about 2σ The DELPHI measurement is nominally the most precise but OPALgives a much more serious discussion of systematic uncertainties We choose to increase theestimated extrapolation errors of the DELPHI measurement by 50 and obtain a weighted av-erage8 of 〈n∆++〉 = 009plusmn0017 5 larger than the PDG value with a 20 larger uncertainty

bull For Σlowast the three measurements on HEPDATA [38 43 48] are likewise discrepant by 2σ minus 3σWe inflate the systematic uncertainties and arrive at 〈nΣlowastplusmn〉 = 0050 plusmn 0006 which is again5 higher than the PDG value with twice as much uncertainty

bull The measurements for Ξplusmn are in good agreement [38 43 48] with a weighted average of〈nΞplusmn〉 = 00266plusmn 00012 slightly larger than the PDG value

bull For Ξlowast0 however the DELPHI measurement [48] gives a far lower number than the OPAL [43]and ALEPH [38] ones and the weighted average differs by more than 10 from the PDGvalue despite the latter claiming an uncertainty smaller than 10 Our weighted average is〈nΞlowast0〉 = 00059plusmn 00012

bull Finally for the Ω baryon the DELPHI [49] and OPAL [43] measurements are in agreementand we use the PDG value 〈nΩ〉 = 00016plusmn 00003

We summarize the constraints on the light-meson and baryon rates used here in tab 1 Note that weexpress them as percentages of the average charged multiplicity

〈nCh〉 = 207 (5)

obtained as a weighted average over MARK-II [50] ALEPH [38] DELPHI [51] OPAL [52] andL3 [53] measurements

The light-flavour-selection parameters for the Monash tune are (see appendix A for a comparisonof these values to the current default ones)

Light-Meson SectorStringFlavProbStoUD = 0217StringFlavmesonUDvector = 05StringFlavmesonSvector = 055

7We note that HEPDATA incorrectly gives the systematic error as 0002 while the value in the OPAL paper is 0010 [43]This has been communicated to the HEPDATA maintainers

8Even with the inflated error the uncertainty on the DELPHI measurement is still less than a third that of the OPAL oneDELPHI therefore still dominates the average

9

Mesons Our Reference Our〈n〉 〈nCh〉 Value (in ) Source

π+ + πminus 822 plusmn09 Pπ0 455 plusmn15 PK+ +Kminus 108 plusmn03 Pη 506 plusmn038 Pηprime 073 plusmn009 Pρ+ + ρminus 116 plusmn21 Pρ0 595 plusmn047 PKlowast+ +Klowastminus 345 plusmn028 Pω 490 plusmn031 Pφ 049 plusmn0035 ADOS

Baryons Our Reference Our〈n〉 〈nCh〉 Value (in ) Source

p+ p 507 plusmn016 PΛ + Λ 181 plusmn032 OΣ+ + Σminus + Σ+ + Σminus 0942 plusmn0087 DLΣ0 + Σ0 0459 plusmn0096 L∆++ + ∆minusminus 0434 plusmn0082 DOΣlowast+ + Σlowastminus + Σlowast+ + Σlowastminus 0242 plusmn0029 ADOΞ+ + Ξminus 0125 plusmn00050 ADOΞlowast0 + Ξlowast0 00285 plusmn00058 ADOΩminus + Ω+ 00077 plusmn00015 P

Table 1 Hadronic Z decays atradics = 912 GeV Measured rates of light-flavour mesons and baryons

expressed as percentages of the average charged-particle multiplicity as used in this work Multiplythe numbers by 207100 to translate the percentages to corresponding production rates Source labelsindicate A (ALEPH) D (DELPHI) L (L3) O (OPAL) S (SLD) P (PDG)

StringFlavetaSup = 060StringFlavetaPrimeSup = 012

Baryon SectorStringFlavprobQQtoQ = 0081StringFlavprobSQtoQQ = 0915StringFlavprobQQ1toQQ0 = 00275StringFlavsuppressLeadingB = offStringFlavpopcornSpair = 09StringFlavpopcornSmeson = 05

Since strange-particle and baryon spectra at the LHC exhibit interesting differences with respectto existing models (see below) we paid particular attention to first obtaining a good description ofthese sectors in e+eminus collisions Specifically we have increased the overall amount of strangenessby about 10 while decreasing the rate of vector mesons by a similar amount9 (these two effectslargely cancel for Klowast) This improves the total Kplusmn ρ0 ω Λ Ξlowast and Ω yields on our combined LEPestimates discussed above The price is that we now overshoot the measured rate of Ξplusmn baryons by10 The resulting identified-meson and -baryon rates expressed as fractions of the average charged-particle multiplicity are plotted in fig 5 Note that the last four bins of the meson plot and the thirdand fourth bins of the baryon plot are not 〈n〉 〈nCh〉 fractions but rather the KlowastK φKlowast φKφπ Λp and ΛK ratios respectively Note also that section 4 on energy scaling below includes acomparison to the average Kaon and Lambda rates as a function of ee CM energy (fig 25)

To provide further information on identified particles we include a limited comparison to momen-tum spectra of Kplusmn p Λ and Ξplusmn which are the states of most immediate interest in the context ofsimilar comparisons now being made at LHC The spectra of Kplusmn mesons and Λ baryons are shownin fig 6 while the pplusmn and Ξplusmn spectra are relegated to appendix B2 The modified parameters of theMonash tune have virtually no effect on the Kaon distribution which still exhibits too many very softKaons (with ln(x) lt minus4 corresponding to x lt 0018 so momentum scales below sim 1 GeV) while

9For reference the current default value of ProbStoUD is 019 while ours is 0217 The increased value also improvesthe agreement with the Ds and Bs rates see section 23 The default values of mesonUDvector and mesonSvectorare 062 and 0725 respectively while ours are 05 and 055

10

plusmnπ 0π plusmnK η η plusmnρ 0ρ plusmnK ω φKK-

RKφ

RK-φ

R-πφ

R

gtch

ltnltngt

-310

-210

-110

1

10Meson Fractions

Pythia 8183Data from PDGHEPDATA

LEP + SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn06

00plusmn12

00plusmn12

V I

N C

I A

R O

O T

plusmnπ 0π plusmnK η η plusmnρ 0ρ plusmnK ω φKK-

RKφ

RK-φ

R-πφ

R

The

ory

Dat

a

06

08

1

12

14

p ΛpΛ

RKΛ

R plusmnΣ 0Σ ++∆ Σ plusmnΞ 0Ξ Ω

gtch

ltnltngt

-410

-310

-210

-110

1Baryon Fractions

Pythia 8183Data from PDGHEPDATA

LEP PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn11

00plusmn22

00plusmn22

V I

N C

I A

R O

O T

p ΛpΛ

RKΛ

R plusmnΣ 0Σ ++∆ Σ plusmnΞ 0Ξ Ω

The

ory

Dat

a

06

08

1

12

14

Figure 5 Hadronic Z decays atradics = 912 GeV Identified-meson and -baryon rates expressed as

fractions of the average charged-particle multiplicity

-4 -2 0

dln

(x)

Kgt

dn

K1

ltn

-310

-210

-110

1

10

) (Combined)plusmnx(K

Pythia 8183Data from ZPC66(1995)355 ZPC63(1994)181 EPJC5(1998)585

LEP (A+D+O)PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn16

00plusmn14

01plusmn19

V I

N C

I A

R O

O T

)p

ln(x-4 -2 0

The

ory

Dat

a

06

08

1

12

14

0 1 2 3 4 5

ξd

Λgt

dn

Λ1

ltn

0

02

04

06)]|0Λ|Ln[x(

Pythia 8183Data from EPJ C16 (2000) 613

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn08

01plusmn15

01plusmn12

V I

N C

I A

R O

O T

pξ

0 1 2 3 4 5

The

ory

Dat

a

06

08

1

12

14

Figure 6 Hadronic Z decays atradics = 912 GeV Kplusmn and Λ momentum-fraction spectra

11

the significant increase in the value of aExtraDiquark from 05 (Default) to 097 (Monash cf sec-tion 21) produces a desirable suppression of very hard Λ baryons The corresponding change in themeasured parts of the p and Ξplusmn spectra (cf appendix B2) are small compared with the experimentaluncertainties

It is interesting however to note that all of these spectra indicate or are at least consistent with amodelling excess of soft identified-particle production below ln(x) sim minus45 corresponding to absolutemomentum scales around 500 MeV while we recall that the inclusive ln(x) spectrum above showedan underproduction around ln(x) sim minus55 Within the constraints of the current theory model wehave not managed to find a way to mitigate these features while remaining consistent with the rest ofthe data Nonetheless it should be mentioned that these observations could have relevance also in thecontext of understanding identified-particle spectra at LHC a possibility which to our knowledge hasso far been ignored

23 Heavy-Quark Fragmentation

Similarly to above we first discuss the inclusive rates of hadrons containing heavy quarks before wediscuss their spectra Unfortunately there are also here substantial disagreements between differentpieces of information We have made the following choices

bull ForD mesons the average Dplusmn rate given in sec 46 of the PDG (0175) is equal to the inclusivebranching fraction for Z rarr DplusmnX given in the Z boson summary table in the same Review(after normalizing the latter to the hadronic Z fraction of 6991 [39]) However the formerought to be substantially larger given that some Z rarr cc events will contain two Dplusmn mesons(counting once in the Z rarr DplusmnX branching fraction but twice in the average Dplusmn multiplicity)We therefore here use a measurement by ALEPH [54] to fix the Dplusmn and D0 rates resulting ina reference value for the average Dplusmn multiplicity almost twice as large as that given by sec 46in the PDG

bull For Λ+c the average multiplicity given in sec 46 of the PDG is twice as large as that indicated

by the branching fraction BR(Z rarr Λ+c X) in the Z boson summary table in the same Review

We here use the branching from the Z boson summary table as our constraint on the Λ+c rate

normalized to the total branching fraction BR(Z rarr hadrons)

bull We also include the average rate of g rarr cc splittings obtained by combining an ALEPH [55]and an OPAL measurement [56] but with an additional 10 systematic uncertainty added toboth measurements to account for possibly larger mismodeling effects in the correction fac-tors [57 58]

bull For B particles we use the quite precise inclusive Z rarr B+X branching fraction from the Zboson summary in the PDG

bull We also use the sum of Bplusmn and B0(B0) in sec 46 of the PDG10

bull TheB0s multiplicity given in sec 46 of the PDG (0057plusmn0013) is more than twice the inclusive

BR(Z rarr B0sX)BR(Z rarr hadrons) branching fraction (00227 plusmn 00019) quoted in the Z

10Note that we have a factor 2 relative to the PDG since it appears the PDG quotes the average rather than the sum Notealso that all the average B meson multiplicities in sec 46 of the PDG are accompanied by a note ldquo(d)rdquo stating that the SMB(Z rarr bb) = 0217 was used for the normalization For completeness the reader should be aware that this is the fractionnormalized to hadronic Z decays the branching fraction relative to all Z decays is 0151 [39]

12

Charm Our Reference Our〈n〉 or BR Value Source

D+ +Dminus 0251 plusmn0047 AD0 + D0 0518 plusmn0063 ADlowast+ +Dlowastminus 0194 plusmn00057 PD+

s +Dminuss 0131 plusmn0021 PBR(Z rarr Λ+

c X) 00220 plusmn00047 ZBR(Z rarr X + cc) 00306 plusmn00047 AOJψ 00052 plusmn00004 Pχc1 00041 plusmn00011 Pψprime 00023 plusmn00004 P

Beauty Our Reference Our〈n〉 or BR Value Source

BR(Z rarr B+X) 0087 plusmn0002 ZB+ +B0 + B0 +Bminus 0330 plusmn0052 PBlowastu +Blowastd +Blowasts 0288 plusmn0026 PBR(Z rarr B0

sX) 00227 plusmn00019 ZBR(Z rarr BbaryonX) 00197 plusmn00032 ZBR(Z rarr X + bb) 000288 plusmn000061 ADSBR(Z rarr bbbbX) 000051 plusmn000019 ZΥ (times10) 00014 plusmn00007 P

Table 2 Hadronic Z decays atradics = MZ Measured rates and inclusive branching fractions of

particles containing c and b quarks as used in this work Note the branching fractions are normalizedto Z rarr hadrons and hence should be interpreted as eg BR(Z rarr B+X)BR(Z rarr hadrons)Note 2 the sum over Blowast states includes both particles and anti-particles Note 3 the Υ rate ismultiplied by a factor 10 Source labels indicate A (ALEPH) D (DELPHI) O (OPAL) P (PDGsection 46) S (SLD) Z (PDG Z Boson Summary Table)

boson summary table We find these two numbers difficult to reconcile and choose to use theinclusive BR(Z rarr B0

sX)BR(Z rarr hadrons) branching fraction as our main constraint

bull We also include the inclusive branching fractions for B-baryons (summed over baryons andantibaryons) the rate of g rarr bb splittings obtained by combining ALEPH [59] DELPHI [60]and SLD [61] measurements (including an additional 10 systematic to account for largerpossible mismodeling effects in the correction factors [57 58]) and the rate of Z rarr bbbb fromthe PDG Z boson summary table [39]

Our constraints on the heavy-quark particle rates are summarized in tab 2 Comparisons to these ratesare shown in fig 7 now without normalizing to the average charged-particle multiplicity Given thatmost of the c and b quarks come directly from Z rarr cc and Z rarr bb decays there is not a lot of roomfor tuning to these numbers apart from the relative rates of vector mesons vs pseudoscalars which iscontrolled by the parameters

Heavy MesonsStringFlavmesonCvector = 088StringFlavmesonBvector = 22

Our parameters are slightly smaller than the current default values leading to slightly smaller Dlowast

and Blowast rates as can be seen from the plots in fig 7 Note also that the increased overall amount ofstrangeness in the fragmentation leads to slightly higherDs andBs fractions in better agreement withthe data Uncertainties are however large and some exotic onium states like χc1 ψprime and Υ are notwell described by the default modeling (It is encouraging that at least the multiplicity of Jψ mesonsis well described though a substantial fraction of this likely owes to the feed-down from B decaysand hence does not depend directly on the string-fragmentation model itself)

We also note that it would be desirable to reduce the rate of g rarr bb and Z rarr bbbb events whilethe g rarr cc one appears consistent with the LEP constraints We suspect that this issue may be tiedto the fixed choice of using pperp as the renormalization scale for both gluon emissions and for g rarr qq

13

plusmnD 0D plusmnD plusmns

D X+

cΛ

ccrarrg ψJ c1χ

3685

ψ

X)

rarrlt

ngt o

r B

R(Z

-410

-310

-210

-110

1

10Charm Rates

Pythia 8185Data from HEPDATAPDG

LEP

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn15

00plusmn18

00plusmn17

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

plusmnD 0Dplusmn

D plusmnsD X+

cΛ ccrarrg ψJ c1χ

3685ψ

The

ory

Dat

a

0

05

1

15

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

X)

rarrlt

ngt o

r B

R(Z

-510

-410

-310

-210

-110

1

10Beauty Rates

Pythia 8185Data from HEPDATAPDG

LEP+SLD

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn17

00plusmn23

00plusmn23

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

The

ory

Dat

a0

05

1

15

Figure 7 Hadronic Z decays atradics = 912 GeV Rates and inclusive Z rarr X branching fractions

(normalized to Z rarr hadrons) of particles containing c and b quarks

splittings in the current version of PYTHIA A more natural choice for g rarr qq could be microR prop mqqas used eg in the VINCIA shower model [29]

We now turn to the dynamics of heavy-quark fragmentation focusing mainly on the b quarkFor heavy quarks the Lund fragmentation function is modified due to the (massive) endpoints not

moving along straight lightcones as the string pulls on them they slow down resulting in the stringtracing out a smaller space-time area than it would for massless quarks This modifies the implicationsof the string area law in a manner captured by the so-called Bowler modification of the fragmentationfunction [62]

fmassive(zmQ) prop f(z)

zbrQm2Q

(6)

with mQ the heavy-quark mass b the same universal parameter that appears in the massless fragmen-tation function eq (3) and rQ a tuning parameter which is unity in the original derivation of Bowlerbut can be assigned values different from unity to reduce (rQ rarr 0) or emphasize (rQ gt 1) the effectSince rQ multiplies the heavy-quark mass (squared) it can also be viewed as an effective rescalingof the mass value The net result is a suppression of the region z rarr 1 hence a relative softening ofthe fragmentation spectrum for heavy flavours (relative since the presence of m2

perp in the exponent ofeq (3) still implies an overall harder fragmentation for higher hadron masses)

We emphasize that this is the only fragmentation function that is self-consistent within the string-fragmentation model [33 62] Although a few alternative forms of the fragmentation functions formassive quarks are available in the code we therefore here work only with the Bowler type As forthe massless function the proportionality sign in eq (6) indicates that the function is normalized tounity

In PYTHIA separate rQ parameters are provided for c and b quarks We consider the one for bquarks first Its default value is rb = 067 but this appears to give too hard b fragmentation spectrawhen compared to LEP and SLD data see below For the Monash tune we instead use

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (DELPHI)weak

Bx

Pythia 8181Data from EurPhysJ C71 (2011) 1557

DELPHI PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn16

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (SLD)weak

Bx

Pythia 8181HepData5111d1-x1-y1

SLDPY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn07

00plusmn15

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a06

08

1

12

14

Figure 8 Hadronic Z decays atradics = 912 GeV Momentum (xB) spectra of weakly decaying B

hadrons compared to data from DELPHI [63] (left) and SLD [64] (right)

StringZrFactB = 0855

which produces softer B spectra and simultaneously agrees better with the theoretically preferredvalue (rb = 1)

A comparison to the scaled-momentum spectra (xB = 2|pB|Ecm) of weakly decayingB hadronsfrom both DELPHI [63] and SLD [64] is given in fig 8 (due to small differences between the twomeasured results we choose to show both) The dampening of the hardest part of the spectrum causedby the increase in the rb parameter is visible in the right-most two bins of the distributions and in thesmaller χ2

5 values for the Monash tune The effects of the modification can be further emphasizedby an analysis of the moments of the distribution in which the higher moments are increasinglydominated by the region xB rarr 1 A comparison to a combined LEP analysis of the moments of thexB distribution [63] is given in fig 9 further emphasizing that the high-xB part of the distribution isnow under better control

The reason we have not increased the rb parameter further is that it comes at a price If theB hadrons are taking less energy then there is more energy left over to produce other particlesand the generated multiplicity distribution in b events already exhibits a slightly high tail towardslarge multiplicities Nonetheless since the revised light-flavour fragmentation parameters produce anoverall narrower fragmentation function the end result is still a slight improvement in the multiplicitydistribution also for b events This is illustrated together with the inclusive momentum distributionfor b-tagged events in fig 10 compared to measurements by L3 [26] Interestingly the multiplicitydistribution still appears to be too wide but within the constraints of the present study we were unableto obtain further improvements As a point of speculation we note that the distribution of the numberof partons before hadronization is also quite wide in PYTHIA and this may be playing a role ineffectively setting a lower limit on the width that can be achieved for the hadron-level distribution

Comparisons to L3 event shapes in b-tagged events are collected in appendix B1 (the left columnof plots contains light-flavour tagged event shapes the right column b-tagged ones) In particular the

15

0 10 20 30 40

Mom

ent

0

02

04

06

08 (moments)weakBx

Pythia 8181Data from Eur Phys J C71 (2011) 1557

LEP (combined)PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn10

00plusmn103

00plusmn129

V I

N C

I A

R O

O T

N0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

Figure 9 Hadronic Z decays atradics = 912 GeV Moments of the B fragmentation function com-

pared to a combined analysis of LEP+SLD data by DELPHI [63]

0 20 40

)ch

Pro

babi

lity(

n

-610

-510

-410

-310

-210

-110

1

10

210 Charged Multiplicity (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

06plusmn45

08plusmn64

13plusmn110

V I

N C

I A

R O

O T

(b)chn0 20 40

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

ch d

nch

1n

-510

-410

-310

-210

-110

1

10

210 Charged Momentum Fraction (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn08

00plusmn06 V

I N

C I

A R

O O

T

)| (b)p

|Ln(x0 2 4 6 8

The

ory

Dat

a

06

08

1

12

14

Figure 10 HadronicZ decays atradics = 912 GeV Charged-hadron multiplicity (left) and momentum-

fraction (right) spectra in b-tagged events

16

0 02 04 06 08 1

dx

Dgt

dn

D1

ltn

0

05

1

15

2

25gt01)

E) (x

plusmnx(D

Pythia 8183Data from EurPhysJ C16 (2000) 597

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn14

02plusmn28

02plusmn32

V I

N C

I A

R O

O T

Ex0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

EX02 04 06 08 1

E)

dX

dN

(DZ

had

1N

0

0002

0004

0006

0008

001

0012

0014

0016

ALEPHHerwig++Sherpa

91 GeV ee Z (hadronic)

mcp

lots

cer

nch

41

M e

vent

sge

Riv

et 1

82

Herwig++ 261a Sherpa 141

ALEPH_1999_S4193598

spectrum (particle-level)+-D

02 04 06 08 105

1

15Ratio to ALEPH

Figure 11 The inclusive Dlowast spectrum in hadronic Z decays [55] Left Monash 2013 tune com-pared with default PYTHIA 8 and the Fischer tune Right comparison with HERWIG (dashed) andSHERPA (dotted) from MCPLOTS [25] Note that the plot in the left-hand pane is normalized tounity while the one in the right-hand pane is normalized to the number of hadronic Z decays

Monash tune gives a significant improvement in the soft region of the jet-broadening parameters inb-tagged events while no significant changes are observed for the other event shapes These smallimprovements are presumably a direct consequence of the softening of the b fragmentation functionit is now less likely to find an isolated ultra-hard B hadron

We round off the discussion of heavy-quark fragmentation by noting that a similarly comprehen-sive study of charm-quark fragmentation would be desirable However charm-quark tagged multi-plicity and event-shape data is not available to our knowledge and most of the D meson spectra onHEPDATA concern only specific decay chains (hence depend on the decay modeling) andor are lim-ited to restricted fiducial regions (limiting their generality) Experimentally the cleanest measurementis obtained from Dlowast decays and an inclusive momentum spectrum for Dlowast mesons has been measuredby ALEPH [55] From this distribution shown in fig 11 we determine a value for rc of

StringZrFactC = 132

We note that the low-x part of the Dlowast spectrum originates from g rarr cc shower splittings whilethe high-x tail represents prompt Dlowast production from leading charm in Z rarr cc (see [55] for a nicefigure illustrating this) The intermediate range contains a large component of feed-down from brarr cdecays hence this distribution is also indirectly sensitive to the b-quark sector The previous defaulttune had a harder spectrum for both b- and c-fragmentation leading to an overestimate of the high-xpart of the Dlowast distribution The undershooting at low xDlowast values which remains unchanged in theMonash tune most likely indicates an underproduction of g rarr cc branchings in the shower We notethat such an underproduction may also be reflected in the LHC data on Dlowast production see eg [65]We return to this issue in the discussion of identified particles at LHC section 35

17

In the leading-colour approximation each perturbative dipole is dual to a non-perturbative stringpiece [31] Quarks thus become string endpoints while gluons become transverse kinks connectingtwo string pieces [32] The Lund string fragmentation model [33] describes the fragmentation of suchstring systems into on-shell hadrons

Since the shower has already resolved all the (perturbative) physics down to a transverse-momentumscale of pTmin = 05 GeV (for the Monash 2013 tune) we find it reasonable that the pperp kicks in-volved in string breaking should effectively average over dynamics in roughly the range 250 MeV =radicκπ lt σperp lt pTmin with the lower bound given by Fermi motion (with κ the string tension

see [34]) Further since we here choose pTmin to be only slightly greater than ΛQCD the size of thenon-perturbative corrections is naturally limited to kickscorrections appropriate for non-perturbativedynamics (in contrast eg to the cluster model [35] which can generate substantially larger kicks oforder the largest allowed cluster mass which can be several GeV [30]) For the Monash 2013 tunewe have settled on a value of σperp = 0335 GeV with a small (1) tail of breaks involving higher pperpvalues carried over from the default settings

StringPTsigma = 0335StringPTenhancedFraction = 001StringPTenhancedWidth = 20

This value is obtained essentially from the first two bins of the Thrust distribution fig 1 and from thebins near zero of the other event shapes see appendix B1 Note that the σperp value is interpreted as thewidth of a Gaussian distribution in the total pperp (measured transversely to the local string directionwhich may differ from the global event axis) such that each of the px and py components have aslightly smaller average value σ2

xy = 12σ

2perp = (0237 GeV)2 Also note that each non-leading hadron

will receive two pperp kicks one from each of the breaks surrounding it hencelangp2perphad

rang= 2σ2

perp =(0474 GeV)2

For massless quarks the longitudinal component of the energy carried by a hadron formed in thestring-breaking process stringrarr hadron+stringprime is governed by the Lund symmetric fragmentationfunction

f(z) prop z(aiminusaj)(1minus z)ajz

exp

(minusbm2

perpz

) (3)

where z is the energy carried by the newly formed (ij) hadron expressed as a fraction of the (light-cone) energy of the quark (or antiquark) endpoint i of the fragmenting string (The remaining energyfraction (1 minus z) goes to the new stringprime system from which another hadron can be split off in thesame manner etc until all the energy is used up) The transverse mass of the produced (ij) hadronis defined by m2

perp = m2had + p2

perphad hence heavier hadrons have harder spectra The proportionalitysign in eq (3) indicates that the function is to be normalized to unity

The a and b parameters govern the shape of the fragmentation function and must be constrainedby fits to data Eq (3) expresses the most general form of the fragmentation function for which the aparameters of the original string-endpoint quark ai and that of the (anti-)quark produced in the stringbreak aj can in principle be different while the b parameter is universal Within the Lund model thea value is normally also taken to be universal the same for all quarks with the only freedom beingthat a larger a parameter can be assigned to diquarks [36] from which baryons are formed and hencemeson and baryon spectra can be decoupled somewhat (See StringZaExtraDiquark below)

Roughly speaking large a parameters suppress the hard region z rarr 1 while a large b parametersuppresses the soft region z rarr 0 By adjusting them independently both the average hardness andthe width of the resulting fragmentation spectra can be modified For example increasing both a andb yields a narrower distribution while changing them in opposite directions moves the average An

5

The a parameter The b parameter

a = 09 a = 01 b = 05 b = 20

02 04 06 08 10

05

10

15

02 04 06 08 10

05

10

15

20

b = 1 GeVminus2 mperp = 1 GeV a = 05 mperp = 1 GeV

Figure 2 Illustration of the Lund symmetric fragmentation function (normalized to unity) for ai =aj equiv a Left variation of the a parameter from 01 (blue) to 09 (red) with fixed b Right variationof the b parameter from 05 (red) to 2 (blue) GeVminus2 with fixed a

illustration of the effect of varying the a and b parameters for ai = aj equiv a is given in fig 2 see alsothe lecture notes in [37] Note that the σperp parameter also affects the hardness with larger σperp valuesgenerating harder hadrons the difference being that the σperp parameter acts mainly in the directiontransverse to the string5 (and is an absolute scale expressed in GeV) while the a and b parameters actlongitudinally (with z a relative scale expressed as a fraction of the endpointrsquos energy)

In the context of this work we included the possibility of letting the a parameter for strangequarks be slightly different from that of u and d quarks but did not find any significant advantagesThe relevant parameters in the code we settled on for the Monash tune are

StringZaLund = 068StringZbLund = 098StringZaExtraDiquark = 097StringZaExtraSquark = 000

The average hardness of the produced hadrons is tightly (anti-)correlated with the average multi-plicity via momentum conservation if each hadron takes a lot of energy then fewer hadrons must bemade and vice versa Thus the σperp value and the a and b parameters of the fragmentation functioncan be well constrained by simultaneously considering both momentum and multiplicity spectra Inorder to be as universal as possible one normally uses the inclusive charged-particle spectra for thispurpose These are shown in fig 3 (Note the Fischer tune only included the average particle mul-tiplicity as a constraint so the full nch distribution is not expected to be reproduced perfectly [30])The momentum fraction in the right-hand plot is defined by

xp =2|p|Ecm

(4)

As above the experimental data come from a measurement by L3 [26] which only includes the fourlightest flavours thus excluding b quarks (which will be treated separately below)

Both of the earlier tunes exhibit a somewhat too broad multiplicity distribution in comparisonwith the L3 data The relatively large Lund a and b values used for the Monash tune combined with

5Explicitly σperp expresses the pperp broadening transverse to the string direction but implicitly its size also enters inthe logitudinal fragmentation function via the m2

perp term in eq (3) causing higher-pperp hadrons to have relatively harderlongitudinal spectra as well

6

0 20 40 60

)ch

Pro

babi

lity(

n

-610

-510

-410

-310

-210

-110

1

10

210 Charged Multiplicity (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn05

01plusmn07

02plusmn21

V I

N C

I A

R O

O T

chn0 20 40 60

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

chgt

dn

ch1

ltn

-310

-210

-110

1

10Charged Momentum Fraction (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn09

00plusmn05

00plusmn05

V I

N C

I A

R O

O T

)|p

|Ln(x0 2 4 6 8

The

ory

Dat

a06

08

1

12

14

Figure 3 Hadronic Z decays atradics = 912 GeV Charged-particle multiplicity (left) and momentum-

fraction (right) spectra

its large σperp value produce a narrower nCh spectrum with in particular a smaller tail towards largemultiplicities All the tunes produce a sensible momentum spectrum The dip around |ln(x)| sim 55corresponds to the extreme soft-pion tail with momenta at or below ΛQCD We did not find it possibleto remove it by retuning since a smaller b parameter would generate significantly too high particlemultiplicities and a smaller σperp would lead to conflict with the event-shape distributions

A zoom on the high-momentum tail is provided by the left-hand plot in fig 4 which shows acomparison on a linear momentum scale to a measurement by ALEPH [38] (now including Z rarr bbevents as well as light-flavour ones) All the tunes exhibit a mild overshooting of the data in the region05 lt xp lt 08 corresponding to 015 lt | ln(x)| lt 07 in which no similar excess was present inthe L3 comparison We therefore do not regard this as a significant issue6 but note that the excess issomewhat milder in the Fischer and Monash tunes

Further information to elucidate the structure of the momentum distribution is provided by theplot in the right-hand pane of fig 4 which uses the same |ln(x)| axis as the right-hand plot in fig 3and shows the relative particle composition in the Monash tune for each histogram bin (The categoryldquoOtherrdquo contains electrons and muons from weak decays) An interesting observation is that therelatively harder spectrum of Kaons implies that for the highest-momentum bins the charged tracksare made up of an almost exactly equal mixture of Kaons and pions despite Kaons on average onlymaking up about 10 of the charged multiplicity

6One might worry whether the effect could be due solely to the Z rarr bb events which are only present in the ALEPHmeasurement and if so whether this could indicate a significant mismodeling of the momentum distribution in b eventsHowever as we show below in the section on b fragmentation the charged-particle momentum distribution in b-taggedevents shows no excess in that region (in fact it shows an undershooting)

7

0 02 04 06 08 1

pd

xch

gt d

nch

1lt

n

-410

-310

-210

-110

1

10Charged Momentum Fraction

Pythia 8183Data from Barate et al Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn14

01plusmn08

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

IDgt

dn

ch1

ltn

0

02

04

06

08

1

12 Particle Composition vs Lnx (udsc)

Pythia 8183

plusmnπplusmnKplusmnp

Other

V I

N C

I A

R O

O T

)|p

|Ln(x0 2 4 6 8

Rat

io06

08

1

12

14

Figure 4 Hadronic Z decays atradics = 912 GeV Charged-particle momentum fraction xp on a linear

scale (left) and relative particle composition (right) for the log-scale distribution shown in fig 3

22 Identified Particles

Continuing on the topic of identified particles we note that the extraction of the a and b parametersfrom the inclusive charged-particle distributions is made slightly more complicated by the fact thatnot all observed particles are ldquoprimaryrdquo (originating directly from string breaks) many lower-massparticles are ldquosecondariesrdquo produced by prompt decays of more massive states (eg ρrarr ππ) whoserelative rates and decay kinematics therefore influence the spectra In the e+eminus measurements weinclude here particles with cτ lt 100 mm were treated as unstable hence leading to secondaries (Forcompleteness we note that the equivalent standard cut at the LHC is normally 10 mm)

The particle composition in PYTHIA 8 was already tuned to a set of reference values provided bythe PDG [39] and the default parameters do reasonably well certainly for the most copiously pro-duced sources of secondaries Nonetheless we have here reoptimized the flavour-selection parametersof the string-fragmentation model using a slightly different set of reference data combining the PDGtables with information provided directly by the LEP experiments via HEPDATA [1] Based on thelevel of agreement or disagreement between different measurements of the same particles we havemade our own judgement as to the level of uncertainty for a few of the particles as follows (Unlessotherwise stated we use the value from the PDG Particles and antiparticles are implicitly summedover and secondaries from particles with cτ lt 100 mm are included)

bull The various LEP and SLD measurements of the φ meson rate on HEPDATA are barely com-patible Eg OPAL [40] reports 〈nφ〉 = 0091 plusmn 0002 plusmn 0003 while ALEPH [38] quotes〈nφ〉 = 0122 plusmn 0004 plusmn 0008 a difference of 30 with uncertainties supposedly less than10 DELPHI [41] and SLD [42] fall in between The PDG value is 〈nφ〉 = 00963 plusmn 0003ie with a combined uncertainty of just 3 We choose to inflate the systematic uncertaintiesand arrive at 〈nφ〉 = 0101plusmn 0007

8

bull For Λ production we use the most precise of the LEP measurements by OPAL7 [43] 〈nΛ〉 =0374plusmn 0002plusmn 0010 about 5 lower than the corresponding PDG value

bull For Σplusmn baryons we use a combination of the two most recent LEP measurements by L3 [44]for Σ+ + Σ

minus and by DELPHI [45] for Σminus + Σ+ for an estimated 〈nΣplusmn〉 = 0195 plusmn 0018

which is roughly 10 higher than the PDG value

bull For Σ0 baryons we use the most recent measurement by L3 [44] 〈nΣ0〉 = 0095 plusmn 0015 plusmn0013 this is about 20 larger than the PDG value The L3 paper comments on their relativelyhigh value by noting that L3 had the best coverage for low-momentum baryons hence smallermodel-dependent correction factors

bull For ∆++ baryons there are only two measurements in HEPDATA [4647] which are mutuallydiscrepant by about 2σ The DELPHI measurement is nominally the most precise but OPALgives a much more serious discussion of systematic uncertainties We choose to increase theestimated extrapolation errors of the DELPHI measurement by 50 and obtain a weighted av-erage8 of 〈n∆++〉 = 009plusmn0017 5 larger than the PDG value with a 20 larger uncertainty

bull For Σlowast the three measurements on HEPDATA [38 43 48] are likewise discrepant by 2σ minus 3σWe inflate the systematic uncertainties and arrive at 〈nΣlowastplusmn〉 = 0050 plusmn 0006 which is again5 higher than the PDG value with twice as much uncertainty

bull The measurements for Ξplusmn are in good agreement [38 43 48] with a weighted average of〈nΞplusmn〉 = 00266plusmn 00012 slightly larger than the PDG value

bull For Ξlowast0 however the DELPHI measurement [48] gives a far lower number than the OPAL [43]and ALEPH [38] ones and the weighted average differs by more than 10 from the PDGvalue despite the latter claiming an uncertainty smaller than 10 Our weighted average is〈nΞlowast0〉 = 00059plusmn 00012

bull Finally for the Ω baryon the DELPHI [49] and OPAL [43] measurements are in agreementand we use the PDG value 〈nΩ〉 = 00016plusmn 00003

We summarize the constraints on the light-meson and baryon rates used here in tab 1 Note that weexpress them as percentages of the average charged multiplicity

〈nCh〉 = 207 (5)

obtained as a weighted average over MARK-II [50] ALEPH [38] DELPHI [51] OPAL [52] andL3 [53] measurements

The light-flavour-selection parameters for the Monash tune are (see appendix A for a comparisonof these values to the current default ones)

Light-Meson SectorStringFlavProbStoUD = 0217StringFlavmesonUDvector = 05StringFlavmesonSvector = 055

7We note that HEPDATA incorrectly gives the systematic error as 0002 while the value in the OPAL paper is 0010 [43]This has been communicated to the HEPDATA maintainers

8Even with the inflated error the uncertainty on the DELPHI measurement is still less than a third that of the OPAL oneDELPHI therefore still dominates the average

9

Mesons Our Reference Our〈n〉 〈nCh〉 Value (in ) Source

π+ + πminus 822 plusmn09 Pπ0 455 plusmn15 PK+ +Kminus 108 plusmn03 Pη 506 plusmn038 Pηprime 073 plusmn009 Pρ+ + ρminus 116 plusmn21 Pρ0 595 plusmn047 PKlowast+ +Klowastminus 345 plusmn028 Pω 490 plusmn031 Pφ 049 plusmn0035 ADOS

Baryons Our Reference Our〈n〉 〈nCh〉 Value (in ) Source

p+ p 507 plusmn016 PΛ + Λ 181 plusmn032 OΣ+ + Σminus + Σ+ + Σminus 0942 plusmn0087 DLΣ0 + Σ0 0459 plusmn0096 L∆++ + ∆minusminus 0434 plusmn0082 DOΣlowast+ + Σlowastminus + Σlowast+ + Σlowastminus 0242 plusmn0029 ADOΞ+ + Ξminus 0125 plusmn00050 ADOΞlowast0 + Ξlowast0 00285 plusmn00058 ADOΩminus + Ω+ 00077 plusmn00015 P

Table 1 Hadronic Z decays atradics = 912 GeV Measured rates of light-flavour mesons and baryons

expressed as percentages of the average charged-particle multiplicity as used in this work Multiplythe numbers by 207100 to translate the percentages to corresponding production rates Source labelsindicate A (ALEPH) D (DELPHI) L (L3) O (OPAL) S (SLD) P (PDG)

StringFlavetaSup = 060StringFlavetaPrimeSup = 012

Baryon SectorStringFlavprobQQtoQ = 0081StringFlavprobSQtoQQ = 0915StringFlavprobQQ1toQQ0 = 00275StringFlavsuppressLeadingB = offStringFlavpopcornSpair = 09StringFlavpopcornSmeson = 05

Since strange-particle and baryon spectra at the LHC exhibit interesting differences with respectto existing models (see below) we paid particular attention to first obtaining a good description ofthese sectors in e+eminus collisions Specifically we have increased the overall amount of strangenessby about 10 while decreasing the rate of vector mesons by a similar amount9 (these two effectslargely cancel for Klowast) This improves the total Kplusmn ρ0 ω Λ Ξlowast and Ω yields on our combined LEPestimates discussed above The price is that we now overshoot the measured rate of Ξplusmn baryons by10 The resulting identified-meson and -baryon rates expressed as fractions of the average charged-particle multiplicity are plotted in fig 5 Note that the last four bins of the meson plot and the thirdand fourth bins of the baryon plot are not 〈n〉 〈nCh〉 fractions but rather the KlowastK φKlowast φKφπ Λp and ΛK ratios respectively Note also that section 4 on energy scaling below includes acomparison to the average Kaon and Lambda rates as a function of ee CM energy (fig 25)

To provide further information on identified particles we include a limited comparison to momen-tum spectra of Kplusmn p Λ and Ξplusmn which are the states of most immediate interest in the context ofsimilar comparisons now being made at LHC The spectra of Kplusmn mesons and Λ baryons are shownin fig 6 while the pplusmn and Ξplusmn spectra are relegated to appendix B2 The modified parameters of theMonash tune have virtually no effect on the Kaon distribution which still exhibits too many very softKaons (with ln(x) lt minus4 corresponding to x lt 0018 so momentum scales below sim 1 GeV) while

9For reference the current default value of ProbStoUD is 019 while ours is 0217 The increased value also improvesthe agreement with the Ds and Bs rates see section 23 The default values of mesonUDvector and mesonSvectorare 062 and 0725 respectively while ours are 05 and 055

10

plusmnπ 0π plusmnK η η plusmnρ 0ρ plusmnK ω φKK-

RKφ

RK-φ

R-πφ

R

gtch

ltnltngt

-310

-210

-110

1

10Meson Fractions

Pythia 8183Data from PDGHEPDATA

LEP + SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn06

00plusmn12

00plusmn12

V I

N C

I A

R O

O T

plusmnπ 0π plusmnK η η plusmnρ 0ρ plusmnK ω φKK-

RKφ

RK-φ

R-πφ

R

The

ory

Dat

a

06

08

1

12

14

p ΛpΛ

RKΛ

R plusmnΣ 0Σ ++∆ Σ plusmnΞ 0Ξ Ω

gtch

ltnltngt

-410

-310

-210

-110

1Baryon Fractions

Pythia 8183Data from PDGHEPDATA

LEP PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn11

00plusmn22

00plusmn22

V I

N C

I A

R O

O T

p ΛpΛ

RKΛ

R plusmnΣ 0Σ ++∆ Σ plusmnΞ 0Ξ Ω

The

ory

Dat

a

06

08

1

12

14

Figure 5 Hadronic Z decays atradics = 912 GeV Identified-meson and -baryon rates expressed as

fractions of the average charged-particle multiplicity

-4 -2 0

dln

(x)

Kgt

dn

K1

ltn

-310

-210

-110

1

10

) (Combined)plusmnx(K

Pythia 8183Data from ZPC66(1995)355 ZPC63(1994)181 EPJC5(1998)585

LEP (A+D+O)PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn16

00plusmn14

01plusmn19

V I

N C

I A

R O

O T

)p

ln(x-4 -2 0

The

ory

Dat

a

06

08

1

12

14

0 1 2 3 4 5

ξd

Λgt

dn

Λ1

ltn

0

02

04

06)]|0Λ|Ln[x(

Pythia 8183Data from EPJ C16 (2000) 613

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn08

01plusmn15

01plusmn12

V I

N C

I A

R O

O T

pξ

0 1 2 3 4 5

The

ory

Dat

a

06

08

1

12

14

Figure 6 Hadronic Z decays atradics = 912 GeV Kplusmn and Λ momentum-fraction spectra

11

the significant increase in the value of aExtraDiquark from 05 (Default) to 097 (Monash cf sec-tion 21) produces a desirable suppression of very hard Λ baryons The corresponding change in themeasured parts of the p and Ξplusmn spectra (cf appendix B2) are small compared with the experimentaluncertainties

It is interesting however to note that all of these spectra indicate or are at least consistent with amodelling excess of soft identified-particle production below ln(x) sim minus45 corresponding to absolutemomentum scales around 500 MeV while we recall that the inclusive ln(x) spectrum above showedan underproduction around ln(x) sim minus55 Within the constraints of the current theory model wehave not managed to find a way to mitigate these features while remaining consistent with the rest ofthe data Nonetheless it should be mentioned that these observations could have relevance also in thecontext of understanding identified-particle spectra at LHC a possibility which to our knowledge hasso far been ignored

23 Heavy-Quark Fragmentation

Similarly to above we first discuss the inclusive rates of hadrons containing heavy quarks before wediscuss their spectra Unfortunately there are also here substantial disagreements between differentpieces of information We have made the following choices

bull ForD mesons the average Dplusmn rate given in sec 46 of the PDG (0175) is equal to the inclusivebranching fraction for Z rarr DplusmnX given in the Z boson summary table in the same Review(after normalizing the latter to the hadronic Z fraction of 6991 [39]) However the formerought to be substantially larger given that some Z rarr cc events will contain two Dplusmn mesons(counting once in the Z rarr DplusmnX branching fraction but twice in the average Dplusmn multiplicity)We therefore here use a measurement by ALEPH [54] to fix the Dplusmn and D0 rates resulting ina reference value for the average Dplusmn multiplicity almost twice as large as that given by sec 46in the PDG

bull For Λ+c the average multiplicity given in sec 46 of the PDG is twice as large as that indicated

by the branching fraction BR(Z rarr Λ+c X) in the Z boson summary table in the same Review

We here use the branching from the Z boson summary table as our constraint on the Λ+c rate

normalized to the total branching fraction BR(Z rarr hadrons)

bull We also include the average rate of g rarr cc splittings obtained by combining an ALEPH [55]and an OPAL measurement [56] but with an additional 10 systematic uncertainty added toboth measurements to account for possibly larger mismodeling effects in the correction fac-tors [57 58]

bull For B particles we use the quite precise inclusive Z rarr B+X branching fraction from the Zboson summary in the PDG

bull We also use the sum of Bplusmn and B0(B0) in sec 46 of the PDG10

bull TheB0s multiplicity given in sec 46 of the PDG (0057plusmn0013) is more than twice the inclusive

BR(Z rarr B0sX)BR(Z rarr hadrons) branching fraction (00227 plusmn 00019) quoted in the Z

10Note that we have a factor 2 relative to the PDG since it appears the PDG quotes the average rather than the sum Notealso that all the average B meson multiplicities in sec 46 of the PDG are accompanied by a note ldquo(d)rdquo stating that the SMB(Z rarr bb) = 0217 was used for the normalization For completeness the reader should be aware that this is the fractionnormalized to hadronic Z decays the branching fraction relative to all Z decays is 0151 [39]

12

Charm Our Reference Our〈n〉 or BR Value Source

D+ +Dminus 0251 plusmn0047 AD0 + D0 0518 plusmn0063 ADlowast+ +Dlowastminus 0194 plusmn00057 PD+

s +Dminuss 0131 plusmn0021 PBR(Z rarr Λ+

c X) 00220 plusmn00047 ZBR(Z rarr X + cc) 00306 plusmn00047 AOJψ 00052 plusmn00004 Pχc1 00041 plusmn00011 Pψprime 00023 plusmn00004 P

Beauty Our Reference Our〈n〉 or BR Value Source

BR(Z rarr B+X) 0087 plusmn0002 ZB+ +B0 + B0 +Bminus 0330 plusmn0052 PBlowastu +Blowastd +Blowasts 0288 plusmn0026 PBR(Z rarr B0

sX) 00227 plusmn00019 ZBR(Z rarr BbaryonX) 00197 plusmn00032 ZBR(Z rarr X + bb) 000288 plusmn000061 ADSBR(Z rarr bbbbX) 000051 plusmn000019 ZΥ (times10) 00014 plusmn00007 P

Table 2 Hadronic Z decays atradics = MZ Measured rates and inclusive branching fractions of

particles containing c and b quarks as used in this work Note the branching fractions are normalizedto Z rarr hadrons and hence should be interpreted as eg BR(Z rarr B+X)BR(Z rarr hadrons)Note 2 the sum over Blowast states includes both particles and anti-particles Note 3 the Υ rate ismultiplied by a factor 10 Source labels indicate A (ALEPH) D (DELPHI) O (OPAL) P (PDGsection 46) S (SLD) Z (PDG Z Boson Summary Table)

boson summary table We find these two numbers difficult to reconcile and choose to use theinclusive BR(Z rarr B0

sX)BR(Z rarr hadrons) branching fraction as our main constraint

bull We also include the inclusive branching fractions for B-baryons (summed over baryons andantibaryons) the rate of g rarr bb splittings obtained by combining ALEPH [59] DELPHI [60]and SLD [61] measurements (including an additional 10 systematic to account for largerpossible mismodeling effects in the correction factors [57 58]) and the rate of Z rarr bbbb fromthe PDG Z boson summary table [39]

Our constraints on the heavy-quark particle rates are summarized in tab 2 Comparisons to these ratesare shown in fig 7 now without normalizing to the average charged-particle multiplicity Given thatmost of the c and b quarks come directly from Z rarr cc and Z rarr bb decays there is not a lot of roomfor tuning to these numbers apart from the relative rates of vector mesons vs pseudoscalars which iscontrolled by the parameters

Heavy MesonsStringFlavmesonCvector = 088StringFlavmesonBvector = 22

Our parameters are slightly smaller than the current default values leading to slightly smaller Dlowast

and Blowast rates as can be seen from the plots in fig 7 Note also that the increased overall amount ofstrangeness in the fragmentation leads to slightly higherDs andBs fractions in better agreement withthe data Uncertainties are however large and some exotic onium states like χc1 ψprime and Υ are notwell described by the default modeling (It is encouraging that at least the multiplicity of Jψ mesonsis well described though a substantial fraction of this likely owes to the feed-down from B decaysand hence does not depend directly on the string-fragmentation model itself)

We also note that it would be desirable to reduce the rate of g rarr bb and Z rarr bbbb events whilethe g rarr cc one appears consistent with the LEP constraints We suspect that this issue may be tiedto the fixed choice of using pperp as the renormalization scale for both gluon emissions and for g rarr qq

13

plusmnD 0D plusmnD plusmns

D X+

cΛ

ccrarrg ψJ c1χ

3685

ψ

X)

rarrlt

ngt o

r B

R(Z

-410

-310

-210

-110

1

10Charm Rates

Pythia 8185Data from HEPDATAPDG

LEP

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn15

00plusmn18

00plusmn17

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

plusmnD 0Dplusmn

D plusmnsD X+

cΛ ccrarrg ψJ c1χ

3685ψ

The

ory

Dat

a

0

05

1

15

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

X)

rarrlt

ngt o

r B

R(Z

-510

-410

-310

-210

-110

1

10Beauty Rates

Pythia 8185Data from HEPDATAPDG

LEP+SLD

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn17

00plusmn23

00plusmn23

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

The

ory

Dat

a0

05

1

15

Figure 7 Hadronic Z decays atradics = 912 GeV Rates and inclusive Z rarr X branching fractions

(normalized to Z rarr hadrons) of particles containing c and b quarks

splittings in the current version of PYTHIA A more natural choice for g rarr qq could be microR prop mqqas used eg in the VINCIA shower model [29]

We now turn to the dynamics of heavy-quark fragmentation focusing mainly on the b quarkFor heavy quarks the Lund fragmentation function is modified due to the (massive) endpoints not

moving along straight lightcones as the string pulls on them they slow down resulting in the stringtracing out a smaller space-time area than it would for massless quarks This modifies the implicationsof the string area law in a manner captured by the so-called Bowler modification of the fragmentationfunction [62]

fmassive(zmQ) prop f(z)

zbrQm2Q

(6)

with mQ the heavy-quark mass b the same universal parameter that appears in the massless fragmen-tation function eq (3) and rQ a tuning parameter which is unity in the original derivation of Bowlerbut can be assigned values different from unity to reduce (rQ rarr 0) or emphasize (rQ gt 1) the effectSince rQ multiplies the heavy-quark mass (squared) it can also be viewed as an effective rescalingof the mass value The net result is a suppression of the region z rarr 1 hence a relative softening ofthe fragmentation spectrum for heavy flavours (relative since the presence of m2

perp in the exponent ofeq (3) still implies an overall harder fragmentation for higher hadron masses)

We emphasize that this is the only fragmentation function that is self-consistent within the string-fragmentation model [33 62] Although a few alternative forms of the fragmentation functions formassive quarks are available in the code we therefore here work only with the Bowler type As forthe massless function the proportionality sign in eq (6) indicates that the function is normalized tounity

In PYTHIA separate rQ parameters are provided for c and b quarks We consider the one for bquarks first Its default value is rb = 067 but this appears to give too hard b fragmentation spectrawhen compared to LEP and SLD data see below For the Monash tune we instead use

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (DELPHI)weak

Bx

Pythia 8181Data from EurPhysJ C71 (2011) 1557

DELPHI PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn16

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (SLD)weak

Bx

Pythia 8181HepData5111d1-x1-y1

SLDPY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn07

00plusmn15

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a06

08

1

12

14

Figure 8 Hadronic Z decays atradics = 912 GeV Momentum (xB) spectra of weakly decaying B

hadrons compared to data from DELPHI [63] (left) and SLD [64] (right)

StringZrFactB = 0855

which produces softer B spectra and simultaneously agrees better with the theoretically preferredvalue (rb = 1)

A comparison to the scaled-momentum spectra (xB = 2|pB|Ecm) of weakly decayingB hadronsfrom both DELPHI [63] and SLD [64] is given in fig 8 (due to small differences between the twomeasured results we choose to show both) The dampening of the hardest part of the spectrum causedby the increase in the rb parameter is visible in the right-most two bins of the distributions and in thesmaller χ2

5 values for the Monash tune The effects of the modification can be further emphasizedby an analysis of the moments of the distribution in which the higher moments are increasinglydominated by the region xB rarr 1 A comparison to a combined LEP analysis of the moments of thexB distribution [63] is given in fig 9 further emphasizing that the high-xB part of the distribution isnow under better control

The reason we have not increased the rb parameter further is that it comes at a price If theB hadrons are taking less energy then there is more energy left over to produce other particlesand the generated multiplicity distribution in b events already exhibits a slightly high tail towardslarge multiplicities Nonetheless since the revised light-flavour fragmentation parameters produce anoverall narrower fragmentation function the end result is still a slight improvement in the multiplicitydistribution also for b events This is illustrated together with the inclusive momentum distributionfor b-tagged events in fig 10 compared to measurements by L3 [26] Interestingly the multiplicitydistribution still appears to be too wide but within the constraints of the present study we were unableto obtain further improvements As a point of speculation we note that the distribution of the numberof partons before hadronization is also quite wide in PYTHIA and this may be playing a role ineffectively setting a lower limit on the width that can be achieved for the hadron-level distribution

Comparisons to L3 event shapes in b-tagged events are collected in appendix B1 (the left columnof plots contains light-flavour tagged event shapes the right column b-tagged ones) In particular the

15

0 10 20 30 40

Mom

ent

0

02

04

06

08 (moments)weakBx

Pythia 8181Data from Eur Phys J C71 (2011) 1557

LEP (combined)PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn10

00plusmn103

00plusmn129

V I

N C

I A

R O

O T

N0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

Figure 9 Hadronic Z decays atradics = 912 GeV Moments of the B fragmentation function com-

pared to a combined analysis of LEP+SLD data by DELPHI [63]

0 20 40

)ch

Pro

babi

lity(

n

-610

-510

-410

-310

-210

-110

1

10

210 Charged Multiplicity (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

06plusmn45

08plusmn64

13plusmn110

V I

N C

I A

R O

O T

(b)chn0 20 40

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

ch d

nch

1n

-510

-410

-310

-210

-110

1

10

210 Charged Momentum Fraction (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn08

00plusmn06 V

I N

C I

A R

O O

T

)| (b)p

|Ln(x0 2 4 6 8

The

ory

Dat

a

06

08

1

12

14

Figure 10 HadronicZ decays atradics = 912 GeV Charged-hadron multiplicity (left) and momentum-

fraction (right) spectra in b-tagged events

16

0 02 04 06 08 1

dx

Dgt

dn

D1

ltn

0

05

1

15

2

25gt01)

E) (x

plusmnx(D

Pythia 8183Data from EurPhysJ C16 (2000) 597

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn14

02plusmn28

02plusmn32

V I

N C

I A

R O

O T

Ex0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

EX02 04 06 08 1

E)

dX

dN

(DZ

had

1N

0

0002

0004

0006

0008

001

0012

0014

0016

ALEPHHerwig++Sherpa

91 GeV ee Z (hadronic)

mcp

lots

cer

nch

41

M e

vent

sge

Riv

et 1

82

Herwig++ 261a Sherpa 141

ALEPH_1999_S4193598

spectrum (particle-level)+-D

02 04 06 08 105

1

15Ratio to ALEPH

Figure 11 The inclusive Dlowast spectrum in hadronic Z decays [55] Left Monash 2013 tune com-pared with default PYTHIA 8 and the Fischer tune Right comparison with HERWIG (dashed) andSHERPA (dotted) from MCPLOTS [25] Note that the plot in the left-hand pane is normalized tounity while the one in the right-hand pane is normalized to the number of hadronic Z decays

Monash tune gives a significant improvement in the soft region of the jet-broadening parameters inb-tagged events while no significant changes are observed for the other event shapes These smallimprovements are presumably a direct consequence of the softening of the b fragmentation functionit is now less likely to find an isolated ultra-hard B hadron

We round off the discussion of heavy-quark fragmentation by noting that a similarly comprehen-sive study of charm-quark fragmentation would be desirable However charm-quark tagged multi-plicity and event-shape data is not available to our knowledge and most of the D meson spectra onHEPDATA concern only specific decay chains (hence depend on the decay modeling) andor are lim-ited to restricted fiducial regions (limiting their generality) Experimentally the cleanest measurementis obtained from Dlowast decays and an inclusive momentum spectrum for Dlowast mesons has been measuredby ALEPH [55] From this distribution shown in fig 11 we determine a value for rc of

StringZrFactC = 132

We note that the low-x part of the Dlowast spectrum originates from g rarr cc shower splittings whilethe high-x tail represents prompt Dlowast production from leading charm in Z rarr cc (see [55] for a nicefigure illustrating this) The intermediate range contains a large component of feed-down from brarr cdecays hence this distribution is also indirectly sensitive to the b-quark sector The previous defaulttune had a harder spectrum for both b- and c-fragmentation leading to an overestimate of the high-xpart of the Dlowast distribution The undershooting at low xDlowast values which remains unchanged in theMonash tune most likely indicates an underproduction of g rarr cc branchings in the shower We notethat such an underproduction may also be reflected in the LHC data on Dlowast production see eg [65]We return to this issue in the discussion of identified particles at LHC section 35

17

The a parameter The b parameter

a = 09 a = 01 b = 05 b = 20

02 04 06 08 10

05

10

15

02 04 06 08 10

05

10

15

20

b = 1 GeVminus2 mperp = 1 GeV a = 05 mperp = 1 GeV

Figure 2 Illustration of the Lund symmetric fragmentation function (normalized to unity) for ai =aj equiv a Left variation of the a parameter from 01 (blue) to 09 (red) with fixed b Right variationof the b parameter from 05 (red) to 2 (blue) GeVminus2 with fixed a

illustration of the effect of varying the a and b parameters for ai = aj equiv a is given in fig 2 see alsothe lecture notes in [37] Note that the σperp parameter also affects the hardness with larger σperp valuesgenerating harder hadrons the difference being that the σperp parameter acts mainly in the directiontransverse to the string5 (and is an absolute scale expressed in GeV) while the a and b parameters actlongitudinally (with z a relative scale expressed as a fraction of the endpointrsquos energy)

In the context of this work we included the possibility of letting the a parameter for strangequarks be slightly different from that of u and d quarks but did not find any significant advantagesThe relevant parameters in the code we settled on for the Monash tune are

StringZaLund = 068StringZbLund = 098StringZaExtraDiquark = 097StringZaExtraSquark = 000

The average hardness of the produced hadrons is tightly (anti-)correlated with the average multi-plicity via momentum conservation if each hadron takes a lot of energy then fewer hadrons must bemade and vice versa Thus the σperp value and the a and b parameters of the fragmentation functioncan be well constrained by simultaneously considering both momentum and multiplicity spectra Inorder to be as universal as possible one normally uses the inclusive charged-particle spectra for thispurpose These are shown in fig 3 (Note the Fischer tune only included the average particle mul-tiplicity as a constraint so the full nch distribution is not expected to be reproduced perfectly [30])The momentum fraction in the right-hand plot is defined by

xp =2|p|Ecm

(4)

As above the experimental data come from a measurement by L3 [26] which only includes the fourlightest flavours thus excluding b quarks (which will be treated separately below)

Both of the earlier tunes exhibit a somewhat too broad multiplicity distribution in comparisonwith the L3 data The relatively large Lund a and b values used for the Monash tune combined with

5Explicitly σperp expresses the pperp broadening transverse to the string direction but implicitly its size also enters inthe logitudinal fragmentation function via the m2

perp term in eq (3) causing higher-pperp hadrons to have relatively harderlongitudinal spectra as well

6

0 20 40 60

)ch

Pro

babi

lity(

n

-610

-510

-410

-310

-210

-110

1

10

210 Charged Multiplicity (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn05

01plusmn07

02plusmn21

V I

N C

I A

R O

O T

chn0 20 40 60

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

chgt

dn

ch1

ltn

-310

-210

-110

1

10Charged Momentum Fraction (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn09

00plusmn05

00plusmn05

V I

N C

I A

R O

O T

)|p

|Ln(x0 2 4 6 8

The

ory

Dat

a06

08

1

12

14

Figure 3 Hadronic Z decays atradics = 912 GeV Charged-particle multiplicity (left) and momentum-

fraction (right) spectra

its large σperp value produce a narrower nCh spectrum with in particular a smaller tail towards largemultiplicities All the tunes produce a sensible momentum spectrum The dip around |ln(x)| sim 55corresponds to the extreme soft-pion tail with momenta at or below ΛQCD We did not find it possibleto remove it by retuning since a smaller b parameter would generate significantly too high particlemultiplicities and a smaller σperp would lead to conflict with the event-shape distributions

A zoom on the high-momentum tail is provided by the left-hand plot in fig 4 which shows acomparison on a linear momentum scale to a measurement by ALEPH [38] (now including Z rarr bbevents as well as light-flavour ones) All the tunes exhibit a mild overshooting of the data in the region05 lt xp lt 08 corresponding to 015 lt | ln(x)| lt 07 in which no similar excess was present inthe L3 comparison We therefore do not regard this as a significant issue6 but note that the excess issomewhat milder in the Fischer and Monash tunes

Further information to elucidate the structure of the momentum distribution is provided by theplot in the right-hand pane of fig 4 which uses the same |ln(x)| axis as the right-hand plot in fig 3and shows the relative particle composition in the Monash tune for each histogram bin (The categoryldquoOtherrdquo contains electrons and muons from weak decays) An interesting observation is that therelatively harder spectrum of Kaons implies that for the highest-momentum bins the charged tracksare made up of an almost exactly equal mixture of Kaons and pions despite Kaons on average onlymaking up about 10 of the charged multiplicity

6One might worry whether the effect could be due solely to the Z rarr bb events which are only present in the ALEPHmeasurement and if so whether this could indicate a significant mismodeling of the momentum distribution in b eventsHowever as we show below in the section on b fragmentation the charged-particle momentum distribution in b-taggedevents shows no excess in that region (in fact it shows an undershooting)

7

0 02 04 06 08 1

pd

xch

gt d

nch

1lt

n

-410

-310

-210

-110

1

10Charged Momentum Fraction

Pythia 8183Data from Barate et al Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn14

01plusmn08

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

IDgt

dn

ch1

ltn

0

02

04

06

08

1

12 Particle Composition vs Lnx (udsc)

Pythia 8183

plusmnπplusmnKplusmnp

Other

V I

N C

I A

R O

O T

)|p

|Ln(x0 2 4 6 8

Rat

io06

08

1

12

14

Figure 4 Hadronic Z decays atradics = 912 GeV Charged-particle momentum fraction xp on a linear

scale (left) and relative particle composition (right) for the log-scale distribution shown in fig 3

22 Identified Particles

Continuing on the topic of identified particles we note that the extraction of the a and b parametersfrom the inclusive charged-particle distributions is made slightly more complicated by the fact thatnot all observed particles are ldquoprimaryrdquo (originating directly from string breaks) many lower-massparticles are ldquosecondariesrdquo produced by prompt decays of more massive states (eg ρrarr ππ) whoserelative rates and decay kinematics therefore influence the spectra In the e+eminus measurements weinclude here particles with cτ lt 100 mm were treated as unstable hence leading to secondaries (Forcompleteness we note that the equivalent standard cut at the LHC is normally 10 mm)

The particle composition in PYTHIA 8 was already tuned to a set of reference values provided bythe PDG [39] and the default parameters do reasonably well certainly for the most copiously pro-duced sources of secondaries Nonetheless we have here reoptimized the flavour-selection parametersof the string-fragmentation model using a slightly different set of reference data combining the PDGtables with information provided directly by the LEP experiments via HEPDATA [1] Based on thelevel of agreement or disagreement between different measurements of the same particles we havemade our own judgement as to the level of uncertainty for a few of the particles as follows (Unlessotherwise stated we use the value from the PDG Particles and antiparticles are implicitly summedover and secondaries from particles with cτ lt 100 mm are included)

bull The various LEP and SLD measurements of the φ meson rate on HEPDATA are barely com-patible Eg OPAL [40] reports 〈nφ〉 = 0091 plusmn 0002 plusmn 0003 while ALEPH [38] quotes〈nφ〉 = 0122 plusmn 0004 plusmn 0008 a difference of 30 with uncertainties supposedly less than10 DELPHI [41] and SLD [42] fall in between The PDG value is 〈nφ〉 = 00963 plusmn 0003ie with a combined uncertainty of just 3 We choose to inflate the systematic uncertaintiesand arrive at 〈nφ〉 = 0101plusmn 0007

8

bull For Λ production we use the most precise of the LEP measurements by OPAL7 [43] 〈nΛ〉 =0374plusmn 0002plusmn 0010 about 5 lower than the corresponding PDG value

bull For Σplusmn baryons we use a combination of the two most recent LEP measurements by L3 [44]for Σ+ + Σ

minus and by DELPHI [45] for Σminus + Σ+ for an estimated 〈nΣplusmn〉 = 0195 plusmn 0018

which is roughly 10 higher than the PDG value

bull For Σ0 baryons we use the most recent measurement by L3 [44] 〈nΣ0〉 = 0095 plusmn 0015 plusmn0013 this is about 20 larger than the PDG value The L3 paper comments on their relativelyhigh value by noting that L3 had the best coverage for low-momentum baryons hence smallermodel-dependent correction factors

bull For ∆++ baryons there are only two measurements in HEPDATA [4647] which are mutuallydiscrepant by about 2σ The DELPHI measurement is nominally the most precise but OPALgives a much more serious discussion of systematic uncertainties We choose to increase theestimated extrapolation errors of the DELPHI measurement by 50 and obtain a weighted av-erage8 of 〈n∆++〉 = 009plusmn0017 5 larger than the PDG value with a 20 larger uncertainty

bull For Σlowast the three measurements on HEPDATA [38 43 48] are likewise discrepant by 2σ minus 3σWe inflate the systematic uncertainties and arrive at 〈nΣlowastplusmn〉 = 0050 plusmn 0006 which is again5 higher than the PDG value with twice as much uncertainty

bull The measurements for Ξplusmn are in good agreement [38 43 48] with a weighted average of〈nΞplusmn〉 = 00266plusmn 00012 slightly larger than the PDG value

bull For Ξlowast0 however the DELPHI measurement [48] gives a far lower number than the OPAL [43]and ALEPH [38] ones and the weighted average differs by more than 10 from the PDGvalue despite the latter claiming an uncertainty smaller than 10 Our weighted average is〈nΞlowast0〉 = 00059plusmn 00012

bull Finally for the Ω baryon the DELPHI [49] and OPAL [43] measurements are in agreementand we use the PDG value 〈nΩ〉 = 00016plusmn 00003

We summarize the constraints on the light-meson and baryon rates used here in tab 1 Note that weexpress them as percentages of the average charged multiplicity

〈nCh〉 = 207 (5)

obtained as a weighted average over MARK-II [50] ALEPH [38] DELPHI [51] OPAL [52] andL3 [53] measurements

The light-flavour-selection parameters for the Monash tune are (see appendix A for a comparisonof these values to the current default ones)

Light-Meson SectorStringFlavProbStoUD = 0217StringFlavmesonUDvector = 05StringFlavmesonSvector = 055

7We note that HEPDATA incorrectly gives the systematic error as 0002 while the value in the OPAL paper is 0010 [43]This has been communicated to the HEPDATA maintainers

8Even with the inflated error the uncertainty on the DELPHI measurement is still less than a third that of the OPAL oneDELPHI therefore still dominates the average

9

Mesons Our Reference Our〈n〉 〈nCh〉 Value (in ) Source

π+ + πminus 822 plusmn09 Pπ0 455 plusmn15 PK+ +Kminus 108 plusmn03 Pη 506 plusmn038 Pηprime 073 plusmn009 Pρ+ + ρminus 116 plusmn21 Pρ0 595 plusmn047 PKlowast+ +Klowastminus 345 plusmn028 Pω 490 plusmn031 Pφ 049 plusmn0035 ADOS

Baryons Our Reference Our〈n〉 〈nCh〉 Value (in ) Source

p+ p 507 plusmn016 PΛ + Λ 181 plusmn032 OΣ+ + Σminus + Σ+ + Σminus 0942 plusmn0087 DLΣ0 + Σ0 0459 plusmn0096 L∆++ + ∆minusminus 0434 plusmn0082 DOΣlowast+ + Σlowastminus + Σlowast+ + Σlowastminus 0242 plusmn0029 ADOΞ+ + Ξminus 0125 plusmn00050 ADOΞlowast0 + Ξlowast0 00285 plusmn00058 ADOΩminus + Ω+ 00077 plusmn00015 P

Table 1 Hadronic Z decays atradics = 912 GeV Measured rates of light-flavour mesons and baryons

expressed as percentages of the average charged-particle multiplicity as used in this work Multiplythe numbers by 207100 to translate the percentages to corresponding production rates Source labelsindicate A (ALEPH) D (DELPHI) L (L3) O (OPAL) S (SLD) P (PDG)

StringFlavetaSup = 060StringFlavetaPrimeSup = 012

Baryon SectorStringFlavprobQQtoQ = 0081StringFlavprobSQtoQQ = 0915StringFlavprobQQ1toQQ0 = 00275StringFlavsuppressLeadingB = offStringFlavpopcornSpair = 09StringFlavpopcornSmeson = 05

Since strange-particle and baryon spectra at the LHC exhibit interesting differences with respectto existing models (see below) we paid particular attention to first obtaining a good description ofthese sectors in e+eminus collisions Specifically we have increased the overall amount of strangenessby about 10 while decreasing the rate of vector mesons by a similar amount9 (these two effectslargely cancel for Klowast) This improves the total Kplusmn ρ0 ω Λ Ξlowast and Ω yields on our combined LEPestimates discussed above The price is that we now overshoot the measured rate of Ξplusmn baryons by10 The resulting identified-meson and -baryon rates expressed as fractions of the average charged-particle multiplicity are plotted in fig 5 Note that the last four bins of the meson plot and the thirdand fourth bins of the baryon plot are not 〈n〉 〈nCh〉 fractions but rather the KlowastK φKlowast φKφπ Λp and ΛK ratios respectively Note also that section 4 on energy scaling below includes acomparison to the average Kaon and Lambda rates as a function of ee CM energy (fig 25)

To provide further information on identified particles we include a limited comparison to momen-tum spectra of Kplusmn p Λ and Ξplusmn which are the states of most immediate interest in the context ofsimilar comparisons now being made at LHC The spectra of Kplusmn mesons and Λ baryons are shownin fig 6 while the pplusmn and Ξplusmn spectra are relegated to appendix B2 The modified parameters of theMonash tune have virtually no effect on the Kaon distribution which still exhibits too many very softKaons (with ln(x) lt minus4 corresponding to x lt 0018 so momentum scales below sim 1 GeV) while

9For reference the current default value of ProbStoUD is 019 while ours is 0217 The increased value also improvesthe agreement with the Ds and Bs rates see section 23 The default values of mesonUDvector and mesonSvectorare 062 and 0725 respectively while ours are 05 and 055

10

plusmnπ 0π plusmnK η η plusmnρ 0ρ plusmnK ω φKK-

RKφ

RK-φ

R-πφ

R

gtch

ltnltngt

-310

-210

-110

1

10Meson Fractions

Pythia 8183Data from PDGHEPDATA

LEP + SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn06

00plusmn12

00plusmn12

V I

N C

I A

R O

O T

plusmnπ 0π plusmnK η η plusmnρ 0ρ plusmnK ω φKK-

RKφ

RK-φ

R-πφ

R

The

ory

Dat

a

06

08

1

12

14

p ΛpΛ

RKΛ

R plusmnΣ 0Σ ++∆ Σ plusmnΞ 0Ξ Ω

gtch

ltnltngt

-410

-310

-210

-110

1Baryon Fractions

Pythia 8183Data from PDGHEPDATA

LEP PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn11

00plusmn22

00plusmn22

V I

N C

I A

R O

O T

p ΛpΛ

RKΛ

R plusmnΣ 0Σ ++∆ Σ plusmnΞ 0Ξ Ω

The

ory

Dat

a

06

08

1

12

14

Figure 5 Hadronic Z decays atradics = 912 GeV Identified-meson and -baryon rates expressed as

fractions of the average charged-particle multiplicity

-4 -2 0

dln

(x)

Kgt

dn

K1

ltn

-310

-210

-110

1

10

) (Combined)plusmnx(K

Pythia 8183Data from ZPC66(1995)355 ZPC63(1994)181 EPJC5(1998)585

LEP (A+D+O)PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn16

00plusmn14

01plusmn19

V I

N C

I A

R O

O T

)p

ln(x-4 -2 0

The

ory

Dat

a

06

08

1

12

14

0 1 2 3 4 5

ξd

Λgt

dn

Λ1

ltn

0

02

04

06)]|0Λ|Ln[x(

Pythia 8183Data from EPJ C16 (2000) 613

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn08

01plusmn15

01plusmn12

V I

N C

I A

R O

O T

pξ

0 1 2 3 4 5

The

ory

Dat

a

06

08

1

12

14

Figure 6 Hadronic Z decays atradics = 912 GeV Kplusmn and Λ momentum-fraction spectra

11

the significant increase in the value of aExtraDiquark from 05 (Default) to 097 (Monash cf sec-tion 21) produces a desirable suppression of very hard Λ baryons The corresponding change in themeasured parts of the p and Ξplusmn spectra (cf appendix B2) are small compared with the experimentaluncertainties

It is interesting however to note that all of these spectra indicate or are at least consistent with amodelling excess of soft identified-particle production below ln(x) sim minus45 corresponding to absolutemomentum scales around 500 MeV while we recall that the inclusive ln(x) spectrum above showedan underproduction around ln(x) sim minus55 Within the constraints of the current theory model wehave not managed to find a way to mitigate these features while remaining consistent with the rest ofthe data Nonetheless it should be mentioned that these observations could have relevance also in thecontext of understanding identified-particle spectra at LHC a possibility which to our knowledge hasso far been ignored

23 Heavy-Quark Fragmentation

Similarly to above we first discuss the inclusive rates of hadrons containing heavy quarks before wediscuss their spectra Unfortunately there are also here substantial disagreements between differentpieces of information We have made the following choices

bull ForD mesons the average Dplusmn rate given in sec 46 of the PDG (0175) is equal to the inclusivebranching fraction for Z rarr DplusmnX given in the Z boson summary table in the same Review(after normalizing the latter to the hadronic Z fraction of 6991 [39]) However the formerought to be substantially larger given that some Z rarr cc events will contain two Dplusmn mesons(counting once in the Z rarr DplusmnX branching fraction but twice in the average Dplusmn multiplicity)We therefore here use a measurement by ALEPH [54] to fix the Dplusmn and D0 rates resulting ina reference value for the average Dplusmn multiplicity almost twice as large as that given by sec 46in the PDG

bull For Λ+c the average multiplicity given in sec 46 of the PDG is twice as large as that indicated

by the branching fraction BR(Z rarr Λ+c X) in the Z boson summary table in the same Review

We here use the branching from the Z boson summary table as our constraint on the Λ+c rate

normalized to the total branching fraction BR(Z rarr hadrons)

bull We also include the average rate of g rarr cc splittings obtained by combining an ALEPH [55]and an OPAL measurement [56] but with an additional 10 systematic uncertainty added toboth measurements to account for possibly larger mismodeling effects in the correction fac-tors [57 58]

bull For B particles we use the quite precise inclusive Z rarr B+X branching fraction from the Zboson summary in the PDG

bull We also use the sum of Bplusmn and B0(B0) in sec 46 of the PDG10

bull TheB0s multiplicity given in sec 46 of the PDG (0057plusmn0013) is more than twice the inclusive

BR(Z rarr B0sX)BR(Z rarr hadrons) branching fraction (00227 plusmn 00019) quoted in the Z

10Note that we have a factor 2 relative to the PDG since it appears the PDG quotes the average rather than the sum Notealso that all the average B meson multiplicities in sec 46 of the PDG are accompanied by a note ldquo(d)rdquo stating that the SMB(Z rarr bb) = 0217 was used for the normalization For completeness the reader should be aware that this is the fractionnormalized to hadronic Z decays the branching fraction relative to all Z decays is 0151 [39]

12

Charm Our Reference Our〈n〉 or BR Value Source

D+ +Dminus 0251 plusmn0047 AD0 + D0 0518 plusmn0063 ADlowast+ +Dlowastminus 0194 plusmn00057 PD+

s +Dminuss 0131 plusmn0021 PBR(Z rarr Λ+

c X) 00220 plusmn00047 ZBR(Z rarr X + cc) 00306 plusmn00047 AOJψ 00052 plusmn00004 Pχc1 00041 plusmn00011 Pψprime 00023 plusmn00004 P

Beauty Our Reference Our〈n〉 or BR Value Source

BR(Z rarr B+X) 0087 plusmn0002 ZB+ +B0 + B0 +Bminus 0330 plusmn0052 PBlowastu +Blowastd +Blowasts 0288 plusmn0026 PBR(Z rarr B0

sX) 00227 plusmn00019 ZBR(Z rarr BbaryonX) 00197 plusmn00032 ZBR(Z rarr X + bb) 000288 plusmn000061 ADSBR(Z rarr bbbbX) 000051 plusmn000019 ZΥ (times10) 00014 plusmn00007 P

Table 2 Hadronic Z decays atradics = MZ Measured rates and inclusive branching fractions of

particles containing c and b quarks as used in this work Note the branching fractions are normalizedto Z rarr hadrons and hence should be interpreted as eg BR(Z rarr B+X)BR(Z rarr hadrons)Note 2 the sum over Blowast states includes both particles and anti-particles Note 3 the Υ rate ismultiplied by a factor 10 Source labels indicate A (ALEPH) D (DELPHI) O (OPAL) P (PDGsection 46) S (SLD) Z (PDG Z Boson Summary Table)

boson summary table We find these two numbers difficult to reconcile and choose to use theinclusive BR(Z rarr B0

sX)BR(Z rarr hadrons) branching fraction as our main constraint

bull We also include the inclusive branching fractions for B-baryons (summed over baryons andantibaryons) the rate of g rarr bb splittings obtained by combining ALEPH [59] DELPHI [60]and SLD [61] measurements (including an additional 10 systematic to account for largerpossible mismodeling effects in the correction factors [57 58]) and the rate of Z rarr bbbb fromthe PDG Z boson summary table [39]

Our constraints on the heavy-quark particle rates are summarized in tab 2 Comparisons to these ratesare shown in fig 7 now without normalizing to the average charged-particle multiplicity Given thatmost of the c and b quarks come directly from Z rarr cc and Z rarr bb decays there is not a lot of roomfor tuning to these numbers apart from the relative rates of vector mesons vs pseudoscalars which iscontrolled by the parameters

Heavy MesonsStringFlavmesonCvector = 088StringFlavmesonBvector = 22

Our parameters are slightly smaller than the current default values leading to slightly smaller Dlowast

and Blowast rates as can be seen from the plots in fig 7 Note also that the increased overall amount ofstrangeness in the fragmentation leads to slightly higherDs andBs fractions in better agreement withthe data Uncertainties are however large and some exotic onium states like χc1 ψprime and Υ are notwell described by the default modeling (It is encouraging that at least the multiplicity of Jψ mesonsis well described though a substantial fraction of this likely owes to the feed-down from B decaysand hence does not depend directly on the string-fragmentation model itself)

We also note that it would be desirable to reduce the rate of g rarr bb and Z rarr bbbb events whilethe g rarr cc one appears consistent with the LEP constraints We suspect that this issue may be tiedto the fixed choice of using pperp as the renormalization scale for both gluon emissions and for g rarr qq

13

plusmnD 0D plusmnD plusmns

D X+

cΛ

ccrarrg ψJ c1χ

3685

ψ

X)

rarrlt

ngt o

r B

R(Z

-410

-310

-210

-110

1

10Charm Rates

Pythia 8185Data from HEPDATAPDG

LEP

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn15

00plusmn18

00plusmn17

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

plusmnD 0Dplusmn

D plusmnsD X+

cΛ ccrarrg ψJ c1χ

3685ψ

The

ory

Dat

a

0

05

1

15

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

X)

rarrlt

ngt o

r B

R(Z

-510

-410

-310

-210

-110

1

10Beauty Rates

Pythia 8185Data from HEPDATAPDG

LEP+SLD

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn17

00plusmn23

00plusmn23

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

The

ory

Dat

a0

05

1

15

Figure 7 Hadronic Z decays atradics = 912 GeV Rates and inclusive Z rarr X branching fractions

(normalized to Z rarr hadrons) of particles containing c and b quarks

splittings in the current version of PYTHIA A more natural choice for g rarr qq could be microR prop mqqas used eg in the VINCIA shower model [29]

We now turn to the dynamics of heavy-quark fragmentation focusing mainly on the b quarkFor heavy quarks the Lund fragmentation function is modified due to the (massive) endpoints not

moving along straight lightcones as the string pulls on them they slow down resulting in the stringtracing out a smaller space-time area than it would for massless quarks This modifies the implicationsof the string area law in a manner captured by the so-called Bowler modification of the fragmentationfunction [62]

fmassive(zmQ) prop f(z)

zbrQm2Q

(6)

with mQ the heavy-quark mass b the same universal parameter that appears in the massless fragmen-tation function eq (3) and rQ a tuning parameter which is unity in the original derivation of Bowlerbut can be assigned values different from unity to reduce (rQ rarr 0) or emphasize (rQ gt 1) the effectSince rQ multiplies the heavy-quark mass (squared) it can also be viewed as an effective rescalingof the mass value The net result is a suppression of the region z rarr 1 hence a relative softening ofthe fragmentation spectrum for heavy flavours (relative since the presence of m2

perp in the exponent ofeq (3) still implies an overall harder fragmentation for higher hadron masses)

We emphasize that this is the only fragmentation function that is self-consistent within the string-fragmentation model [33 62] Although a few alternative forms of the fragmentation functions formassive quarks are available in the code we therefore here work only with the Bowler type As forthe massless function the proportionality sign in eq (6) indicates that the function is normalized tounity

In PYTHIA separate rQ parameters are provided for c and b quarks We consider the one for bquarks first Its default value is rb = 067 but this appears to give too hard b fragmentation spectrawhen compared to LEP and SLD data see below For the Monash tune we instead use

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (DELPHI)weak

Bx

Pythia 8181Data from EurPhysJ C71 (2011) 1557

DELPHI PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn16

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (SLD)weak

Bx

Pythia 8181HepData5111d1-x1-y1

SLDPY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn07

00plusmn15

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a06

08

1

12

14

Figure 8 Hadronic Z decays atradics = 912 GeV Momentum (xB) spectra of weakly decaying B

hadrons compared to data from DELPHI [63] (left) and SLD [64] (right)

StringZrFactB = 0855

which produces softer B spectra and simultaneously agrees better with the theoretically preferredvalue (rb = 1)

A comparison to the scaled-momentum spectra (xB = 2|pB|Ecm) of weakly decayingB hadronsfrom both DELPHI [63] and SLD [64] is given in fig 8 (due to small differences between the twomeasured results we choose to show both) The dampening of the hardest part of the spectrum causedby the increase in the rb parameter is visible in the right-most two bins of the distributions and in thesmaller χ2

5 values for the Monash tune The effects of the modification can be further emphasizedby an analysis of the moments of the distribution in which the higher moments are increasinglydominated by the region xB rarr 1 A comparison to a combined LEP analysis of the moments of thexB distribution [63] is given in fig 9 further emphasizing that the high-xB part of the distribution isnow under better control

The reason we have not increased the rb parameter further is that it comes at a price If theB hadrons are taking less energy then there is more energy left over to produce other particlesand the generated multiplicity distribution in b events already exhibits a slightly high tail towardslarge multiplicities Nonetheless since the revised light-flavour fragmentation parameters produce anoverall narrower fragmentation function the end result is still a slight improvement in the multiplicitydistribution also for b events This is illustrated together with the inclusive momentum distributionfor b-tagged events in fig 10 compared to measurements by L3 [26] Interestingly the multiplicitydistribution still appears to be too wide but within the constraints of the present study we were unableto obtain further improvements As a point of speculation we note that the distribution of the numberof partons before hadronization is also quite wide in PYTHIA and this may be playing a role ineffectively setting a lower limit on the width that can be achieved for the hadron-level distribution

Comparisons to L3 event shapes in b-tagged events are collected in appendix B1 (the left columnof plots contains light-flavour tagged event shapes the right column b-tagged ones) In particular the

15

0 10 20 30 40

Mom

ent

0

02

04

06

08 (moments)weakBx

Pythia 8181Data from Eur Phys J C71 (2011) 1557

LEP (combined)PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn10

00plusmn103

00plusmn129

V I

N C

I A

R O

O T

N0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

Figure 9 Hadronic Z decays atradics = 912 GeV Moments of the B fragmentation function com-

pared to a combined analysis of LEP+SLD data by DELPHI [63]

0 20 40

)ch

Pro

babi

lity(

n

-610

-510

-410

-310

-210

-110

1

10

210 Charged Multiplicity (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

06plusmn45

08plusmn64

13plusmn110

V I

N C

I A

R O

O T

(b)chn0 20 40

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

ch d

nch

1n

-510

-410

-310

-210

-110

1

10

210 Charged Momentum Fraction (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn08

00plusmn06 V

I N

C I

A R

O O

T

)| (b)p

|Ln(x0 2 4 6 8

The

ory

Dat

a

06

08

1

12

14

Figure 10 HadronicZ decays atradics = 912 GeV Charged-hadron multiplicity (left) and momentum-

fraction (right) spectra in b-tagged events

16

0 02 04 06 08 1

dx

Dgt

dn

D1

ltn

0

05

1

15

2

25gt01)

E) (x

plusmnx(D

Pythia 8183Data from EurPhysJ C16 (2000) 597

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn14

02plusmn28

02plusmn32

V I

N C

I A

R O

O T

Ex0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

EX02 04 06 08 1

E)

dX

dN

(DZ

had

1N

0

0002

0004

0006

0008

001

0012

0014

0016

ALEPHHerwig++Sherpa

91 GeV ee Z (hadronic)

mcp

lots

cer

nch

41

M e

vent

sge

Riv

et 1

82

Herwig++ 261a Sherpa 141

ALEPH_1999_S4193598

spectrum (particle-level)+-D

02 04 06 08 105

1

15Ratio to ALEPH

Figure 11 The inclusive Dlowast spectrum in hadronic Z decays [55] Left Monash 2013 tune com-pared with default PYTHIA 8 and the Fischer tune Right comparison with HERWIG (dashed) andSHERPA (dotted) from MCPLOTS [25] Note that the plot in the left-hand pane is normalized tounity while the one in the right-hand pane is normalized to the number of hadronic Z decays

Monash tune gives a significant improvement in the soft region of the jet-broadening parameters inb-tagged events while no significant changes are observed for the other event shapes These smallimprovements are presumably a direct consequence of the softening of the b fragmentation functionit is now less likely to find an isolated ultra-hard B hadron

We round off the discussion of heavy-quark fragmentation by noting that a similarly comprehen-sive study of charm-quark fragmentation would be desirable However charm-quark tagged multi-plicity and event-shape data is not available to our knowledge and most of the D meson spectra onHEPDATA concern only specific decay chains (hence depend on the decay modeling) andor are lim-ited to restricted fiducial regions (limiting their generality) Experimentally the cleanest measurementis obtained from Dlowast decays and an inclusive momentum spectrum for Dlowast mesons has been measuredby ALEPH [55] From this distribution shown in fig 11 we determine a value for rc of

StringZrFactC = 132

We note that the low-x part of the Dlowast spectrum originates from g rarr cc shower splittings whilethe high-x tail represents prompt Dlowast production from leading charm in Z rarr cc (see [55] for a nicefigure illustrating this) The intermediate range contains a large component of feed-down from brarr cdecays hence this distribution is also indirectly sensitive to the b-quark sector The previous defaulttune had a harder spectrum for both b- and c-fragmentation leading to an overestimate of the high-xpart of the Dlowast distribution The undershooting at low xDlowast values which remains unchanged in theMonash tune most likely indicates an underproduction of g rarr cc branchings in the shower We notethat such an underproduction may also be reflected in the LHC data on Dlowast production see eg [65]We return to this issue in the discussion of identified particles at LHC section 35

17

0 20 40 60

)ch

Pro

babi

lity(

n

-610

-510

-410

-310

-210

-110

1

10

210 Charged Multiplicity (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn05

01plusmn07

02plusmn21

V I

N C

I A

R O

O T

chn0 20 40 60

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

chgt

dn

ch1

ltn

-310

-210

-110

1

10Charged Momentum Fraction (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn09

00plusmn05

00plusmn05

V I

N C

I A

R O

O T

)|p

|Ln(x0 2 4 6 8

The

ory

Dat

a06

08

1

12

14

Figure 3 Hadronic Z decays atradics = 912 GeV Charged-particle multiplicity (left) and momentum-

fraction (right) spectra

its large σperp value produce a narrower nCh spectrum with in particular a smaller tail towards largemultiplicities All the tunes produce a sensible momentum spectrum The dip around |ln(x)| sim 55corresponds to the extreme soft-pion tail with momenta at or below ΛQCD We did not find it possibleto remove it by retuning since a smaller b parameter would generate significantly too high particlemultiplicities and a smaller σperp would lead to conflict with the event-shape distributions

A zoom on the high-momentum tail is provided by the left-hand plot in fig 4 which shows acomparison on a linear momentum scale to a measurement by ALEPH [38] (now including Z rarr bbevents as well as light-flavour ones) All the tunes exhibit a mild overshooting of the data in the region05 lt xp lt 08 corresponding to 015 lt | ln(x)| lt 07 in which no similar excess was present inthe L3 comparison We therefore do not regard this as a significant issue6 but note that the excess issomewhat milder in the Fischer and Monash tunes

Further information to elucidate the structure of the momentum distribution is provided by theplot in the right-hand pane of fig 4 which uses the same |ln(x)| axis as the right-hand plot in fig 3and shows the relative particle composition in the Monash tune for each histogram bin (The categoryldquoOtherrdquo contains electrons and muons from weak decays) An interesting observation is that therelatively harder spectrum of Kaons implies that for the highest-momentum bins the charged tracksare made up of an almost exactly equal mixture of Kaons and pions despite Kaons on average onlymaking up about 10 of the charged multiplicity

6One might worry whether the effect could be due solely to the Z rarr bb events which are only present in the ALEPHmeasurement and if so whether this could indicate a significant mismodeling of the momentum distribution in b eventsHowever as we show below in the section on b fragmentation the charged-particle momentum distribution in b-taggedevents shows no excess in that region (in fact it shows an undershooting)

7

0 02 04 06 08 1

pd

xch

gt d

nch

1lt

n

-410

-310

-210

-110

1

10Charged Momentum Fraction

Pythia 8183Data from Barate et al Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn14

01plusmn08

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

IDgt

dn

ch1

ltn

0

02

04

06

08

1

12 Particle Composition vs Lnx (udsc)

Pythia 8183

plusmnπplusmnKplusmnp

Other

V I

N C

I A

R O

O T

)|p

|Ln(x0 2 4 6 8

Rat

io06

08

1

12

14

Figure 4 Hadronic Z decays atradics = 912 GeV Charged-particle momentum fraction xp on a linear

scale (left) and relative particle composition (right) for the log-scale distribution shown in fig 3

22 Identified Particles

Continuing on the topic of identified particles we note that the extraction of the a and b parametersfrom the inclusive charged-particle distributions is made slightly more complicated by the fact thatnot all observed particles are ldquoprimaryrdquo (originating directly from string breaks) many lower-massparticles are ldquosecondariesrdquo produced by prompt decays of more massive states (eg ρrarr ππ) whoserelative rates and decay kinematics therefore influence the spectra In the e+eminus measurements weinclude here particles with cτ lt 100 mm were treated as unstable hence leading to secondaries (Forcompleteness we note that the equivalent standard cut at the LHC is normally 10 mm)

The particle composition in PYTHIA 8 was already tuned to a set of reference values provided bythe PDG [39] and the default parameters do reasonably well certainly for the most copiously pro-duced sources of secondaries Nonetheless we have here reoptimized the flavour-selection parametersof the string-fragmentation model using a slightly different set of reference data combining the PDGtables with information provided directly by the LEP experiments via HEPDATA [1] Based on thelevel of agreement or disagreement between different measurements of the same particles we havemade our own judgement as to the level of uncertainty for a few of the particles as follows (Unlessotherwise stated we use the value from the PDG Particles and antiparticles are implicitly summedover and secondaries from particles with cτ lt 100 mm are included)

bull The various LEP and SLD measurements of the φ meson rate on HEPDATA are barely com-patible Eg OPAL [40] reports 〈nφ〉 = 0091 plusmn 0002 plusmn 0003 while ALEPH [38] quotes〈nφ〉 = 0122 plusmn 0004 plusmn 0008 a difference of 30 with uncertainties supposedly less than10 DELPHI [41] and SLD [42] fall in between The PDG value is 〈nφ〉 = 00963 plusmn 0003ie with a combined uncertainty of just 3 We choose to inflate the systematic uncertaintiesand arrive at 〈nφ〉 = 0101plusmn 0007

8

bull For Λ production we use the most precise of the LEP measurements by OPAL7 [43] 〈nΛ〉 =0374plusmn 0002plusmn 0010 about 5 lower than the corresponding PDG value

bull For Σplusmn baryons we use a combination of the two most recent LEP measurements by L3 [44]for Σ+ + Σ

minus and by DELPHI [45] for Σminus + Σ+ for an estimated 〈nΣplusmn〉 = 0195 plusmn 0018

which is roughly 10 higher than the PDG value

bull For Σ0 baryons we use the most recent measurement by L3 [44] 〈nΣ0〉 = 0095 plusmn 0015 plusmn0013 this is about 20 larger than the PDG value The L3 paper comments on their relativelyhigh value by noting that L3 had the best coverage for low-momentum baryons hence smallermodel-dependent correction factors

bull For ∆++ baryons there are only two measurements in HEPDATA [4647] which are mutuallydiscrepant by about 2σ The DELPHI measurement is nominally the most precise but OPALgives a much more serious discussion of systematic uncertainties We choose to increase theestimated extrapolation errors of the DELPHI measurement by 50 and obtain a weighted av-erage8 of 〈n∆++〉 = 009plusmn0017 5 larger than the PDG value with a 20 larger uncertainty

bull For Σlowast the three measurements on HEPDATA [38 43 48] are likewise discrepant by 2σ minus 3σWe inflate the systematic uncertainties and arrive at 〈nΣlowastplusmn〉 = 0050 plusmn 0006 which is again5 higher than the PDG value with twice as much uncertainty

bull The measurements for Ξplusmn are in good agreement [38 43 48] with a weighted average of〈nΞplusmn〉 = 00266plusmn 00012 slightly larger than the PDG value

bull For Ξlowast0 however the DELPHI measurement [48] gives a far lower number than the OPAL [43]and ALEPH [38] ones and the weighted average differs by more than 10 from the PDGvalue despite the latter claiming an uncertainty smaller than 10 Our weighted average is〈nΞlowast0〉 = 00059plusmn 00012

bull Finally for the Ω baryon the DELPHI [49] and OPAL [43] measurements are in agreementand we use the PDG value 〈nΩ〉 = 00016plusmn 00003

We summarize the constraints on the light-meson and baryon rates used here in tab 1 Note that weexpress them as percentages of the average charged multiplicity

〈nCh〉 = 207 (5)

obtained as a weighted average over MARK-II [50] ALEPH [38] DELPHI [51] OPAL [52] andL3 [53] measurements

The light-flavour-selection parameters for the Monash tune are (see appendix A for a comparisonof these values to the current default ones)

Light-Meson SectorStringFlavProbStoUD = 0217StringFlavmesonUDvector = 05StringFlavmesonSvector = 055

7We note that HEPDATA incorrectly gives the systematic error as 0002 while the value in the OPAL paper is 0010 [43]This has been communicated to the HEPDATA maintainers

8Even with the inflated error the uncertainty on the DELPHI measurement is still less than a third that of the OPAL oneDELPHI therefore still dominates the average

9

Mesons Our Reference Our〈n〉 〈nCh〉 Value (in ) Source

π+ + πminus 822 plusmn09 Pπ0 455 plusmn15 PK+ +Kminus 108 plusmn03 Pη 506 plusmn038 Pηprime 073 plusmn009 Pρ+ + ρminus 116 plusmn21 Pρ0 595 plusmn047 PKlowast+ +Klowastminus 345 plusmn028 Pω 490 plusmn031 Pφ 049 plusmn0035 ADOS

Baryons Our Reference Our〈n〉 〈nCh〉 Value (in ) Source

p+ p 507 plusmn016 PΛ + Λ 181 plusmn032 OΣ+ + Σminus + Σ+ + Σminus 0942 plusmn0087 DLΣ0 + Σ0 0459 plusmn0096 L∆++ + ∆minusminus 0434 plusmn0082 DOΣlowast+ + Σlowastminus + Σlowast+ + Σlowastminus 0242 plusmn0029 ADOΞ+ + Ξminus 0125 plusmn00050 ADOΞlowast0 + Ξlowast0 00285 plusmn00058 ADOΩminus + Ω+ 00077 plusmn00015 P

Table 1 Hadronic Z decays atradics = 912 GeV Measured rates of light-flavour mesons and baryons

expressed as percentages of the average charged-particle multiplicity as used in this work Multiplythe numbers by 207100 to translate the percentages to corresponding production rates Source labelsindicate A (ALEPH) D (DELPHI) L (L3) O (OPAL) S (SLD) P (PDG)

StringFlavetaSup = 060StringFlavetaPrimeSup = 012

Baryon SectorStringFlavprobQQtoQ = 0081StringFlavprobSQtoQQ = 0915StringFlavprobQQ1toQQ0 = 00275StringFlavsuppressLeadingB = offStringFlavpopcornSpair = 09StringFlavpopcornSmeson = 05

Since strange-particle and baryon spectra at the LHC exhibit interesting differences with respectto existing models (see below) we paid particular attention to first obtaining a good description ofthese sectors in e+eminus collisions Specifically we have increased the overall amount of strangenessby about 10 while decreasing the rate of vector mesons by a similar amount9 (these two effectslargely cancel for Klowast) This improves the total Kplusmn ρ0 ω Λ Ξlowast and Ω yields on our combined LEPestimates discussed above The price is that we now overshoot the measured rate of Ξplusmn baryons by10 The resulting identified-meson and -baryon rates expressed as fractions of the average charged-particle multiplicity are plotted in fig 5 Note that the last four bins of the meson plot and the thirdand fourth bins of the baryon plot are not 〈n〉 〈nCh〉 fractions but rather the KlowastK φKlowast φKφπ Λp and ΛK ratios respectively Note also that section 4 on energy scaling below includes acomparison to the average Kaon and Lambda rates as a function of ee CM energy (fig 25)

To provide further information on identified particles we include a limited comparison to momen-tum spectra of Kplusmn p Λ and Ξplusmn which are the states of most immediate interest in the context ofsimilar comparisons now being made at LHC The spectra of Kplusmn mesons and Λ baryons are shownin fig 6 while the pplusmn and Ξplusmn spectra are relegated to appendix B2 The modified parameters of theMonash tune have virtually no effect on the Kaon distribution which still exhibits too many very softKaons (with ln(x) lt minus4 corresponding to x lt 0018 so momentum scales below sim 1 GeV) while

9For reference the current default value of ProbStoUD is 019 while ours is 0217 The increased value also improvesthe agreement with the Ds and Bs rates see section 23 The default values of mesonUDvector and mesonSvectorare 062 and 0725 respectively while ours are 05 and 055

10

plusmnπ 0π plusmnK η η plusmnρ 0ρ plusmnK ω φKK-

RKφ

RK-φ

R-πφ

R

gtch

ltnltngt

-310

-210

-110

1

10Meson Fractions

Pythia 8183Data from PDGHEPDATA

LEP + SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn06

00plusmn12

00plusmn12

V I

N C

I A

R O

O T

plusmnπ 0π plusmnK η η plusmnρ 0ρ plusmnK ω φKK-

RKφ

RK-φ

R-πφ

R

The

ory

Dat

a

06

08

1

12

14

p ΛpΛ

RKΛ

R plusmnΣ 0Σ ++∆ Σ plusmnΞ 0Ξ Ω

gtch

ltnltngt

-410

-310

-210

-110

1Baryon Fractions

Pythia 8183Data from PDGHEPDATA

LEP PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn11

00plusmn22

00plusmn22

V I

N C

I A

R O

O T

p ΛpΛ

RKΛ

R plusmnΣ 0Σ ++∆ Σ plusmnΞ 0Ξ Ω

The

ory

Dat

a

06

08

1

12

14

Figure 5 Hadronic Z decays atradics = 912 GeV Identified-meson and -baryon rates expressed as

fractions of the average charged-particle multiplicity

-4 -2 0

dln

(x)

Kgt

dn

K1

ltn

-310

-210

-110

1

10

) (Combined)plusmnx(K

Pythia 8183Data from ZPC66(1995)355 ZPC63(1994)181 EPJC5(1998)585

LEP (A+D+O)PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn16

00plusmn14

01plusmn19

V I

N C

I A

R O

O T

)p

ln(x-4 -2 0

The

ory

Dat

a

06

08

1

12

14

0 1 2 3 4 5

ξd

Λgt

dn

Λ1

ltn

0

02

04

06)]|0Λ|Ln[x(

Pythia 8183Data from EPJ C16 (2000) 613

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn08

01plusmn15

01plusmn12

V I

N C

I A

R O

O T

pξ

0 1 2 3 4 5

The

ory

Dat

a

06

08

1

12

14

Figure 6 Hadronic Z decays atradics = 912 GeV Kplusmn and Λ momentum-fraction spectra

11

the significant increase in the value of aExtraDiquark from 05 (Default) to 097 (Monash cf sec-tion 21) produces a desirable suppression of very hard Λ baryons The corresponding change in themeasured parts of the p and Ξplusmn spectra (cf appendix B2) are small compared with the experimentaluncertainties

It is interesting however to note that all of these spectra indicate or are at least consistent with amodelling excess of soft identified-particle production below ln(x) sim minus45 corresponding to absolutemomentum scales around 500 MeV while we recall that the inclusive ln(x) spectrum above showedan underproduction around ln(x) sim minus55 Within the constraints of the current theory model wehave not managed to find a way to mitigate these features while remaining consistent with the rest ofthe data Nonetheless it should be mentioned that these observations could have relevance also in thecontext of understanding identified-particle spectra at LHC a possibility which to our knowledge hasso far been ignored

23 Heavy-Quark Fragmentation

Similarly to above we first discuss the inclusive rates of hadrons containing heavy quarks before wediscuss their spectra Unfortunately there are also here substantial disagreements between differentpieces of information We have made the following choices

bull ForD mesons the average Dplusmn rate given in sec 46 of the PDG (0175) is equal to the inclusivebranching fraction for Z rarr DplusmnX given in the Z boson summary table in the same Review(after normalizing the latter to the hadronic Z fraction of 6991 [39]) However the formerought to be substantially larger given that some Z rarr cc events will contain two Dplusmn mesons(counting once in the Z rarr DplusmnX branching fraction but twice in the average Dplusmn multiplicity)We therefore here use a measurement by ALEPH [54] to fix the Dplusmn and D0 rates resulting ina reference value for the average Dplusmn multiplicity almost twice as large as that given by sec 46in the PDG

bull For Λ+c the average multiplicity given in sec 46 of the PDG is twice as large as that indicated

by the branching fraction BR(Z rarr Λ+c X) in the Z boson summary table in the same Review

We here use the branching from the Z boson summary table as our constraint on the Λ+c rate

normalized to the total branching fraction BR(Z rarr hadrons)

bull We also include the average rate of g rarr cc splittings obtained by combining an ALEPH [55]and an OPAL measurement [56] but with an additional 10 systematic uncertainty added toboth measurements to account for possibly larger mismodeling effects in the correction fac-tors [57 58]

bull For B particles we use the quite precise inclusive Z rarr B+X branching fraction from the Zboson summary in the PDG

bull We also use the sum of Bplusmn and B0(B0) in sec 46 of the PDG10

bull TheB0s multiplicity given in sec 46 of the PDG (0057plusmn0013) is more than twice the inclusive

BR(Z rarr B0sX)BR(Z rarr hadrons) branching fraction (00227 plusmn 00019) quoted in the Z

10Note that we have a factor 2 relative to the PDG since it appears the PDG quotes the average rather than the sum Notealso that all the average B meson multiplicities in sec 46 of the PDG are accompanied by a note ldquo(d)rdquo stating that the SMB(Z rarr bb) = 0217 was used for the normalization For completeness the reader should be aware that this is the fractionnormalized to hadronic Z decays the branching fraction relative to all Z decays is 0151 [39]

12

Charm Our Reference Our〈n〉 or BR Value Source

D+ +Dminus 0251 plusmn0047 AD0 + D0 0518 plusmn0063 ADlowast+ +Dlowastminus 0194 plusmn00057 PD+

s +Dminuss 0131 plusmn0021 PBR(Z rarr Λ+

c X) 00220 plusmn00047 ZBR(Z rarr X + cc) 00306 plusmn00047 AOJψ 00052 plusmn00004 Pχc1 00041 plusmn00011 Pψprime 00023 plusmn00004 P

Beauty Our Reference Our〈n〉 or BR Value Source

BR(Z rarr B+X) 0087 plusmn0002 ZB+ +B0 + B0 +Bminus 0330 plusmn0052 PBlowastu +Blowastd +Blowasts 0288 plusmn0026 PBR(Z rarr B0

sX) 00227 plusmn00019 ZBR(Z rarr BbaryonX) 00197 plusmn00032 ZBR(Z rarr X + bb) 000288 plusmn000061 ADSBR(Z rarr bbbbX) 000051 plusmn000019 ZΥ (times10) 00014 plusmn00007 P

Table 2 Hadronic Z decays atradics = MZ Measured rates and inclusive branching fractions of

particles containing c and b quarks as used in this work Note the branching fractions are normalizedto Z rarr hadrons and hence should be interpreted as eg BR(Z rarr B+X)BR(Z rarr hadrons)Note 2 the sum over Blowast states includes both particles and anti-particles Note 3 the Υ rate ismultiplied by a factor 10 Source labels indicate A (ALEPH) D (DELPHI) O (OPAL) P (PDGsection 46) S (SLD) Z (PDG Z Boson Summary Table)

boson summary table We find these two numbers difficult to reconcile and choose to use theinclusive BR(Z rarr B0

sX)BR(Z rarr hadrons) branching fraction as our main constraint

bull We also include the inclusive branching fractions for B-baryons (summed over baryons andantibaryons) the rate of g rarr bb splittings obtained by combining ALEPH [59] DELPHI [60]and SLD [61] measurements (including an additional 10 systematic to account for largerpossible mismodeling effects in the correction factors [57 58]) and the rate of Z rarr bbbb fromthe PDG Z boson summary table [39]

Our constraints on the heavy-quark particle rates are summarized in tab 2 Comparisons to these ratesare shown in fig 7 now without normalizing to the average charged-particle multiplicity Given thatmost of the c and b quarks come directly from Z rarr cc and Z rarr bb decays there is not a lot of roomfor tuning to these numbers apart from the relative rates of vector mesons vs pseudoscalars which iscontrolled by the parameters

Heavy MesonsStringFlavmesonCvector = 088StringFlavmesonBvector = 22

Our parameters are slightly smaller than the current default values leading to slightly smaller Dlowast

and Blowast rates as can be seen from the plots in fig 7 Note also that the increased overall amount ofstrangeness in the fragmentation leads to slightly higherDs andBs fractions in better agreement withthe data Uncertainties are however large and some exotic onium states like χc1 ψprime and Υ are notwell described by the default modeling (It is encouraging that at least the multiplicity of Jψ mesonsis well described though a substantial fraction of this likely owes to the feed-down from B decaysand hence does not depend directly on the string-fragmentation model itself)

We also note that it would be desirable to reduce the rate of g rarr bb and Z rarr bbbb events whilethe g rarr cc one appears consistent with the LEP constraints We suspect that this issue may be tiedto the fixed choice of using pperp as the renormalization scale for both gluon emissions and for g rarr qq

13

plusmnD 0D plusmnD plusmns

D X+

cΛ

ccrarrg ψJ c1χ

3685

ψ

X)

rarrlt

ngt o

r B

R(Z

-410

-310

-210

-110

1

10Charm Rates

Pythia 8185Data from HEPDATAPDG

LEP

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn15

00plusmn18

00plusmn17

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

plusmnD 0Dplusmn

D plusmnsD X+

cΛ ccrarrg ψJ c1χ

3685ψ

The

ory

Dat

a

0

05

1

15

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

X)

rarrlt

ngt o

r B

R(Z

-510

-410

-310

-210

-110

1

10Beauty Rates

Pythia 8185Data from HEPDATAPDG

LEP+SLD

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn17

00plusmn23

00plusmn23

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

The

ory

Dat

a0

05

1

15

Figure 7 Hadronic Z decays atradics = 912 GeV Rates and inclusive Z rarr X branching fractions

(normalized to Z rarr hadrons) of particles containing c and b quarks

splittings in the current version of PYTHIA A more natural choice for g rarr qq could be microR prop mqqas used eg in the VINCIA shower model [29]

We now turn to the dynamics of heavy-quark fragmentation focusing mainly on the b quarkFor heavy quarks the Lund fragmentation function is modified due to the (massive) endpoints not

moving along straight lightcones as the string pulls on them they slow down resulting in the stringtracing out a smaller space-time area than it would for massless quarks This modifies the implicationsof the string area law in a manner captured by the so-called Bowler modification of the fragmentationfunction [62]

fmassive(zmQ) prop f(z)

zbrQm2Q

(6)

with mQ the heavy-quark mass b the same universal parameter that appears in the massless fragmen-tation function eq (3) and rQ a tuning parameter which is unity in the original derivation of Bowlerbut can be assigned values different from unity to reduce (rQ rarr 0) or emphasize (rQ gt 1) the effectSince rQ multiplies the heavy-quark mass (squared) it can also be viewed as an effective rescalingof the mass value The net result is a suppression of the region z rarr 1 hence a relative softening ofthe fragmentation spectrum for heavy flavours (relative since the presence of m2

perp in the exponent ofeq (3) still implies an overall harder fragmentation for higher hadron masses)

We emphasize that this is the only fragmentation function that is self-consistent within the string-fragmentation model [33 62] Although a few alternative forms of the fragmentation functions formassive quarks are available in the code we therefore here work only with the Bowler type As forthe massless function the proportionality sign in eq (6) indicates that the function is normalized tounity

In PYTHIA separate rQ parameters are provided for c and b quarks We consider the one for bquarks first Its default value is rb = 067 but this appears to give too hard b fragmentation spectrawhen compared to LEP and SLD data see below For the Monash tune we instead use

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (DELPHI)weak

Bx

Pythia 8181Data from EurPhysJ C71 (2011) 1557

DELPHI PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn16

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (SLD)weak

Bx

Pythia 8181HepData5111d1-x1-y1

SLDPY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn07

00plusmn15

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a06

08

1

12

14

Figure 8 Hadronic Z decays atradics = 912 GeV Momentum (xB) spectra of weakly decaying B

hadrons compared to data from DELPHI [63] (left) and SLD [64] (right)

StringZrFactB = 0855

which produces softer B spectra and simultaneously agrees better with the theoretically preferredvalue (rb = 1)

A comparison to the scaled-momentum spectra (xB = 2|pB|Ecm) of weakly decayingB hadronsfrom both DELPHI [63] and SLD [64] is given in fig 8 (due to small differences between the twomeasured results we choose to show both) The dampening of the hardest part of the spectrum causedby the increase in the rb parameter is visible in the right-most two bins of the distributions and in thesmaller χ2

5 values for the Monash tune The effects of the modification can be further emphasizedby an analysis of the moments of the distribution in which the higher moments are increasinglydominated by the region xB rarr 1 A comparison to a combined LEP analysis of the moments of thexB distribution [63] is given in fig 9 further emphasizing that the high-xB part of the distribution isnow under better control

The reason we have not increased the rb parameter further is that it comes at a price If theB hadrons are taking less energy then there is more energy left over to produce other particlesand the generated multiplicity distribution in b events already exhibits a slightly high tail towardslarge multiplicities Nonetheless since the revised light-flavour fragmentation parameters produce anoverall narrower fragmentation function the end result is still a slight improvement in the multiplicitydistribution also for b events This is illustrated together with the inclusive momentum distributionfor b-tagged events in fig 10 compared to measurements by L3 [26] Interestingly the multiplicitydistribution still appears to be too wide but within the constraints of the present study we were unableto obtain further improvements As a point of speculation we note that the distribution of the numberof partons before hadronization is also quite wide in PYTHIA and this may be playing a role ineffectively setting a lower limit on the width that can be achieved for the hadron-level distribution

Comparisons to L3 event shapes in b-tagged events are collected in appendix B1 (the left columnof plots contains light-flavour tagged event shapes the right column b-tagged ones) In particular the

15

0 10 20 30 40

Mom

ent

0

02

04

06

08 (moments)weakBx

Pythia 8181Data from Eur Phys J C71 (2011) 1557

LEP (combined)PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn10

00plusmn103

00plusmn129

V I

N C

I A

R O

O T

N0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

Figure 9 Hadronic Z decays atradics = 912 GeV Moments of the B fragmentation function com-

pared to a combined analysis of LEP+SLD data by DELPHI [63]

0 20 40

)ch

Pro

babi

lity(

n

-610

-510

-410

-310

-210

-110

1

10

210 Charged Multiplicity (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

06plusmn45

08plusmn64

13plusmn110

V I

N C

I A

R O

O T

(b)chn0 20 40

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

ch d

nch

1n

-510

-410

-310

-210

-110

1

10

210 Charged Momentum Fraction (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn08

00plusmn06 V

I N

C I

A R

O O

T

)| (b)p

|Ln(x0 2 4 6 8

The

ory

Dat

a

06

08

1

12

14

Figure 10 HadronicZ decays atradics = 912 GeV Charged-hadron multiplicity (left) and momentum-

fraction (right) spectra in b-tagged events

16

0 02 04 06 08 1

dx

Dgt

dn

D1

ltn

0

05

1

15

2

25gt01)

E) (x

plusmnx(D

Pythia 8183Data from EurPhysJ C16 (2000) 597

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn14

02plusmn28

02plusmn32

V I

N C

I A

R O

O T

Ex0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

EX02 04 06 08 1

E)

dX

dN

(DZ

had

1N

0

0002

0004

0006

0008

001

0012

0014

0016

ALEPHHerwig++Sherpa

91 GeV ee Z (hadronic)

mcp

lots

cer

nch

41

M e

vent

sge

Riv

et 1

82

Herwig++ 261a Sherpa 141

ALEPH_1999_S4193598

spectrum (particle-level)+-D

02 04 06 08 105

1

15Ratio to ALEPH

Figure 11 The inclusive Dlowast spectrum in hadronic Z decays [55] Left Monash 2013 tune com-pared with default PYTHIA 8 and the Fischer tune Right comparison with HERWIG (dashed) andSHERPA (dotted) from MCPLOTS [25] Note that the plot in the left-hand pane is normalized tounity while the one in the right-hand pane is normalized to the number of hadronic Z decays

Monash tune gives a significant improvement in the soft region of the jet-broadening parameters inb-tagged events while no significant changes are observed for the other event shapes These smallimprovements are presumably a direct consequence of the softening of the b fragmentation functionit is now less likely to find an isolated ultra-hard B hadron

We round off the discussion of heavy-quark fragmentation by noting that a similarly comprehen-sive study of charm-quark fragmentation would be desirable However charm-quark tagged multi-plicity and event-shape data is not available to our knowledge and most of the D meson spectra onHEPDATA concern only specific decay chains (hence depend on the decay modeling) andor are lim-ited to restricted fiducial regions (limiting their generality) Experimentally the cleanest measurementis obtained from Dlowast decays and an inclusive momentum spectrum for Dlowast mesons has been measuredby ALEPH [55] From this distribution shown in fig 11 we determine a value for rc of

StringZrFactC = 132

We note that the low-x part of the Dlowast spectrum originates from g rarr cc shower splittings whilethe high-x tail represents prompt Dlowast production from leading charm in Z rarr cc (see [55] for a nicefigure illustrating this) The intermediate range contains a large component of feed-down from brarr cdecays hence this distribution is also indirectly sensitive to the b-quark sector The previous defaulttune had a harder spectrum for both b- and c-fragmentation leading to an overestimate of the high-xpart of the Dlowast distribution The undershooting at low xDlowast values which remains unchanged in theMonash tune most likely indicates an underproduction of g rarr cc branchings in the shower We notethat such an underproduction may also be reflected in the LHC data on Dlowast production see eg [65]We return to this issue in the discussion of identified particles at LHC section 35

17

0 02 04 06 08 1

pd

xch

gt d

nch

1lt

n

-410

-310

-210

-110

1

10Charged Momentum Fraction

Pythia 8183Data from Barate et al Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn14

01plusmn08

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

IDgt

dn

ch1

ltn

0

02

04

06

08

1

12 Particle Composition vs Lnx (udsc)

Pythia 8183

plusmnπplusmnKplusmnp

Other

V I

N C

I A

R O

O T

)|p

|Ln(x0 2 4 6 8

Rat

io06

08

1

12

14

Figure 4 Hadronic Z decays atradics = 912 GeV Charged-particle momentum fraction xp on a linear

scale (left) and relative particle composition (right) for the log-scale distribution shown in fig 3

22 Identified Particles

Continuing on the topic of identified particles we note that the extraction of the a and b parametersfrom the inclusive charged-particle distributions is made slightly more complicated by the fact thatnot all observed particles are ldquoprimaryrdquo (originating directly from string breaks) many lower-massparticles are ldquosecondariesrdquo produced by prompt decays of more massive states (eg ρrarr ππ) whoserelative rates and decay kinematics therefore influence the spectra In the e+eminus measurements weinclude here particles with cτ lt 100 mm were treated as unstable hence leading to secondaries (Forcompleteness we note that the equivalent standard cut at the LHC is normally 10 mm)

The particle composition in PYTHIA 8 was already tuned to a set of reference values provided bythe PDG [39] and the default parameters do reasonably well certainly for the most copiously pro-duced sources of secondaries Nonetheless we have here reoptimized the flavour-selection parametersof the string-fragmentation model using a slightly different set of reference data combining the PDGtables with information provided directly by the LEP experiments via HEPDATA [1] Based on thelevel of agreement or disagreement between different measurements of the same particles we havemade our own judgement as to the level of uncertainty for a few of the particles as follows (Unlessotherwise stated we use the value from the PDG Particles and antiparticles are implicitly summedover and secondaries from particles with cτ lt 100 mm are included)

bull The various LEP and SLD measurements of the φ meson rate on HEPDATA are barely com-patible Eg OPAL [40] reports 〈nφ〉 = 0091 plusmn 0002 plusmn 0003 while ALEPH [38] quotes〈nφ〉 = 0122 plusmn 0004 plusmn 0008 a difference of 30 with uncertainties supposedly less than10 DELPHI [41] and SLD [42] fall in between The PDG value is 〈nφ〉 = 00963 plusmn 0003ie with a combined uncertainty of just 3 We choose to inflate the systematic uncertaintiesand arrive at 〈nφ〉 = 0101plusmn 0007

8

bull For Λ production we use the most precise of the LEP measurements by OPAL7 [43] 〈nΛ〉 =0374plusmn 0002plusmn 0010 about 5 lower than the corresponding PDG value

bull For Σplusmn baryons we use a combination of the two most recent LEP measurements by L3 [44]for Σ+ + Σ

minus and by DELPHI [45] for Σminus + Σ+ for an estimated 〈nΣplusmn〉 = 0195 plusmn 0018

which is roughly 10 higher than the PDG value

bull For Σ0 baryons we use the most recent measurement by L3 [44] 〈nΣ0〉 = 0095 plusmn 0015 plusmn0013 this is about 20 larger than the PDG value The L3 paper comments on their relativelyhigh value by noting that L3 had the best coverage for low-momentum baryons hence smallermodel-dependent correction factors

bull For ∆++ baryons there are only two measurements in HEPDATA [4647] which are mutuallydiscrepant by about 2σ The DELPHI measurement is nominally the most precise but OPALgives a much more serious discussion of systematic uncertainties We choose to increase theestimated extrapolation errors of the DELPHI measurement by 50 and obtain a weighted av-erage8 of 〈n∆++〉 = 009plusmn0017 5 larger than the PDG value with a 20 larger uncertainty

bull For Σlowast the three measurements on HEPDATA [38 43 48] are likewise discrepant by 2σ minus 3σWe inflate the systematic uncertainties and arrive at 〈nΣlowastplusmn〉 = 0050 plusmn 0006 which is again5 higher than the PDG value with twice as much uncertainty

bull The measurements for Ξplusmn are in good agreement [38 43 48] with a weighted average of〈nΞplusmn〉 = 00266plusmn 00012 slightly larger than the PDG value

bull For Ξlowast0 however the DELPHI measurement [48] gives a far lower number than the OPAL [43]and ALEPH [38] ones and the weighted average differs by more than 10 from the PDGvalue despite the latter claiming an uncertainty smaller than 10 Our weighted average is〈nΞlowast0〉 = 00059plusmn 00012

bull Finally for the Ω baryon the DELPHI [49] and OPAL [43] measurements are in agreementand we use the PDG value 〈nΩ〉 = 00016plusmn 00003

We summarize the constraints on the light-meson and baryon rates used here in tab 1 Note that weexpress them as percentages of the average charged multiplicity

〈nCh〉 = 207 (5)

obtained as a weighted average over MARK-II [50] ALEPH [38] DELPHI [51] OPAL [52] andL3 [53] measurements

The light-flavour-selection parameters for the Monash tune are (see appendix A for a comparisonof these values to the current default ones)

Light-Meson SectorStringFlavProbStoUD = 0217StringFlavmesonUDvector = 05StringFlavmesonSvector = 055

7We note that HEPDATA incorrectly gives the systematic error as 0002 while the value in the OPAL paper is 0010 [43]This has been communicated to the HEPDATA maintainers

8Even with the inflated error the uncertainty on the DELPHI measurement is still less than a third that of the OPAL oneDELPHI therefore still dominates the average

9

Mesons Our Reference Our〈n〉 〈nCh〉 Value (in ) Source

π+ + πminus 822 plusmn09 Pπ0 455 plusmn15 PK+ +Kminus 108 plusmn03 Pη 506 plusmn038 Pηprime 073 plusmn009 Pρ+ + ρminus 116 plusmn21 Pρ0 595 plusmn047 PKlowast+ +Klowastminus 345 plusmn028 Pω 490 plusmn031 Pφ 049 plusmn0035 ADOS

Baryons Our Reference Our〈n〉 〈nCh〉 Value (in ) Source

p+ p 507 plusmn016 PΛ + Λ 181 plusmn032 OΣ+ + Σminus + Σ+ + Σminus 0942 plusmn0087 DLΣ0 + Σ0 0459 plusmn0096 L∆++ + ∆minusminus 0434 plusmn0082 DOΣlowast+ + Σlowastminus + Σlowast+ + Σlowastminus 0242 plusmn0029 ADOΞ+ + Ξminus 0125 plusmn00050 ADOΞlowast0 + Ξlowast0 00285 plusmn00058 ADOΩminus + Ω+ 00077 plusmn00015 P

Table 1 Hadronic Z decays atradics = 912 GeV Measured rates of light-flavour mesons and baryons

expressed as percentages of the average charged-particle multiplicity as used in this work Multiplythe numbers by 207100 to translate the percentages to corresponding production rates Source labelsindicate A (ALEPH) D (DELPHI) L (L3) O (OPAL) S (SLD) P (PDG)

StringFlavetaSup = 060StringFlavetaPrimeSup = 012

Baryon SectorStringFlavprobQQtoQ = 0081StringFlavprobSQtoQQ = 0915StringFlavprobQQ1toQQ0 = 00275StringFlavsuppressLeadingB = offStringFlavpopcornSpair = 09StringFlavpopcornSmeson = 05

Since strange-particle and baryon spectra at the LHC exhibit interesting differences with respectto existing models (see below) we paid particular attention to first obtaining a good description ofthese sectors in e+eminus collisions Specifically we have increased the overall amount of strangenessby about 10 while decreasing the rate of vector mesons by a similar amount9 (these two effectslargely cancel for Klowast) This improves the total Kplusmn ρ0 ω Λ Ξlowast and Ω yields on our combined LEPestimates discussed above The price is that we now overshoot the measured rate of Ξplusmn baryons by10 The resulting identified-meson and -baryon rates expressed as fractions of the average charged-particle multiplicity are plotted in fig 5 Note that the last four bins of the meson plot and the thirdand fourth bins of the baryon plot are not 〈n〉 〈nCh〉 fractions but rather the KlowastK φKlowast φKφπ Λp and ΛK ratios respectively Note also that section 4 on energy scaling below includes acomparison to the average Kaon and Lambda rates as a function of ee CM energy (fig 25)

To provide further information on identified particles we include a limited comparison to momen-tum spectra of Kplusmn p Λ and Ξplusmn which are the states of most immediate interest in the context ofsimilar comparisons now being made at LHC The spectra of Kplusmn mesons and Λ baryons are shownin fig 6 while the pplusmn and Ξplusmn spectra are relegated to appendix B2 The modified parameters of theMonash tune have virtually no effect on the Kaon distribution which still exhibits too many very softKaons (with ln(x) lt minus4 corresponding to x lt 0018 so momentum scales below sim 1 GeV) while

9For reference the current default value of ProbStoUD is 019 while ours is 0217 The increased value also improvesthe agreement with the Ds and Bs rates see section 23 The default values of mesonUDvector and mesonSvectorare 062 and 0725 respectively while ours are 05 and 055

10

plusmnπ 0π plusmnK η η plusmnρ 0ρ plusmnK ω φKK-

RKφ

RK-φ

R-πφ

R

gtch

ltnltngt

-310

-210

-110

1

10Meson Fractions

Pythia 8183Data from PDGHEPDATA

LEP + SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn06

00plusmn12

00plusmn12

V I

N C

I A

R O

O T

plusmnπ 0π plusmnK η η plusmnρ 0ρ plusmnK ω φKK-

RKφ

RK-φ

R-πφ

R

The

ory

Dat

a

06

08

1

12

14

p ΛpΛ

RKΛ

R plusmnΣ 0Σ ++∆ Σ plusmnΞ 0Ξ Ω

gtch

ltnltngt

-410

-310

-210

-110

1Baryon Fractions

Pythia 8183Data from PDGHEPDATA

LEP PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn11

00plusmn22

00plusmn22

V I

N C

I A

R O

O T

p ΛpΛ

RKΛ

R plusmnΣ 0Σ ++∆ Σ plusmnΞ 0Ξ Ω

The

ory

Dat

a

06

08

1

12

14

Figure 5 Hadronic Z decays atradics = 912 GeV Identified-meson and -baryon rates expressed as

fractions of the average charged-particle multiplicity

-4 -2 0

dln

(x)

Kgt

dn

K1

ltn

-310

-210

-110

1

10

) (Combined)plusmnx(K

Pythia 8183Data from ZPC66(1995)355 ZPC63(1994)181 EPJC5(1998)585

LEP (A+D+O)PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn16

00plusmn14

01plusmn19

V I

N C

I A

R O

O T

)p

ln(x-4 -2 0

The

ory

Dat

a

06

08

1

12

14

0 1 2 3 4 5

ξd

Λgt

dn

Λ1

ltn

0

02

04

06)]|0Λ|Ln[x(

Pythia 8183Data from EPJ C16 (2000) 613

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn08

01plusmn15

01plusmn12

V I

N C

I A

R O

O T

pξ

0 1 2 3 4 5

The

ory

Dat

a

06

08

1

12

14

Figure 6 Hadronic Z decays atradics = 912 GeV Kplusmn and Λ momentum-fraction spectra

11

the significant increase in the value of aExtraDiquark from 05 (Default) to 097 (Monash cf sec-tion 21) produces a desirable suppression of very hard Λ baryons The corresponding change in themeasured parts of the p and Ξplusmn spectra (cf appendix B2) are small compared with the experimentaluncertainties

It is interesting however to note that all of these spectra indicate or are at least consistent with amodelling excess of soft identified-particle production below ln(x) sim minus45 corresponding to absolutemomentum scales around 500 MeV while we recall that the inclusive ln(x) spectrum above showedan underproduction around ln(x) sim minus55 Within the constraints of the current theory model wehave not managed to find a way to mitigate these features while remaining consistent with the rest ofthe data Nonetheless it should be mentioned that these observations could have relevance also in thecontext of understanding identified-particle spectra at LHC a possibility which to our knowledge hasso far been ignored

23 Heavy-Quark Fragmentation

Similarly to above we first discuss the inclusive rates of hadrons containing heavy quarks before wediscuss their spectra Unfortunately there are also here substantial disagreements between differentpieces of information We have made the following choices

bull ForD mesons the average Dplusmn rate given in sec 46 of the PDG (0175) is equal to the inclusivebranching fraction for Z rarr DplusmnX given in the Z boson summary table in the same Review(after normalizing the latter to the hadronic Z fraction of 6991 [39]) However the formerought to be substantially larger given that some Z rarr cc events will contain two Dplusmn mesons(counting once in the Z rarr DplusmnX branching fraction but twice in the average Dplusmn multiplicity)We therefore here use a measurement by ALEPH [54] to fix the Dplusmn and D0 rates resulting ina reference value for the average Dplusmn multiplicity almost twice as large as that given by sec 46in the PDG

bull For Λ+c the average multiplicity given in sec 46 of the PDG is twice as large as that indicated

by the branching fraction BR(Z rarr Λ+c X) in the Z boson summary table in the same Review

We here use the branching from the Z boson summary table as our constraint on the Λ+c rate

normalized to the total branching fraction BR(Z rarr hadrons)

bull We also include the average rate of g rarr cc splittings obtained by combining an ALEPH [55]and an OPAL measurement [56] but with an additional 10 systematic uncertainty added toboth measurements to account for possibly larger mismodeling effects in the correction fac-tors [57 58]

bull For B particles we use the quite precise inclusive Z rarr B+X branching fraction from the Zboson summary in the PDG

bull We also use the sum of Bplusmn and B0(B0) in sec 46 of the PDG10

bull TheB0s multiplicity given in sec 46 of the PDG (0057plusmn0013) is more than twice the inclusive

BR(Z rarr B0sX)BR(Z rarr hadrons) branching fraction (00227 plusmn 00019) quoted in the Z

10Note that we have a factor 2 relative to the PDG since it appears the PDG quotes the average rather than the sum Notealso that all the average B meson multiplicities in sec 46 of the PDG are accompanied by a note ldquo(d)rdquo stating that the SMB(Z rarr bb) = 0217 was used for the normalization For completeness the reader should be aware that this is the fractionnormalized to hadronic Z decays the branching fraction relative to all Z decays is 0151 [39]

12

Charm Our Reference Our〈n〉 or BR Value Source

D+ +Dminus 0251 plusmn0047 AD0 + D0 0518 plusmn0063 ADlowast+ +Dlowastminus 0194 plusmn00057 PD+

s +Dminuss 0131 plusmn0021 PBR(Z rarr Λ+

c X) 00220 plusmn00047 ZBR(Z rarr X + cc) 00306 plusmn00047 AOJψ 00052 plusmn00004 Pχc1 00041 plusmn00011 Pψprime 00023 plusmn00004 P

Beauty Our Reference Our〈n〉 or BR Value Source

BR(Z rarr B+X) 0087 plusmn0002 ZB+ +B0 + B0 +Bminus 0330 plusmn0052 PBlowastu +Blowastd +Blowasts 0288 plusmn0026 PBR(Z rarr B0

sX) 00227 plusmn00019 ZBR(Z rarr BbaryonX) 00197 plusmn00032 ZBR(Z rarr X + bb) 000288 plusmn000061 ADSBR(Z rarr bbbbX) 000051 plusmn000019 ZΥ (times10) 00014 plusmn00007 P

Table 2 Hadronic Z decays atradics = MZ Measured rates and inclusive branching fractions of

particles containing c and b quarks as used in this work Note the branching fractions are normalizedto Z rarr hadrons and hence should be interpreted as eg BR(Z rarr B+X)BR(Z rarr hadrons)Note 2 the sum over Blowast states includes both particles and anti-particles Note 3 the Υ rate ismultiplied by a factor 10 Source labels indicate A (ALEPH) D (DELPHI) O (OPAL) P (PDGsection 46) S (SLD) Z (PDG Z Boson Summary Table)

boson summary table We find these two numbers difficult to reconcile and choose to use theinclusive BR(Z rarr B0

sX)BR(Z rarr hadrons) branching fraction as our main constraint

bull We also include the inclusive branching fractions for B-baryons (summed over baryons andantibaryons) the rate of g rarr bb splittings obtained by combining ALEPH [59] DELPHI [60]and SLD [61] measurements (including an additional 10 systematic to account for largerpossible mismodeling effects in the correction factors [57 58]) and the rate of Z rarr bbbb fromthe PDG Z boson summary table [39]

Our constraints on the heavy-quark particle rates are summarized in tab 2 Comparisons to these ratesare shown in fig 7 now without normalizing to the average charged-particle multiplicity Given thatmost of the c and b quarks come directly from Z rarr cc and Z rarr bb decays there is not a lot of roomfor tuning to these numbers apart from the relative rates of vector mesons vs pseudoscalars which iscontrolled by the parameters

Heavy MesonsStringFlavmesonCvector = 088StringFlavmesonBvector = 22

Our parameters are slightly smaller than the current default values leading to slightly smaller Dlowast

and Blowast rates as can be seen from the plots in fig 7 Note also that the increased overall amount ofstrangeness in the fragmentation leads to slightly higherDs andBs fractions in better agreement withthe data Uncertainties are however large and some exotic onium states like χc1 ψprime and Υ are notwell described by the default modeling (It is encouraging that at least the multiplicity of Jψ mesonsis well described though a substantial fraction of this likely owes to the feed-down from B decaysand hence does not depend directly on the string-fragmentation model itself)

We also note that it would be desirable to reduce the rate of g rarr bb and Z rarr bbbb events whilethe g rarr cc one appears consistent with the LEP constraints We suspect that this issue may be tiedto the fixed choice of using pperp as the renormalization scale for both gluon emissions and for g rarr qq

13

plusmnD 0D plusmnD plusmns

D X+

cΛ

ccrarrg ψJ c1χ

3685

ψ

X)

rarrlt

ngt o

r B

R(Z

-410

-310

-210

-110

1

10Charm Rates

Pythia 8185Data from HEPDATAPDG

LEP

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn15

00plusmn18

00plusmn17

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

plusmnD 0Dplusmn

D plusmnsD X+

cΛ ccrarrg ψJ c1χ

3685ψ

The

ory

Dat

a

0

05

1

15

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

X)

rarrlt

ngt o

r B

R(Z

-510

-410

-310

-210

-110

1

10Beauty Rates

Pythia 8185Data from HEPDATAPDG

LEP+SLD

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn17

00plusmn23

00plusmn23

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

The

ory

Dat

a0

05

1

15

Figure 7 Hadronic Z decays atradics = 912 GeV Rates and inclusive Z rarr X branching fractions

(normalized to Z rarr hadrons) of particles containing c and b quarks

splittings in the current version of PYTHIA A more natural choice for g rarr qq could be microR prop mqqas used eg in the VINCIA shower model [29]

We now turn to the dynamics of heavy-quark fragmentation focusing mainly on the b quarkFor heavy quarks the Lund fragmentation function is modified due to the (massive) endpoints not

moving along straight lightcones as the string pulls on them they slow down resulting in the stringtracing out a smaller space-time area than it would for massless quarks This modifies the implicationsof the string area law in a manner captured by the so-called Bowler modification of the fragmentationfunction [62]

fmassive(zmQ) prop f(z)

zbrQm2Q

(6)

with mQ the heavy-quark mass b the same universal parameter that appears in the massless fragmen-tation function eq (3) and rQ a tuning parameter which is unity in the original derivation of Bowlerbut can be assigned values different from unity to reduce (rQ rarr 0) or emphasize (rQ gt 1) the effectSince rQ multiplies the heavy-quark mass (squared) it can also be viewed as an effective rescalingof the mass value The net result is a suppression of the region z rarr 1 hence a relative softening ofthe fragmentation spectrum for heavy flavours (relative since the presence of m2

perp in the exponent ofeq (3) still implies an overall harder fragmentation for higher hadron masses)

We emphasize that this is the only fragmentation function that is self-consistent within the string-fragmentation model [33 62] Although a few alternative forms of the fragmentation functions formassive quarks are available in the code we therefore here work only with the Bowler type As forthe massless function the proportionality sign in eq (6) indicates that the function is normalized tounity

In PYTHIA separate rQ parameters are provided for c and b quarks We consider the one for bquarks first Its default value is rb = 067 but this appears to give too hard b fragmentation spectrawhen compared to LEP and SLD data see below For the Monash tune we instead use

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (DELPHI)weak

Bx

Pythia 8181Data from EurPhysJ C71 (2011) 1557

DELPHI PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn16

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (SLD)weak

Bx

Pythia 8181HepData5111d1-x1-y1

SLDPY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn07

00plusmn15

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a06

08

1

12

14

Figure 8 Hadronic Z decays atradics = 912 GeV Momentum (xB) spectra of weakly decaying B

hadrons compared to data from DELPHI [63] (left) and SLD [64] (right)

StringZrFactB = 0855

which produces softer B spectra and simultaneously agrees better with the theoretically preferredvalue (rb = 1)

A comparison to the scaled-momentum spectra (xB = 2|pB|Ecm) of weakly decayingB hadronsfrom both DELPHI [63] and SLD [64] is given in fig 8 (due to small differences between the twomeasured results we choose to show both) The dampening of the hardest part of the spectrum causedby the increase in the rb parameter is visible in the right-most two bins of the distributions and in thesmaller χ2

5 values for the Monash tune The effects of the modification can be further emphasizedby an analysis of the moments of the distribution in which the higher moments are increasinglydominated by the region xB rarr 1 A comparison to a combined LEP analysis of the moments of thexB distribution [63] is given in fig 9 further emphasizing that the high-xB part of the distribution isnow under better control

The reason we have not increased the rb parameter further is that it comes at a price If theB hadrons are taking less energy then there is more energy left over to produce other particlesand the generated multiplicity distribution in b events already exhibits a slightly high tail towardslarge multiplicities Nonetheless since the revised light-flavour fragmentation parameters produce anoverall narrower fragmentation function the end result is still a slight improvement in the multiplicitydistribution also for b events This is illustrated together with the inclusive momentum distributionfor b-tagged events in fig 10 compared to measurements by L3 [26] Interestingly the multiplicitydistribution still appears to be too wide but within the constraints of the present study we were unableto obtain further improvements As a point of speculation we note that the distribution of the numberof partons before hadronization is also quite wide in PYTHIA and this may be playing a role ineffectively setting a lower limit on the width that can be achieved for the hadron-level distribution

Comparisons to L3 event shapes in b-tagged events are collected in appendix B1 (the left columnof plots contains light-flavour tagged event shapes the right column b-tagged ones) In particular the

15

0 10 20 30 40

Mom

ent

0

02

04

06

08 (moments)weakBx

Pythia 8181Data from Eur Phys J C71 (2011) 1557

LEP (combined)PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn10

00plusmn103

00plusmn129

V I

N C

I A

R O

O T

N0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

Figure 9 Hadronic Z decays atradics = 912 GeV Moments of the B fragmentation function com-

pared to a combined analysis of LEP+SLD data by DELPHI [63]

0 20 40

)ch

Pro

babi

lity(

n

-610

-510

-410

-310

-210

-110

1

10

210 Charged Multiplicity (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

06plusmn45

08plusmn64

13plusmn110

V I

N C

I A

R O

O T

(b)chn0 20 40

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

ch d

nch

1n

-510

-410

-310

-210

-110

1

10

210 Charged Momentum Fraction (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn08

00plusmn06 V

I N

C I

A R

O O

T

)| (b)p

|Ln(x0 2 4 6 8

The

ory

Dat

a

06

08

1

12

14

Figure 10 HadronicZ decays atradics = 912 GeV Charged-hadron multiplicity (left) and momentum-

fraction (right) spectra in b-tagged events

16

0 02 04 06 08 1

dx

Dgt

dn

D1

ltn

0

05

1

15

2

25gt01)

E) (x

plusmnx(D

Pythia 8183Data from EurPhysJ C16 (2000) 597

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn14

02plusmn28

02plusmn32

V I

N C

I A

R O

O T

Ex0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

EX02 04 06 08 1

E)

dX

dN

(DZ

had

1N

0

0002

0004

0006

0008

001

0012

0014

0016

ALEPHHerwig++Sherpa

91 GeV ee Z (hadronic)

mcp

lots

cer

nch

41

M e

vent

sge

Riv

et 1

82

Herwig++ 261a Sherpa 141

ALEPH_1999_S4193598

spectrum (particle-level)+-D

02 04 06 08 105

1

15Ratio to ALEPH

Figure 11 The inclusive Dlowast spectrum in hadronic Z decays [55] Left Monash 2013 tune com-pared with default PYTHIA 8 and the Fischer tune Right comparison with HERWIG (dashed) andSHERPA (dotted) from MCPLOTS [25] Note that the plot in the left-hand pane is normalized tounity while the one in the right-hand pane is normalized to the number of hadronic Z decays

Monash tune gives a significant improvement in the soft region of the jet-broadening parameters inb-tagged events while no significant changes are observed for the other event shapes These smallimprovements are presumably a direct consequence of the softening of the b fragmentation functionit is now less likely to find an isolated ultra-hard B hadron

We round off the discussion of heavy-quark fragmentation by noting that a similarly comprehen-sive study of charm-quark fragmentation would be desirable However charm-quark tagged multi-plicity and event-shape data is not available to our knowledge and most of the D meson spectra onHEPDATA concern only specific decay chains (hence depend on the decay modeling) andor are lim-ited to restricted fiducial regions (limiting their generality) Experimentally the cleanest measurementis obtained from Dlowast decays and an inclusive momentum spectrum for Dlowast mesons has been measuredby ALEPH [55] From this distribution shown in fig 11 we determine a value for rc of

StringZrFactC = 132

We note that the low-x part of the Dlowast spectrum originates from g rarr cc shower splittings whilethe high-x tail represents prompt Dlowast production from leading charm in Z rarr cc (see [55] for a nicefigure illustrating this) The intermediate range contains a large component of feed-down from brarr cdecays hence this distribution is also indirectly sensitive to the b-quark sector The previous defaulttune had a harder spectrum for both b- and c-fragmentation leading to an overestimate of the high-xpart of the Dlowast distribution The undershooting at low xDlowast values which remains unchanged in theMonash tune most likely indicates an underproduction of g rarr cc branchings in the shower We notethat such an underproduction may also be reflected in the LHC data on Dlowast production see eg [65]We return to this issue in the discussion of identified particles at LHC section 35

17

bull For Λ production we use the most precise of the LEP measurements by OPAL7 [43] 〈nΛ〉 =0374plusmn 0002plusmn 0010 about 5 lower than the corresponding PDG value

bull For Σplusmn baryons we use a combination of the two most recent LEP measurements by L3 [44]for Σ+ + Σ

minus and by DELPHI [45] for Σminus + Σ+ for an estimated 〈nΣplusmn〉 = 0195 plusmn 0018

which is roughly 10 higher than the PDG value

bull For Σ0 baryons we use the most recent measurement by L3 [44] 〈nΣ0〉 = 0095 plusmn 0015 plusmn0013 this is about 20 larger than the PDG value The L3 paper comments on their relativelyhigh value by noting that L3 had the best coverage for low-momentum baryons hence smallermodel-dependent correction factors

bull For ∆++ baryons there are only two measurements in HEPDATA [4647] which are mutuallydiscrepant by about 2σ The DELPHI measurement is nominally the most precise but OPALgives a much more serious discussion of systematic uncertainties We choose to increase theestimated extrapolation errors of the DELPHI measurement by 50 and obtain a weighted av-erage8 of 〈n∆++〉 = 009plusmn0017 5 larger than the PDG value with a 20 larger uncertainty

bull For Σlowast the three measurements on HEPDATA [38 43 48] are likewise discrepant by 2σ minus 3σWe inflate the systematic uncertainties and arrive at 〈nΣlowastplusmn〉 = 0050 plusmn 0006 which is again5 higher than the PDG value with twice as much uncertainty

bull The measurements for Ξplusmn are in good agreement [38 43 48] with a weighted average of〈nΞplusmn〉 = 00266plusmn 00012 slightly larger than the PDG value

bull For Ξlowast0 however the DELPHI measurement [48] gives a far lower number than the OPAL [43]and ALEPH [38] ones and the weighted average differs by more than 10 from the PDGvalue despite the latter claiming an uncertainty smaller than 10 Our weighted average is〈nΞlowast0〉 = 00059plusmn 00012

bull Finally for the Ω baryon the DELPHI [49] and OPAL [43] measurements are in agreementand we use the PDG value 〈nΩ〉 = 00016plusmn 00003

We summarize the constraints on the light-meson and baryon rates used here in tab 1 Note that weexpress them as percentages of the average charged multiplicity

〈nCh〉 = 207 (5)

obtained as a weighted average over MARK-II [50] ALEPH [38] DELPHI [51] OPAL [52] andL3 [53] measurements

The light-flavour-selection parameters for the Monash tune are (see appendix A for a comparisonof these values to the current default ones)

Light-Meson SectorStringFlavProbStoUD = 0217StringFlavmesonUDvector = 05StringFlavmesonSvector = 055

7We note that HEPDATA incorrectly gives the systematic error as 0002 while the value in the OPAL paper is 0010 [43]This has been communicated to the HEPDATA maintainers

8Even with the inflated error the uncertainty on the DELPHI measurement is still less than a third that of the OPAL oneDELPHI therefore still dominates the average

9

Mesons Our Reference Our〈n〉 〈nCh〉 Value (in ) Source

π+ + πminus 822 plusmn09 Pπ0 455 plusmn15 PK+ +Kminus 108 plusmn03 Pη 506 plusmn038 Pηprime 073 plusmn009 Pρ+ + ρminus 116 plusmn21 Pρ0 595 plusmn047 PKlowast+ +Klowastminus 345 plusmn028 Pω 490 plusmn031 Pφ 049 plusmn0035 ADOS

Baryons Our Reference Our〈n〉 〈nCh〉 Value (in ) Source

p+ p 507 plusmn016 PΛ + Λ 181 plusmn032 OΣ+ + Σminus + Σ+ + Σminus 0942 plusmn0087 DLΣ0 + Σ0 0459 plusmn0096 L∆++ + ∆minusminus 0434 plusmn0082 DOΣlowast+ + Σlowastminus + Σlowast+ + Σlowastminus 0242 plusmn0029 ADOΞ+ + Ξminus 0125 plusmn00050 ADOΞlowast0 + Ξlowast0 00285 plusmn00058 ADOΩminus + Ω+ 00077 plusmn00015 P

Table 1 Hadronic Z decays atradics = 912 GeV Measured rates of light-flavour mesons and baryons

expressed as percentages of the average charged-particle multiplicity as used in this work Multiplythe numbers by 207100 to translate the percentages to corresponding production rates Source labelsindicate A (ALEPH) D (DELPHI) L (L3) O (OPAL) S (SLD) P (PDG)

StringFlavetaSup = 060StringFlavetaPrimeSup = 012

Baryon SectorStringFlavprobQQtoQ = 0081StringFlavprobSQtoQQ = 0915StringFlavprobQQ1toQQ0 = 00275StringFlavsuppressLeadingB = offStringFlavpopcornSpair = 09StringFlavpopcornSmeson = 05

Since strange-particle and baryon spectra at the LHC exhibit interesting differences with respectto existing models (see below) we paid particular attention to first obtaining a good description ofthese sectors in e+eminus collisions Specifically we have increased the overall amount of strangenessby about 10 while decreasing the rate of vector mesons by a similar amount9 (these two effectslargely cancel for Klowast) This improves the total Kplusmn ρ0 ω Λ Ξlowast and Ω yields on our combined LEPestimates discussed above The price is that we now overshoot the measured rate of Ξplusmn baryons by10 The resulting identified-meson and -baryon rates expressed as fractions of the average charged-particle multiplicity are plotted in fig 5 Note that the last four bins of the meson plot and the thirdand fourth bins of the baryon plot are not 〈n〉 〈nCh〉 fractions but rather the KlowastK φKlowast φKφπ Λp and ΛK ratios respectively Note also that section 4 on energy scaling below includes acomparison to the average Kaon and Lambda rates as a function of ee CM energy (fig 25)

To provide further information on identified particles we include a limited comparison to momen-tum spectra of Kplusmn p Λ and Ξplusmn which are the states of most immediate interest in the context ofsimilar comparisons now being made at LHC The spectra of Kplusmn mesons and Λ baryons are shownin fig 6 while the pplusmn and Ξplusmn spectra are relegated to appendix B2 The modified parameters of theMonash tune have virtually no effect on the Kaon distribution which still exhibits too many very softKaons (with ln(x) lt minus4 corresponding to x lt 0018 so momentum scales below sim 1 GeV) while

9For reference the current default value of ProbStoUD is 019 while ours is 0217 The increased value also improvesthe agreement with the Ds and Bs rates see section 23 The default values of mesonUDvector and mesonSvectorare 062 and 0725 respectively while ours are 05 and 055

10

plusmnπ 0π plusmnK η η plusmnρ 0ρ plusmnK ω φKK-

RKφ

RK-φ

R-πφ

R

gtch

ltnltngt

-310

-210

-110

1

10Meson Fractions

Pythia 8183Data from PDGHEPDATA

LEP + SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn06

00plusmn12

00plusmn12

V I

N C

I A

R O

O T

plusmnπ 0π plusmnK η η plusmnρ 0ρ plusmnK ω φKK-

RKφ

RK-φ

R-πφ

R

The

ory

Dat

a

06

08

1

12

14

p ΛpΛ

RKΛ

R plusmnΣ 0Σ ++∆ Σ plusmnΞ 0Ξ Ω

gtch

ltnltngt

-410

-310

-210

-110

1Baryon Fractions

Pythia 8183Data from PDGHEPDATA

LEP PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn11

00plusmn22

00plusmn22

V I

N C

I A

R O

O T

p ΛpΛ

RKΛ

R plusmnΣ 0Σ ++∆ Σ plusmnΞ 0Ξ Ω

The

ory

Dat

a

06

08

1

12

14

Figure 5 Hadronic Z decays atradics = 912 GeV Identified-meson and -baryon rates expressed as

fractions of the average charged-particle multiplicity

-4 -2 0

dln

(x)

Kgt

dn

K1

ltn

-310

-210

-110

1

10

) (Combined)plusmnx(K

Pythia 8183Data from ZPC66(1995)355 ZPC63(1994)181 EPJC5(1998)585

LEP (A+D+O)PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn16

00plusmn14

01plusmn19

V I

N C

I A

R O

O T

)p

ln(x-4 -2 0

The

ory

Dat

a

06

08

1

12

14

0 1 2 3 4 5

ξd

Λgt

dn

Λ1

ltn

0

02

04

06)]|0Λ|Ln[x(

Pythia 8183Data from EPJ C16 (2000) 613

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn08

01plusmn15

01plusmn12

V I

N C

I A

R O

O T

pξ

0 1 2 3 4 5

The

ory

Dat

a

06

08

1

12

14

Figure 6 Hadronic Z decays atradics = 912 GeV Kplusmn and Λ momentum-fraction spectra

11

the significant increase in the value of aExtraDiquark from 05 (Default) to 097 (Monash cf sec-tion 21) produces a desirable suppression of very hard Λ baryons The corresponding change in themeasured parts of the p and Ξplusmn spectra (cf appendix B2) are small compared with the experimentaluncertainties

It is interesting however to note that all of these spectra indicate or are at least consistent with amodelling excess of soft identified-particle production below ln(x) sim minus45 corresponding to absolutemomentum scales around 500 MeV while we recall that the inclusive ln(x) spectrum above showedan underproduction around ln(x) sim minus55 Within the constraints of the current theory model wehave not managed to find a way to mitigate these features while remaining consistent with the rest ofthe data Nonetheless it should be mentioned that these observations could have relevance also in thecontext of understanding identified-particle spectra at LHC a possibility which to our knowledge hasso far been ignored

23 Heavy-Quark Fragmentation

Similarly to above we first discuss the inclusive rates of hadrons containing heavy quarks before wediscuss their spectra Unfortunately there are also here substantial disagreements between differentpieces of information We have made the following choices

bull ForD mesons the average Dplusmn rate given in sec 46 of the PDG (0175) is equal to the inclusivebranching fraction for Z rarr DplusmnX given in the Z boson summary table in the same Review(after normalizing the latter to the hadronic Z fraction of 6991 [39]) However the formerought to be substantially larger given that some Z rarr cc events will contain two Dplusmn mesons(counting once in the Z rarr DplusmnX branching fraction but twice in the average Dplusmn multiplicity)We therefore here use a measurement by ALEPH [54] to fix the Dplusmn and D0 rates resulting ina reference value for the average Dplusmn multiplicity almost twice as large as that given by sec 46in the PDG

bull For Λ+c the average multiplicity given in sec 46 of the PDG is twice as large as that indicated

by the branching fraction BR(Z rarr Λ+c X) in the Z boson summary table in the same Review

We here use the branching from the Z boson summary table as our constraint on the Λ+c rate

normalized to the total branching fraction BR(Z rarr hadrons)

bull We also include the average rate of g rarr cc splittings obtained by combining an ALEPH [55]and an OPAL measurement [56] but with an additional 10 systematic uncertainty added toboth measurements to account for possibly larger mismodeling effects in the correction fac-tors [57 58]

bull For B particles we use the quite precise inclusive Z rarr B+X branching fraction from the Zboson summary in the PDG

bull We also use the sum of Bplusmn and B0(B0) in sec 46 of the PDG10

bull TheB0s multiplicity given in sec 46 of the PDG (0057plusmn0013) is more than twice the inclusive

BR(Z rarr B0sX)BR(Z rarr hadrons) branching fraction (00227 plusmn 00019) quoted in the Z

10Note that we have a factor 2 relative to the PDG since it appears the PDG quotes the average rather than the sum Notealso that all the average B meson multiplicities in sec 46 of the PDG are accompanied by a note ldquo(d)rdquo stating that the SMB(Z rarr bb) = 0217 was used for the normalization For completeness the reader should be aware that this is the fractionnormalized to hadronic Z decays the branching fraction relative to all Z decays is 0151 [39]

12

Charm Our Reference Our〈n〉 or BR Value Source

D+ +Dminus 0251 plusmn0047 AD0 + D0 0518 plusmn0063 ADlowast+ +Dlowastminus 0194 plusmn00057 PD+

s +Dminuss 0131 plusmn0021 PBR(Z rarr Λ+

c X) 00220 plusmn00047 ZBR(Z rarr X + cc) 00306 plusmn00047 AOJψ 00052 plusmn00004 Pχc1 00041 plusmn00011 Pψprime 00023 plusmn00004 P

Beauty Our Reference Our〈n〉 or BR Value Source

BR(Z rarr B+X) 0087 plusmn0002 ZB+ +B0 + B0 +Bminus 0330 plusmn0052 PBlowastu +Blowastd +Blowasts 0288 plusmn0026 PBR(Z rarr B0

sX) 00227 plusmn00019 ZBR(Z rarr BbaryonX) 00197 plusmn00032 ZBR(Z rarr X + bb) 000288 plusmn000061 ADSBR(Z rarr bbbbX) 000051 plusmn000019 ZΥ (times10) 00014 plusmn00007 P

Table 2 Hadronic Z decays atradics = MZ Measured rates and inclusive branching fractions of

particles containing c and b quarks as used in this work Note the branching fractions are normalizedto Z rarr hadrons and hence should be interpreted as eg BR(Z rarr B+X)BR(Z rarr hadrons)Note 2 the sum over Blowast states includes both particles and anti-particles Note 3 the Υ rate ismultiplied by a factor 10 Source labels indicate A (ALEPH) D (DELPHI) O (OPAL) P (PDGsection 46) S (SLD) Z (PDG Z Boson Summary Table)

boson summary table We find these two numbers difficult to reconcile and choose to use theinclusive BR(Z rarr B0

sX)BR(Z rarr hadrons) branching fraction as our main constraint

bull We also include the inclusive branching fractions for B-baryons (summed over baryons andantibaryons) the rate of g rarr bb splittings obtained by combining ALEPH [59] DELPHI [60]and SLD [61] measurements (including an additional 10 systematic to account for largerpossible mismodeling effects in the correction factors [57 58]) and the rate of Z rarr bbbb fromthe PDG Z boson summary table [39]

Our constraints on the heavy-quark particle rates are summarized in tab 2 Comparisons to these ratesare shown in fig 7 now without normalizing to the average charged-particle multiplicity Given thatmost of the c and b quarks come directly from Z rarr cc and Z rarr bb decays there is not a lot of roomfor tuning to these numbers apart from the relative rates of vector mesons vs pseudoscalars which iscontrolled by the parameters

Heavy MesonsStringFlavmesonCvector = 088StringFlavmesonBvector = 22

Our parameters are slightly smaller than the current default values leading to slightly smaller Dlowast

and Blowast rates as can be seen from the plots in fig 7 Note also that the increased overall amount ofstrangeness in the fragmentation leads to slightly higherDs andBs fractions in better agreement withthe data Uncertainties are however large and some exotic onium states like χc1 ψprime and Υ are notwell described by the default modeling (It is encouraging that at least the multiplicity of Jψ mesonsis well described though a substantial fraction of this likely owes to the feed-down from B decaysand hence does not depend directly on the string-fragmentation model itself)

We also note that it would be desirable to reduce the rate of g rarr bb and Z rarr bbbb events whilethe g rarr cc one appears consistent with the LEP constraints We suspect that this issue may be tiedto the fixed choice of using pperp as the renormalization scale for both gluon emissions and for g rarr qq

13

plusmnD 0D plusmnD plusmns

D X+

cΛ

ccrarrg ψJ c1χ

3685

ψ

X)

rarrlt

ngt o

r B

R(Z

-410

-310

-210

-110

1

10Charm Rates

Pythia 8185Data from HEPDATAPDG

LEP

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn15

00plusmn18

00plusmn17

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

plusmnD 0Dplusmn

D plusmnsD X+

cΛ ccrarrg ψJ c1χ

3685ψ

The

ory

Dat

a

0

05

1

15

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

X)

rarrlt

ngt o

r B

R(Z

-510

-410

-310

-210

-110

1

10Beauty Rates

Pythia 8185Data from HEPDATAPDG

LEP+SLD

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn17

00plusmn23

00plusmn23

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

The

ory

Dat

a0

05

1

15

Figure 7 Hadronic Z decays atradics = 912 GeV Rates and inclusive Z rarr X branching fractions

(normalized to Z rarr hadrons) of particles containing c and b quarks

splittings in the current version of PYTHIA A more natural choice for g rarr qq could be microR prop mqqas used eg in the VINCIA shower model [29]

We now turn to the dynamics of heavy-quark fragmentation focusing mainly on the b quarkFor heavy quarks the Lund fragmentation function is modified due to the (massive) endpoints not

moving along straight lightcones as the string pulls on them they slow down resulting in the stringtracing out a smaller space-time area than it would for massless quarks This modifies the implicationsof the string area law in a manner captured by the so-called Bowler modification of the fragmentationfunction [62]

fmassive(zmQ) prop f(z)

zbrQm2Q

(6)

with mQ the heavy-quark mass b the same universal parameter that appears in the massless fragmen-tation function eq (3) and rQ a tuning parameter which is unity in the original derivation of Bowlerbut can be assigned values different from unity to reduce (rQ rarr 0) or emphasize (rQ gt 1) the effectSince rQ multiplies the heavy-quark mass (squared) it can also be viewed as an effective rescalingof the mass value The net result is a suppression of the region z rarr 1 hence a relative softening ofthe fragmentation spectrum for heavy flavours (relative since the presence of m2

perp in the exponent ofeq (3) still implies an overall harder fragmentation for higher hadron masses)

We emphasize that this is the only fragmentation function that is self-consistent within the string-fragmentation model [33 62] Although a few alternative forms of the fragmentation functions formassive quarks are available in the code we therefore here work only with the Bowler type As forthe massless function the proportionality sign in eq (6) indicates that the function is normalized tounity

In PYTHIA separate rQ parameters are provided for c and b quarks We consider the one for bquarks first Its default value is rb = 067 but this appears to give too hard b fragmentation spectrawhen compared to LEP and SLD data see below For the Monash tune we instead use

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (DELPHI)weak

Bx

Pythia 8181Data from EurPhysJ C71 (2011) 1557

DELPHI PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn16

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (SLD)weak

Bx

Pythia 8181HepData5111d1-x1-y1

SLDPY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn07

00plusmn15

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a06

08

1

12

14

Figure 8 Hadronic Z decays atradics = 912 GeV Momentum (xB) spectra of weakly decaying B

hadrons compared to data from DELPHI [63] (left) and SLD [64] (right)

StringZrFactB = 0855

which produces softer B spectra and simultaneously agrees better with the theoretically preferredvalue (rb = 1)

A comparison to the scaled-momentum spectra (xB = 2|pB|Ecm) of weakly decayingB hadronsfrom both DELPHI [63] and SLD [64] is given in fig 8 (due to small differences between the twomeasured results we choose to show both) The dampening of the hardest part of the spectrum causedby the increase in the rb parameter is visible in the right-most two bins of the distributions and in thesmaller χ2

5 values for the Monash tune The effects of the modification can be further emphasizedby an analysis of the moments of the distribution in which the higher moments are increasinglydominated by the region xB rarr 1 A comparison to a combined LEP analysis of the moments of thexB distribution [63] is given in fig 9 further emphasizing that the high-xB part of the distribution isnow under better control

The reason we have not increased the rb parameter further is that it comes at a price If theB hadrons are taking less energy then there is more energy left over to produce other particlesand the generated multiplicity distribution in b events already exhibits a slightly high tail towardslarge multiplicities Nonetheless since the revised light-flavour fragmentation parameters produce anoverall narrower fragmentation function the end result is still a slight improvement in the multiplicitydistribution also for b events This is illustrated together with the inclusive momentum distributionfor b-tagged events in fig 10 compared to measurements by L3 [26] Interestingly the multiplicitydistribution still appears to be too wide but within the constraints of the present study we were unableto obtain further improvements As a point of speculation we note that the distribution of the numberof partons before hadronization is also quite wide in PYTHIA and this may be playing a role ineffectively setting a lower limit on the width that can be achieved for the hadron-level distribution

Comparisons to L3 event shapes in b-tagged events are collected in appendix B1 (the left columnof plots contains light-flavour tagged event shapes the right column b-tagged ones) In particular the

15

0 10 20 30 40

Mom

ent

0

02

04

06

08 (moments)weakBx

Pythia 8181Data from Eur Phys J C71 (2011) 1557

LEP (combined)PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn10

00plusmn103

00plusmn129

V I

N C

I A

R O

O T

N0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

Figure 9 Hadronic Z decays atradics = 912 GeV Moments of the B fragmentation function com-

pared to a combined analysis of LEP+SLD data by DELPHI [63]

0 20 40

)ch

Pro

babi

lity(

n

-610

-510

-410

-310

-210

-110

1

10

210 Charged Multiplicity (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

06plusmn45

08plusmn64

13plusmn110

V I

N C

I A

R O

O T

(b)chn0 20 40

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

ch d

nch

1n

-510

-410

-310

-210

-110

1

10

210 Charged Momentum Fraction (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn08

00plusmn06 V

I N

C I

A R

O O

T

)| (b)p

|Ln(x0 2 4 6 8

The

ory

Dat

a

06

08

1

12

14

Figure 10 HadronicZ decays atradics = 912 GeV Charged-hadron multiplicity (left) and momentum-

fraction (right) spectra in b-tagged events

16

0 02 04 06 08 1

dx

Dgt

dn

D1

ltn

0

05

1

15

2

25gt01)

E) (x

plusmnx(D

Pythia 8183Data from EurPhysJ C16 (2000) 597

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn14

02plusmn28

02plusmn32

V I

N C

I A

R O

O T

Ex0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

EX02 04 06 08 1

E)

dX

dN

(DZ

had

1N

0

0002

0004

0006

0008

001

0012

0014

0016

ALEPHHerwig++Sherpa

91 GeV ee Z (hadronic)

mcp

lots

cer

nch

41

M e

vent

sge

Riv

et 1

82

Herwig++ 261a Sherpa 141

ALEPH_1999_S4193598

spectrum (particle-level)+-D

02 04 06 08 105

1

15Ratio to ALEPH

Figure 11 The inclusive Dlowast spectrum in hadronic Z decays [55] Left Monash 2013 tune com-pared with default PYTHIA 8 and the Fischer tune Right comparison with HERWIG (dashed) andSHERPA (dotted) from MCPLOTS [25] Note that the plot in the left-hand pane is normalized tounity while the one in the right-hand pane is normalized to the number of hadronic Z decays

Monash tune gives a significant improvement in the soft region of the jet-broadening parameters inb-tagged events while no significant changes are observed for the other event shapes These smallimprovements are presumably a direct consequence of the softening of the b fragmentation functionit is now less likely to find an isolated ultra-hard B hadron

We round off the discussion of heavy-quark fragmentation by noting that a similarly comprehen-sive study of charm-quark fragmentation would be desirable However charm-quark tagged multi-plicity and event-shape data is not available to our knowledge and most of the D meson spectra onHEPDATA concern only specific decay chains (hence depend on the decay modeling) andor are lim-ited to restricted fiducial regions (limiting their generality) Experimentally the cleanest measurementis obtained from Dlowast decays and an inclusive momentum spectrum for Dlowast mesons has been measuredby ALEPH [55] From this distribution shown in fig 11 we determine a value for rc of

StringZrFactC = 132

We note that the low-x part of the Dlowast spectrum originates from g rarr cc shower splittings whilethe high-x tail represents prompt Dlowast production from leading charm in Z rarr cc (see [55] for a nicefigure illustrating this) The intermediate range contains a large component of feed-down from brarr cdecays hence this distribution is also indirectly sensitive to the b-quark sector The previous defaulttune had a harder spectrum for both b- and c-fragmentation leading to an overestimate of the high-xpart of the Dlowast distribution The undershooting at low xDlowast values which remains unchanged in theMonash tune most likely indicates an underproduction of g rarr cc branchings in the shower We notethat such an underproduction may also be reflected in the LHC data on Dlowast production see eg [65]We return to this issue in the discussion of identified particles at LHC section 35

17

Mesons Our Reference Our〈n〉 〈nCh〉 Value (in ) Source

π+ + πminus 822 plusmn09 Pπ0 455 plusmn15 PK+ +Kminus 108 plusmn03 Pη 506 plusmn038 Pηprime 073 plusmn009 Pρ+ + ρminus 116 plusmn21 Pρ0 595 plusmn047 PKlowast+ +Klowastminus 345 plusmn028 Pω 490 plusmn031 Pφ 049 plusmn0035 ADOS

Baryons Our Reference Our〈n〉 〈nCh〉 Value (in ) Source

p+ p 507 plusmn016 PΛ + Λ 181 plusmn032 OΣ+ + Σminus + Σ+ + Σminus 0942 plusmn0087 DLΣ0 + Σ0 0459 plusmn0096 L∆++ + ∆minusminus 0434 plusmn0082 DOΣlowast+ + Σlowastminus + Σlowast+ + Σlowastminus 0242 plusmn0029 ADOΞ+ + Ξminus 0125 plusmn00050 ADOΞlowast0 + Ξlowast0 00285 plusmn00058 ADOΩminus + Ω+ 00077 plusmn00015 P

Table 1 Hadronic Z decays atradics = 912 GeV Measured rates of light-flavour mesons and baryons

expressed as percentages of the average charged-particle multiplicity as used in this work Multiplythe numbers by 207100 to translate the percentages to corresponding production rates Source labelsindicate A (ALEPH) D (DELPHI) L (L3) O (OPAL) S (SLD) P (PDG)

StringFlavetaSup = 060StringFlavetaPrimeSup = 012

Baryon SectorStringFlavprobQQtoQ = 0081StringFlavprobSQtoQQ = 0915StringFlavprobQQ1toQQ0 = 00275StringFlavsuppressLeadingB = offStringFlavpopcornSpair = 09StringFlavpopcornSmeson = 05

Since strange-particle and baryon spectra at the LHC exhibit interesting differences with respectto existing models (see below) we paid particular attention to first obtaining a good description ofthese sectors in e+eminus collisions Specifically we have increased the overall amount of strangenessby about 10 while decreasing the rate of vector mesons by a similar amount9 (these two effectslargely cancel for Klowast) This improves the total Kplusmn ρ0 ω Λ Ξlowast and Ω yields on our combined LEPestimates discussed above The price is that we now overshoot the measured rate of Ξplusmn baryons by10 The resulting identified-meson and -baryon rates expressed as fractions of the average charged-particle multiplicity are plotted in fig 5 Note that the last four bins of the meson plot and the thirdand fourth bins of the baryon plot are not 〈n〉 〈nCh〉 fractions but rather the KlowastK φKlowast φKφπ Λp and ΛK ratios respectively Note also that section 4 on energy scaling below includes acomparison to the average Kaon and Lambda rates as a function of ee CM energy (fig 25)

To provide further information on identified particles we include a limited comparison to momen-tum spectra of Kplusmn p Λ and Ξplusmn which are the states of most immediate interest in the context ofsimilar comparisons now being made at LHC The spectra of Kplusmn mesons and Λ baryons are shownin fig 6 while the pplusmn and Ξplusmn spectra are relegated to appendix B2 The modified parameters of theMonash tune have virtually no effect on the Kaon distribution which still exhibits too many very softKaons (with ln(x) lt minus4 corresponding to x lt 0018 so momentum scales below sim 1 GeV) while

9For reference the current default value of ProbStoUD is 019 while ours is 0217 The increased value also improvesthe agreement with the Ds and Bs rates see section 23 The default values of mesonUDvector and mesonSvectorare 062 and 0725 respectively while ours are 05 and 055

10

plusmnπ 0π plusmnK η η plusmnρ 0ρ plusmnK ω φKK-

RKφ

RK-φ

R-πφ

R

gtch

ltnltngt

-310

-210

-110

1

10Meson Fractions

Pythia 8183Data from PDGHEPDATA

LEP + SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn06

00plusmn12

00plusmn12

V I

N C

I A

R O

O T

plusmnπ 0π plusmnK η η plusmnρ 0ρ plusmnK ω φKK-

RKφ

RK-φ

R-πφ

R

The

ory

Dat

a

06

08

1

12

14

p ΛpΛ

RKΛ

R plusmnΣ 0Σ ++∆ Σ plusmnΞ 0Ξ Ω

gtch

ltnltngt

-410

-310

-210

-110

1Baryon Fractions

Pythia 8183Data from PDGHEPDATA

LEP PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn11

00plusmn22

00plusmn22

V I

N C

I A

R O

O T

p ΛpΛ

RKΛ

R plusmnΣ 0Σ ++∆ Σ plusmnΞ 0Ξ Ω

The

ory

Dat

a

06

08

1

12

14

Figure 5 Hadronic Z decays atradics = 912 GeV Identified-meson and -baryon rates expressed as

fractions of the average charged-particle multiplicity

-4 -2 0

dln

(x)

Kgt

dn

K1

ltn

-310

-210

-110

1

10

) (Combined)plusmnx(K

Pythia 8183Data from ZPC66(1995)355 ZPC63(1994)181 EPJC5(1998)585

LEP (A+D+O)PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn16

00plusmn14

01plusmn19

V I

N C

I A

R O

O T

)p

ln(x-4 -2 0

The

ory

Dat

a

06

08

1

12

14

0 1 2 3 4 5

ξd

Λgt

dn

Λ1

ltn

0

02

04

06)]|0Λ|Ln[x(

Pythia 8183Data from EPJ C16 (2000) 613

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn08

01plusmn15

01plusmn12

V I

N C

I A

R O

O T

pξ

0 1 2 3 4 5

The

ory

Dat

a

06

08

1

12

14

Figure 6 Hadronic Z decays atradics = 912 GeV Kplusmn and Λ momentum-fraction spectra

11

the significant increase in the value of aExtraDiquark from 05 (Default) to 097 (Monash cf sec-tion 21) produces a desirable suppression of very hard Λ baryons The corresponding change in themeasured parts of the p and Ξplusmn spectra (cf appendix B2) are small compared with the experimentaluncertainties

It is interesting however to note that all of these spectra indicate or are at least consistent with amodelling excess of soft identified-particle production below ln(x) sim minus45 corresponding to absolutemomentum scales around 500 MeV while we recall that the inclusive ln(x) spectrum above showedan underproduction around ln(x) sim minus55 Within the constraints of the current theory model wehave not managed to find a way to mitigate these features while remaining consistent with the rest ofthe data Nonetheless it should be mentioned that these observations could have relevance also in thecontext of understanding identified-particle spectra at LHC a possibility which to our knowledge hasso far been ignored

23 Heavy-Quark Fragmentation

Similarly to above we first discuss the inclusive rates of hadrons containing heavy quarks before wediscuss their spectra Unfortunately there are also here substantial disagreements between differentpieces of information We have made the following choices

bull ForD mesons the average Dplusmn rate given in sec 46 of the PDG (0175) is equal to the inclusivebranching fraction for Z rarr DplusmnX given in the Z boson summary table in the same Review(after normalizing the latter to the hadronic Z fraction of 6991 [39]) However the formerought to be substantially larger given that some Z rarr cc events will contain two Dplusmn mesons(counting once in the Z rarr DplusmnX branching fraction but twice in the average Dplusmn multiplicity)We therefore here use a measurement by ALEPH [54] to fix the Dplusmn and D0 rates resulting ina reference value for the average Dplusmn multiplicity almost twice as large as that given by sec 46in the PDG

bull For Λ+c the average multiplicity given in sec 46 of the PDG is twice as large as that indicated

by the branching fraction BR(Z rarr Λ+c X) in the Z boson summary table in the same Review

We here use the branching from the Z boson summary table as our constraint on the Λ+c rate

normalized to the total branching fraction BR(Z rarr hadrons)

bull We also include the average rate of g rarr cc splittings obtained by combining an ALEPH [55]and an OPAL measurement [56] but with an additional 10 systematic uncertainty added toboth measurements to account for possibly larger mismodeling effects in the correction fac-tors [57 58]

bull For B particles we use the quite precise inclusive Z rarr B+X branching fraction from the Zboson summary in the PDG

bull We also use the sum of Bplusmn and B0(B0) in sec 46 of the PDG10

bull TheB0s multiplicity given in sec 46 of the PDG (0057plusmn0013) is more than twice the inclusive

BR(Z rarr B0sX)BR(Z rarr hadrons) branching fraction (00227 plusmn 00019) quoted in the Z

10Note that we have a factor 2 relative to the PDG since it appears the PDG quotes the average rather than the sum Notealso that all the average B meson multiplicities in sec 46 of the PDG are accompanied by a note ldquo(d)rdquo stating that the SMB(Z rarr bb) = 0217 was used for the normalization For completeness the reader should be aware that this is the fractionnormalized to hadronic Z decays the branching fraction relative to all Z decays is 0151 [39]

12

Charm Our Reference Our〈n〉 or BR Value Source

D+ +Dminus 0251 plusmn0047 AD0 + D0 0518 plusmn0063 ADlowast+ +Dlowastminus 0194 plusmn00057 PD+

s +Dminuss 0131 plusmn0021 PBR(Z rarr Λ+

c X) 00220 plusmn00047 ZBR(Z rarr X + cc) 00306 plusmn00047 AOJψ 00052 plusmn00004 Pχc1 00041 plusmn00011 Pψprime 00023 plusmn00004 P

Beauty Our Reference Our〈n〉 or BR Value Source

BR(Z rarr B+X) 0087 plusmn0002 ZB+ +B0 + B0 +Bminus 0330 plusmn0052 PBlowastu +Blowastd +Blowasts 0288 plusmn0026 PBR(Z rarr B0

sX) 00227 plusmn00019 ZBR(Z rarr BbaryonX) 00197 plusmn00032 ZBR(Z rarr X + bb) 000288 plusmn000061 ADSBR(Z rarr bbbbX) 000051 plusmn000019 ZΥ (times10) 00014 plusmn00007 P

Table 2 Hadronic Z decays atradics = MZ Measured rates and inclusive branching fractions of

particles containing c and b quarks as used in this work Note the branching fractions are normalizedto Z rarr hadrons and hence should be interpreted as eg BR(Z rarr B+X)BR(Z rarr hadrons)Note 2 the sum over Blowast states includes both particles and anti-particles Note 3 the Υ rate ismultiplied by a factor 10 Source labels indicate A (ALEPH) D (DELPHI) O (OPAL) P (PDGsection 46) S (SLD) Z (PDG Z Boson Summary Table)

boson summary table We find these two numbers difficult to reconcile and choose to use theinclusive BR(Z rarr B0

sX)BR(Z rarr hadrons) branching fraction as our main constraint

bull We also include the inclusive branching fractions for B-baryons (summed over baryons andantibaryons) the rate of g rarr bb splittings obtained by combining ALEPH [59] DELPHI [60]and SLD [61] measurements (including an additional 10 systematic to account for largerpossible mismodeling effects in the correction factors [57 58]) and the rate of Z rarr bbbb fromthe PDG Z boson summary table [39]

Our constraints on the heavy-quark particle rates are summarized in tab 2 Comparisons to these ratesare shown in fig 7 now without normalizing to the average charged-particle multiplicity Given thatmost of the c and b quarks come directly from Z rarr cc and Z rarr bb decays there is not a lot of roomfor tuning to these numbers apart from the relative rates of vector mesons vs pseudoscalars which iscontrolled by the parameters

Heavy MesonsStringFlavmesonCvector = 088StringFlavmesonBvector = 22

Our parameters are slightly smaller than the current default values leading to slightly smaller Dlowast

and Blowast rates as can be seen from the plots in fig 7 Note also that the increased overall amount ofstrangeness in the fragmentation leads to slightly higherDs andBs fractions in better agreement withthe data Uncertainties are however large and some exotic onium states like χc1 ψprime and Υ are notwell described by the default modeling (It is encouraging that at least the multiplicity of Jψ mesonsis well described though a substantial fraction of this likely owes to the feed-down from B decaysand hence does not depend directly on the string-fragmentation model itself)

We also note that it would be desirable to reduce the rate of g rarr bb and Z rarr bbbb events whilethe g rarr cc one appears consistent with the LEP constraints We suspect that this issue may be tiedto the fixed choice of using pperp as the renormalization scale for both gluon emissions and for g rarr qq

13

plusmnD 0D plusmnD plusmns

D X+

cΛ

ccrarrg ψJ c1χ

3685

ψ

X)

rarrlt

ngt o

r B

R(Z

-410

-310

-210

-110

1

10Charm Rates

Pythia 8185Data from HEPDATAPDG

LEP

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn15

00plusmn18

00plusmn17

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

plusmnD 0Dplusmn

D plusmnsD X+

cΛ ccrarrg ψJ c1χ

3685ψ

The

ory

Dat

a

0

05

1

15

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

X)

rarrlt

ngt o

r B

R(Z

-510

-410

-310

-210

-110

1

10Beauty Rates

Pythia 8185Data from HEPDATAPDG

LEP+SLD

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn17

00plusmn23

00plusmn23

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

The

ory

Dat

a0

05

1

15

Figure 7 Hadronic Z decays atradics = 912 GeV Rates and inclusive Z rarr X branching fractions

(normalized to Z rarr hadrons) of particles containing c and b quarks

splittings in the current version of PYTHIA A more natural choice for g rarr qq could be microR prop mqqas used eg in the VINCIA shower model [29]

We now turn to the dynamics of heavy-quark fragmentation focusing mainly on the b quarkFor heavy quarks the Lund fragmentation function is modified due to the (massive) endpoints not

moving along straight lightcones as the string pulls on them they slow down resulting in the stringtracing out a smaller space-time area than it would for massless quarks This modifies the implicationsof the string area law in a manner captured by the so-called Bowler modification of the fragmentationfunction [62]

fmassive(zmQ) prop f(z)

zbrQm2Q

(6)

with mQ the heavy-quark mass b the same universal parameter that appears in the massless fragmen-tation function eq (3) and rQ a tuning parameter which is unity in the original derivation of Bowlerbut can be assigned values different from unity to reduce (rQ rarr 0) or emphasize (rQ gt 1) the effectSince rQ multiplies the heavy-quark mass (squared) it can also be viewed as an effective rescalingof the mass value The net result is a suppression of the region z rarr 1 hence a relative softening ofthe fragmentation spectrum for heavy flavours (relative since the presence of m2

perp in the exponent ofeq (3) still implies an overall harder fragmentation for higher hadron masses)

We emphasize that this is the only fragmentation function that is self-consistent within the string-fragmentation model [33 62] Although a few alternative forms of the fragmentation functions formassive quarks are available in the code we therefore here work only with the Bowler type As forthe massless function the proportionality sign in eq (6) indicates that the function is normalized tounity

In PYTHIA separate rQ parameters are provided for c and b quarks We consider the one for bquarks first Its default value is rb = 067 but this appears to give too hard b fragmentation spectrawhen compared to LEP and SLD data see below For the Monash tune we instead use

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (DELPHI)weak

Bx

Pythia 8181Data from EurPhysJ C71 (2011) 1557

DELPHI PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn16

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (SLD)weak

Bx

Pythia 8181HepData5111d1-x1-y1

SLDPY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn07

00plusmn15

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a06

08

1

12

14

Figure 8 Hadronic Z decays atradics = 912 GeV Momentum (xB) spectra of weakly decaying B

hadrons compared to data from DELPHI [63] (left) and SLD [64] (right)

StringZrFactB = 0855

which produces softer B spectra and simultaneously agrees better with the theoretically preferredvalue (rb = 1)

A comparison to the scaled-momentum spectra (xB = 2|pB|Ecm) of weakly decayingB hadronsfrom both DELPHI [63] and SLD [64] is given in fig 8 (due to small differences between the twomeasured results we choose to show both) The dampening of the hardest part of the spectrum causedby the increase in the rb parameter is visible in the right-most two bins of the distributions and in thesmaller χ2

5 values for the Monash tune The effects of the modification can be further emphasizedby an analysis of the moments of the distribution in which the higher moments are increasinglydominated by the region xB rarr 1 A comparison to a combined LEP analysis of the moments of thexB distribution [63] is given in fig 9 further emphasizing that the high-xB part of the distribution isnow under better control

The reason we have not increased the rb parameter further is that it comes at a price If theB hadrons are taking less energy then there is more energy left over to produce other particlesand the generated multiplicity distribution in b events already exhibits a slightly high tail towardslarge multiplicities Nonetheless since the revised light-flavour fragmentation parameters produce anoverall narrower fragmentation function the end result is still a slight improvement in the multiplicitydistribution also for b events This is illustrated together with the inclusive momentum distributionfor b-tagged events in fig 10 compared to measurements by L3 [26] Interestingly the multiplicitydistribution still appears to be too wide but within the constraints of the present study we were unableto obtain further improvements As a point of speculation we note that the distribution of the numberof partons before hadronization is also quite wide in PYTHIA and this may be playing a role ineffectively setting a lower limit on the width that can be achieved for the hadron-level distribution

Comparisons to L3 event shapes in b-tagged events are collected in appendix B1 (the left columnof plots contains light-flavour tagged event shapes the right column b-tagged ones) In particular the

15

0 10 20 30 40

Mom

ent

0

02

04

06

08 (moments)weakBx

Pythia 8181Data from Eur Phys J C71 (2011) 1557

LEP (combined)PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn10

00plusmn103

00plusmn129

V I

N C

I A

R O

O T

N0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

Figure 9 Hadronic Z decays atradics = 912 GeV Moments of the B fragmentation function com-

pared to a combined analysis of LEP+SLD data by DELPHI [63]

0 20 40

)ch

Pro

babi

lity(

n

-610

-510

-410

-310

-210

-110

1

10

210 Charged Multiplicity (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

06plusmn45

08plusmn64

13plusmn110

V I

N C

I A

R O

O T

(b)chn0 20 40

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

ch d

nch

1n

-510

-410

-310

-210

-110

1

10

210 Charged Momentum Fraction (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn08

00plusmn06 V

I N

C I

A R

O O

T

)| (b)p

|Ln(x0 2 4 6 8

The

ory

Dat

a

06

08

1

12

14

Figure 10 HadronicZ decays atradics = 912 GeV Charged-hadron multiplicity (left) and momentum-

fraction (right) spectra in b-tagged events

16

0 02 04 06 08 1

dx

Dgt

dn

D1

ltn

0

05

1

15

2

25gt01)

E) (x

plusmnx(D

Pythia 8183Data from EurPhysJ C16 (2000) 597

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn14

02plusmn28

02plusmn32

V I

N C

I A

R O

O T

Ex0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

EX02 04 06 08 1

E)

dX

dN

(DZ

had

1N

0

0002

0004

0006

0008

001

0012

0014

0016

ALEPHHerwig++Sherpa

91 GeV ee Z (hadronic)

mcp

lots

cer

nch

41

M e

vent

sge

Riv

et 1

82

Herwig++ 261a Sherpa 141

ALEPH_1999_S4193598

spectrum (particle-level)+-D

02 04 06 08 105

1

15Ratio to ALEPH

Figure 11 The inclusive Dlowast spectrum in hadronic Z decays [55] Left Monash 2013 tune com-pared with default PYTHIA 8 and the Fischer tune Right comparison with HERWIG (dashed) andSHERPA (dotted) from MCPLOTS [25] Note that the plot in the left-hand pane is normalized tounity while the one in the right-hand pane is normalized to the number of hadronic Z decays

Monash tune gives a significant improvement in the soft region of the jet-broadening parameters inb-tagged events while no significant changes are observed for the other event shapes These smallimprovements are presumably a direct consequence of the softening of the b fragmentation functionit is now less likely to find an isolated ultra-hard B hadron

We round off the discussion of heavy-quark fragmentation by noting that a similarly comprehen-sive study of charm-quark fragmentation would be desirable However charm-quark tagged multi-plicity and event-shape data is not available to our knowledge and most of the D meson spectra onHEPDATA concern only specific decay chains (hence depend on the decay modeling) andor are lim-ited to restricted fiducial regions (limiting their generality) Experimentally the cleanest measurementis obtained from Dlowast decays and an inclusive momentum spectrum for Dlowast mesons has been measuredby ALEPH [55] From this distribution shown in fig 11 we determine a value for rc of

StringZrFactC = 132

We note that the low-x part of the Dlowast spectrum originates from g rarr cc shower splittings whilethe high-x tail represents prompt Dlowast production from leading charm in Z rarr cc (see [55] for a nicefigure illustrating this) The intermediate range contains a large component of feed-down from brarr cdecays hence this distribution is also indirectly sensitive to the b-quark sector The previous defaulttune had a harder spectrum for both b- and c-fragmentation leading to an overestimate of the high-xpart of the Dlowast distribution The undershooting at low xDlowast values which remains unchanged in theMonash tune most likely indicates an underproduction of g rarr cc branchings in the shower We notethat such an underproduction may also be reflected in the LHC data on Dlowast production see eg [65]We return to this issue in the discussion of identified particles at LHC section 35

17

plusmnπ 0π plusmnK η η plusmnρ 0ρ plusmnK ω φKK-

RKφ

RK-φ

R-πφ

R

gtch

ltnltngt

-310

-210

-110

1

10Meson Fractions

Pythia 8183Data from PDGHEPDATA

LEP + SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn06

00plusmn12

00plusmn12

V I

N C

I A

R O

O T

plusmnπ 0π plusmnK η η plusmnρ 0ρ plusmnK ω φKK-

RKφ

RK-φ

R-πφ

R

The

ory

Dat

a

06

08

1

12

14

p ΛpΛ

RKΛ

R plusmnΣ 0Σ ++∆ Σ plusmnΞ 0Ξ Ω

gtch

ltnltngt

-410

-310

-210

-110

1Baryon Fractions

Pythia 8183Data from PDGHEPDATA

LEP PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn11

00plusmn22

00plusmn22

V I

N C

I A

R O

O T

p ΛpΛ

RKΛ

R plusmnΣ 0Σ ++∆ Σ plusmnΞ 0Ξ Ω

The

ory

Dat

a

06

08

1

12

14

Figure 5 Hadronic Z decays atradics = 912 GeV Identified-meson and -baryon rates expressed as

fractions of the average charged-particle multiplicity

-4 -2 0

dln

(x)

Kgt

dn

K1

ltn

-310

-210

-110

1

10

) (Combined)plusmnx(K

Pythia 8183Data from ZPC66(1995)355 ZPC63(1994)181 EPJC5(1998)585

LEP (A+D+O)PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn16

00plusmn14

01plusmn19

V I

N C

I A

R O

O T

)p

ln(x-4 -2 0

The

ory

Dat

a

06

08

1

12

14

0 1 2 3 4 5

ξd

Λgt

dn

Λ1

ltn

0

02

04

06)]|0Λ|Ln[x(

Pythia 8183Data from EPJ C16 (2000) 613

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn08

01plusmn15

01plusmn12

V I

N C

I A

R O

O T

pξ

0 1 2 3 4 5

The

ory

Dat

a

06

08

1

12

14

Figure 6 Hadronic Z decays atradics = 912 GeV Kplusmn and Λ momentum-fraction spectra

11

the significant increase in the value of aExtraDiquark from 05 (Default) to 097 (Monash cf sec-tion 21) produces a desirable suppression of very hard Λ baryons The corresponding change in themeasured parts of the p and Ξplusmn spectra (cf appendix B2) are small compared with the experimentaluncertainties

It is interesting however to note that all of these spectra indicate or are at least consistent with amodelling excess of soft identified-particle production below ln(x) sim minus45 corresponding to absolutemomentum scales around 500 MeV while we recall that the inclusive ln(x) spectrum above showedan underproduction around ln(x) sim minus55 Within the constraints of the current theory model wehave not managed to find a way to mitigate these features while remaining consistent with the rest ofthe data Nonetheless it should be mentioned that these observations could have relevance also in thecontext of understanding identified-particle spectra at LHC a possibility which to our knowledge hasso far been ignored

23 Heavy-Quark Fragmentation

Similarly to above we first discuss the inclusive rates of hadrons containing heavy quarks before wediscuss their spectra Unfortunately there are also here substantial disagreements between differentpieces of information We have made the following choices

bull ForD mesons the average Dplusmn rate given in sec 46 of the PDG (0175) is equal to the inclusivebranching fraction for Z rarr DplusmnX given in the Z boson summary table in the same Review(after normalizing the latter to the hadronic Z fraction of 6991 [39]) However the formerought to be substantially larger given that some Z rarr cc events will contain two Dplusmn mesons(counting once in the Z rarr DplusmnX branching fraction but twice in the average Dplusmn multiplicity)We therefore here use a measurement by ALEPH [54] to fix the Dplusmn and D0 rates resulting ina reference value for the average Dplusmn multiplicity almost twice as large as that given by sec 46in the PDG

bull For Λ+c the average multiplicity given in sec 46 of the PDG is twice as large as that indicated

by the branching fraction BR(Z rarr Λ+c X) in the Z boson summary table in the same Review

We here use the branching from the Z boson summary table as our constraint on the Λ+c rate

normalized to the total branching fraction BR(Z rarr hadrons)

bull We also include the average rate of g rarr cc splittings obtained by combining an ALEPH [55]and an OPAL measurement [56] but with an additional 10 systematic uncertainty added toboth measurements to account for possibly larger mismodeling effects in the correction fac-tors [57 58]

bull For B particles we use the quite precise inclusive Z rarr B+X branching fraction from the Zboson summary in the PDG

bull We also use the sum of Bplusmn and B0(B0) in sec 46 of the PDG10

bull TheB0s multiplicity given in sec 46 of the PDG (0057plusmn0013) is more than twice the inclusive

BR(Z rarr B0sX)BR(Z rarr hadrons) branching fraction (00227 plusmn 00019) quoted in the Z

10Note that we have a factor 2 relative to the PDG since it appears the PDG quotes the average rather than the sum Notealso that all the average B meson multiplicities in sec 46 of the PDG are accompanied by a note ldquo(d)rdquo stating that the SMB(Z rarr bb) = 0217 was used for the normalization For completeness the reader should be aware that this is the fractionnormalized to hadronic Z decays the branching fraction relative to all Z decays is 0151 [39]

12

Charm Our Reference Our〈n〉 or BR Value Source

D+ +Dminus 0251 plusmn0047 AD0 + D0 0518 plusmn0063 ADlowast+ +Dlowastminus 0194 plusmn00057 PD+

s +Dminuss 0131 plusmn0021 PBR(Z rarr Λ+

c X) 00220 plusmn00047 ZBR(Z rarr X + cc) 00306 plusmn00047 AOJψ 00052 plusmn00004 Pχc1 00041 plusmn00011 Pψprime 00023 plusmn00004 P

Beauty Our Reference Our〈n〉 or BR Value Source

BR(Z rarr B+X) 0087 plusmn0002 ZB+ +B0 + B0 +Bminus 0330 plusmn0052 PBlowastu +Blowastd +Blowasts 0288 plusmn0026 PBR(Z rarr B0

sX) 00227 plusmn00019 ZBR(Z rarr BbaryonX) 00197 plusmn00032 ZBR(Z rarr X + bb) 000288 plusmn000061 ADSBR(Z rarr bbbbX) 000051 plusmn000019 ZΥ (times10) 00014 plusmn00007 P

Table 2 Hadronic Z decays atradics = MZ Measured rates and inclusive branching fractions of

particles containing c and b quarks as used in this work Note the branching fractions are normalizedto Z rarr hadrons and hence should be interpreted as eg BR(Z rarr B+X)BR(Z rarr hadrons)Note 2 the sum over Blowast states includes both particles and anti-particles Note 3 the Υ rate ismultiplied by a factor 10 Source labels indicate A (ALEPH) D (DELPHI) O (OPAL) P (PDGsection 46) S (SLD) Z (PDG Z Boson Summary Table)

boson summary table We find these two numbers difficult to reconcile and choose to use theinclusive BR(Z rarr B0

sX)BR(Z rarr hadrons) branching fraction as our main constraint

bull We also include the inclusive branching fractions for B-baryons (summed over baryons andantibaryons) the rate of g rarr bb splittings obtained by combining ALEPH [59] DELPHI [60]and SLD [61] measurements (including an additional 10 systematic to account for largerpossible mismodeling effects in the correction factors [57 58]) and the rate of Z rarr bbbb fromthe PDG Z boson summary table [39]

Our constraints on the heavy-quark particle rates are summarized in tab 2 Comparisons to these ratesare shown in fig 7 now without normalizing to the average charged-particle multiplicity Given thatmost of the c and b quarks come directly from Z rarr cc and Z rarr bb decays there is not a lot of roomfor tuning to these numbers apart from the relative rates of vector mesons vs pseudoscalars which iscontrolled by the parameters

Heavy MesonsStringFlavmesonCvector = 088StringFlavmesonBvector = 22

Our parameters are slightly smaller than the current default values leading to slightly smaller Dlowast

and Blowast rates as can be seen from the plots in fig 7 Note also that the increased overall amount ofstrangeness in the fragmentation leads to slightly higherDs andBs fractions in better agreement withthe data Uncertainties are however large and some exotic onium states like χc1 ψprime and Υ are notwell described by the default modeling (It is encouraging that at least the multiplicity of Jψ mesonsis well described though a substantial fraction of this likely owes to the feed-down from B decaysand hence does not depend directly on the string-fragmentation model itself)

We also note that it would be desirable to reduce the rate of g rarr bb and Z rarr bbbb events whilethe g rarr cc one appears consistent with the LEP constraints We suspect that this issue may be tiedto the fixed choice of using pperp as the renormalization scale for both gluon emissions and for g rarr qq

13

plusmnD 0D plusmnD plusmns

D X+

cΛ

ccrarrg ψJ c1χ

3685

ψ

X)

rarrlt

ngt o

r B

R(Z

-410

-310

-210

-110

1

10Charm Rates

Pythia 8185Data from HEPDATAPDG

LEP

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn15

00plusmn18

00plusmn17

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

plusmnD 0Dplusmn

D plusmnsD X+

cΛ ccrarrg ψJ c1χ

3685ψ

The

ory

Dat

a

0

05

1

15

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

X)

rarrlt

ngt o

r B

R(Z

-510

-410

-310

-210

-110

1

10Beauty Rates

Pythia 8185Data from HEPDATAPDG

LEP+SLD

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn17

00plusmn23

00plusmn23

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

The

ory

Dat

a0

05

1

15

Figure 7 Hadronic Z decays atradics = 912 GeV Rates and inclusive Z rarr X branching fractions

(normalized to Z rarr hadrons) of particles containing c and b quarks

splittings in the current version of PYTHIA A more natural choice for g rarr qq could be microR prop mqqas used eg in the VINCIA shower model [29]

We now turn to the dynamics of heavy-quark fragmentation focusing mainly on the b quarkFor heavy quarks the Lund fragmentation function is modified due to the (massive) endpoints not

moving along straight lightcones as the string pulls on them they slow down resulting in the stringtracing out a smaller space-time area than it would for massless quarks This modifies the implicationsof the string area law in a manner captured by the so-called Bowler modification of the fragmentationfunction [62]

fmassive(zmQ) prop f(z)

zbrQm2Q

(6)

with mQ the heavy-quark mass b the same universal parameter that appears in the massless fragmen-tation function eq (3) and rQ a tuning parameter which is unity in the original derivation of Bowlerbut can be assigned values different from unity to reduce (rQ rarr 0) or emphasize (rQ gt 1) the effectSince rQ multiplies the heavy-quark mass (squared) it can also be viewed as an effective rescalingof the mass value The net result is a suppression of the region z rarr 1 hence a relative softening ofthe fragmentation spectrum for heavy flavours (relative since the presence of m2

perp in the exponent ofeq (3) still implies an overall harder fragmentation for higher hadron masses)

We emphasize that this is the only fragmentation function that is self-consistent within the string-fragmentation model [33 62] Although a few alternative forms of the fragmentation functions formassive quarks are available in the code we therefore here work only with the Bowler type As forthe massless function the proportionality sign in eq (6) indicates that the function is normalized tounity

In PYTHIA separate rQ parameters are provided for c and b quarks We consider the one for bquarks first Its default value is rb = 067 but this appears to give too hard b fragmentation spectrawhen compared to LEP and SLD data see below For the Monash tune we instead use

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (DELPHI)weak

Bx

Pythia 8181Data from EurPhysJ C71 (2011) 1557

DELPHI PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn16

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (SLD)weak

Bx

Pythia 8181HepData5111d1-x1-y1

SLDPY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn07

00plusmn15

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a06

08

1

12

14

Figure 8 Hadronic Z decays atradics = 912 GeV Momentum (xB) spectra of weakly decaying B

hadrons compared to data from DELPHI [63] (left) and SLD [64] (right)

StringZrFactB = 0855

which produces softer B spectra and simultaneously agrees better with the theoretically preferredvalue (rb = 1)

A comparison to the scaled-momentum spectra (xB = 2|pB|Ecm) of weakly decayingB hadronsfrom both DELPHI [63] and SLD [64] is given in fig 8 (due to small differences between the twomeasured results we choose to show both) The dampening of the hardest part of the spectrum causedby the increase in the rb parameter is visible in the right-most two bins of the distributions and in thesmaller χ2

5 values for the Monash tune The effects of the modification can be further emphasizedby an analysis of the moments of the distribution in which the higher moments are increasinglydominated by the region xB rarr 1 A comparison to a combined LEP analysis of the moments of thexB distribution [63] is given in fig 9 further emphasizing that the high-xB part of the distribution isnow under better control

The reason we have not increased the rb parameter further is that it comes at a price If theB hadrons are taking less energy then there is more energy left over to produce other particlesand the generated multiplicity distribution in b events already exhibits a slightly high tail towardslarge multiplicities Nonetheless since the revised light-flavour fragmentation parameters produce anoverall narrower fragmentation function the end result is still a slight improvement in the multiplicitydistribution also for b events This is illustrated together with the inclusive momentum distributionfor b-tagged events in fig 10 compared to measurements by L3 [26] Interestingly the multiplicitydistribution still appears to be too wide but within the constraints of the present study we were unableto obtain further improvements As a point of speculation we note that the distribution of the numberof partons before hadronization is also quite wide in PYTHIA and this may be playing a role ineffectively setting a lower limit on the width that can be achieved for the hadron-level distribution

Comparisons to L3 event shapes in b-tagged events are collected in appendix B1 (the left columnof plots contains light-flavour tagged event shapes the right column b-tagged ones) In particular the

15

0 10 20 30 40

Mom

ent

0

02

04

06

08 (moments)weakBx

Pythia 8181Data from Eur Phys J C71 (2011) 1557

LEP (combined)PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn10

00plusmn103

00plusmn129

V I

N C

I A

R O

O T

N0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

Figure 9 Hadronic Z decays atradics = 912 GeV Moments of the B fragmentation function com-

pared to a combined analysis of LEP+SLD data by DELPHI [63]

0 20 40

)ch

Pro

babi

lity(

n

-610

-510

-410

-310

-210

-110

1

10

210 Charged Multiplicity (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

06plusmn45

08plusmn64

13plusmn110

V I

N C

I A

R O

O T

(b)chn0 20 40

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

ch d

nch

1n

-510

-410

-310

-210

-110

1

10

210 Charged Momentum Fraction (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn08

00plusmn06 V

I N

C I

A R

O O

T

)| (b)p

|Ln(x0 2 4 6 8

The

ory

Dat

a

06

08

1

12

14

Figure 10 HadronicZ decays atradics = 912 GeV Charged-hadron multiplicity (left) and momentum-

fraction (right) spectra in b-tagged events

16

0 02 04 06 08 1

dx

Dgt

dn

D1

ltn

0

05

1

15

2

25gt01)

E) (x

plusmnx(D

Pythia 8183Data from EurPhysJ C16 (2000) 597

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn14

02plusmn28

02plusmn32

V I

N C

I A

R O

O T

Ex0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

EX02 04 06 08 1

E)

dX

dN

(DZ

had

1N

0

0002

0004

0006

0008

001

0012

0014

0016

ALEPHHerwig++Sherpa

91 GeV ee Z (hadronic)

mcp

lots

cer

nch

41

M e

vent

sge

Riv

et 1

82

Herwig++ 261a Sherpa 141

ALEPH_1999_S4193598

spectrum (particle-level)+-D

02 04 06 08 105

1

15Ratio to ALEPH

Figure 11 The inclusive Dlowast spectrum in hadronic Z decays [55] Left Monash 2013 tune com-pared with default PYTHIA 8 and the Fischer tune Right comparison with HERWIG (dashed) andSHERPA (dotted) from MCPLOTS [25] Note that the plot in the left-hand pane is normalized tounity while the one in the right-hand pane is normalized to the number of hadronic Z decays

Monash tune gives a significant improvement in the soft region of the jet-broadening parameters inb-tagged events while no significant changes are observed for the other event shapes These smallimprovements are presumably a direct consequence of the softening of the b fragmentation functionit is now less likely to find an isolated ultra-hard B hadron

We round off the discussion of heavy-quark fragmentation by noting that a similarly comprehen-sive study of charm-quark fragmentation would be desirable However charm-quark tagged multi-plicity and event-shape data is not available to our knowledge and most of the D meson spectra onHEPDATA concern only specific decay chains (hence depend on the decay modeling) andor are lim-ited to restricted fiducial regions (limiting their generality) Experimentally the cleanest measurementis obtained from Dlowast decays and an inclusive momentum spectrum for Dlowast mesons has been measuredby ALEPH [55] From this distribution shown in fig 11 we determine a value for rc of

StringZrFactC = 132

We note that the low-x part of the Dlowast spectrum originates from g rarr cc shower splittings whilethe high-x tail represents prompt Dlowast production from leading charm in Z rarr cc (see [55] for a nicefigure illustrating this) The intermediate range contains a large component of feed-down from brarr cdecays hence this distribution is also indirectly sensitive to the b-quark sector The previous defaulttune had a harder spectrum for both b- and c-fragmentation leading to an overestimate of the high-xpart of the Dlowast distribution The undershooting at low xDlowast values which remains unchanged in theMonash tune most likely indicates an underproduction of g rarr cc branchings in the shower We notethat such an underproduction may also be reflected in the LHC data on Dlowast production see eg [65]We return to this issue in the discussion of identified particles at LHC section 35

17

the significant increase in the value of aExtraDiquark from 05 (Default) to 097 (Monash cf sec-tion 21) produces a desirable suppression of very hard Λ baryons The corresponding change in themeasured parts of the p and Ξplusmn spectra (cf appendix B2) are small compared with the experimentaluncertainties

It is interesting however to note that all of these spectra indicate or are at least consistent with amodelling excess of soft identified-particle production below ln(x) sim minus45 corresponding to absolutemomentum scales around 500 MeV while we recall that the inclusive ln(x) spectrum above showedan underproduction around ln(x) sim minus55 Within the constraints of the current theory model wehave not managed to find a way to mitigate these features while remaining consistent with the rest ofthe data Nonetheless it should be mentioned that these observations could have relevance also in thecontext of understanding identified-particle spectra at LHC a possibility which to our knowledge hasso far been ignored

23 Heavy-Quark Fragmentation

Similarly to above we first discuss the inclusive rates of hadrons containing heavy quarks before wediscuss their spectra Unfortunately there are also here substantial disagreements between differentpieces of information We have made the following choices

bull ForD mesons the average Dplusmn rate given in sec 46 of the PDG (0175) is equal to the inclusivebranching fraction for Z rarr DplusmnX given in the Z boson summary table in the same Review(after normalizing the latter to the hadronic Z fraction of 6991 [39]) However the formerought to be substantially larger given that some Z rarr cc events will contain two Dplusmn mesons(counting once in the Z rarr DplusmnX branching fraction but twice in the average Dplusmn multiplicity)We therefore here use a measurement by ALEPH [54] to fix the Dplusmn and D0 rates resulting ina reference value for the average Dplusmn multiplicity almost twice as large as that given by sec 46in the PDG

bull For Λ+c the average multiplicity given in sec 46 of the PDG is twice as large as that indicated

by the branching fraction BR(Z rarr Λ+c X) in the Z boson summary table in the same Review

We here use the branching from the Z boson summary table as our constraint on the Λ+c rate

normalized to the total branching fraction BR(Z rarr hadrons)

bull We also include the average rate of g rarr cc splittings obtained by combining an ALEPH [55]and an OPAL measurement [56] but with an additional 10 systematic uncertainty added toboth measurements to account for possibly larger mismodeling effects in the correction fac-tors [57 58]

bull For B particles we use the quite precise inclusive Z rarr B+X branching fraction from the Zboson summary in the PDG

bull We also use the sum of Bplusmn and B0(B0) in sec 46 of the PDG10

bull TheB0s multiplicity given in sec 46 of the PDG (0057plusmn0013) is more than twice the inclusive

BR(Z rarr B0sX)BR(Z rarr hadrons) branching fraction (00227 plusmn 00019) quoted in the Z

10Note that we have a factor 2 relative to the PDG since it appears the PDG quotes the average rather than the sum Notealso that all the average B meson multiplicities in sec 46 of the PDG are accompanied by a note ldquo(d)rdquo stating that the SMB(Z rarr bb) = 0217 was used for the normalization For completeness the reader should be aware that this is the fractionnormalized to hadronic Z decays the branching fraction relative to all Z decays is 0151 [39]

12

Charm Our Reference Our〈n〉 or BR Value Source

D+ +Dminus 0251 plusmn0047 AD0 + D0 0518 plusmn0063 ADlowast+ +Dlowastminus 0194 plusmn00057 PD+

s +Dminuss 0131 plusmn0021 PBR(Z rarr Λ+

c X) 00220 plusmn00047 ZBR(Z rarr X + cc) 00306 plusmn00047 AOJψ 00052 plusmn00004 Pχc1 00041 plusmn00011 Pψprime 00023 plusmn00004 P

Beauty Our Reference Our〈n〉 or BR Value Source

BR(Z rarr B+X) 0087 plusmn0002 ZB+ +B0 + B0 +Bminus 0330 plusmn0052 PBlowastu +Blowastd +Blowasts 0288 plusmn0026 PBR(Z rarr B0

sX) 00227 plusmn00019 ZBR(Z rarr BbaryonX) 00197 plusmn00032 ZBR(Z rarr X + bb) 000288 plusmn000061 ADSBR(Z rarr bbbbX) 000051 plusmn000019 ZΥ (times10) 00014 plusmn00007 P

Table 2 Hadronic Z decays atradics = MZ Measured rates and inclusive branching fractions of

particles containing c and b quarks as used in this work Note the branching fractions are normalizedto Z rarr hadrons and hence should be interpreted as eg BR(Z rarr B+X)BR(Z rarr hadrons)Note 2 the sum over Blowast states includes both particles and anti-particles Note 3 the Υ rate ismultiplied by a factor 10 Source labels indicate A (ALEPH) D (DELPHI) O (OPAL) P (PDGsection 46) S (SLD) Z (PDG Z Boson Summary Table)

boson summary table We find these two numbers difficult to reconcile and choose to use theinclusive BR(Z rarr B0

sX)BR(Z rarr hadrons) branching fraction as our main constraint

bull We also include the inclusive branching fractions for B-baryons (summed over baryons andantibaryons) the rate of g rarr bb splittings obtained by combining ALEPH [59] DELPHI [60]and SLD [61] measurements (including an additional 10 systematic to account for largerpossible mismodeling effects in the correction factors [57 58]) and the rate of Z rarr bbbb fromthe PDG Z boson summary table [39]

Our constraints on the heavy-quark particle rates are summarized in tab 2 Comparisons to these ratesare shown in fig 7 now without normalizing to the average charged-particle multiplicity Given thatmost of the c and b quarks come directly from Z rarr cc and Z rarr bb decays there is not a lot of roomfor tuning to these numbers apart from the relative rates of vector mesons vs pseudoscalars which iscontrolled by the parameters

Heavy MesonsStringFlavmesonCvector = 088StringFlavmesonBvector = 22

Our parameters are slightly smaller than the current default values leading to slightly smaller Dlowast

and Blowast rates as can be seen from the plots in fig 7 Note also that the increased overall amount ofstrangeness in the fragmentation leads to slightly higherDs andBs fractions in better agreement withthe data Uncertainties are however large and some exotic onium states like χc1 ψprime and Υ are notwell described by the default modeling (It is encouraging that at least the multiplicity of Jψ mesonsis well described though a substantial fraction of this likely owes to the feed-down from B decaysand hence does not depend directly on the string-fragmentation model itself)

We also note that it would be desirable to reduce the rate of g rarr bb and Z rarr bbbb events whilethe g rarr cc one appears consistent with the LEP constraints We suspect that this issue may be tiedto the fixed choice of using pperp as the renormalization scale for both gluon emissions and for g rarr qq

13

plusmnD 0D plusmnD plusmns

D X+

cΛ

ccrarrg ψJ c1χ

3685

ψ

X)

rarrlt

ngt o

r B

R(Z

-410

-310

-210

-110

1

10Charm Rates

Pythia 8185Data from HEPDATAPDG

LEP

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn15

00plusmn18

00plusmn17

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

plusmnD 0Dplusmn

D plusmnsD X+

cΛ ccrarrg ψJ c1χ

3685ψ

The

ory

Dat

a

0

05

1

15

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

X)

rarrlt

ngt o

r B

R(Z

-510

-410

-310

-210

-110

1

10Beauty Rates

Pythia 8185Data from HEPDATAPDG

LEP+SLD

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn17

00plusmn23

00plusmn23

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

The

ory

Dat

a0

05

1

15

Figure 7 Hadronic Z decays atradics = 912 GeV Rates and inclusive Z rarr X branching fractions

(normalized to Z rarr hadrons) of particles containing c and b quarks

splittings in the current version of PYTHIA A more natural choice for g rarr qq could be microR prop mqqas used eg in the VINCIA shower model [29]

We now turn to the dynamics of heavy-quark fragmentation focusing mainly on the b quarkFor heavy quarks the Lund fragmentation function is modified due to the (massive) endpoints not

moving along straight lightcones as the string pulls on them they slow down resulting in the stringtracing out a smaller space-time area than it would for massless quarks This modifies the implicationsof the string area law in a manner captured by the so-called Bowler modification of the fragmentationfunction [62]

fmassive(zmQ) prop f(z)

zbrQm2Q

(6)

with mQ the heavy-quark mass b the same universal parameter that appears in the massless fragmen-tation function eq (3) and rQ a tuning parameter which is unity in the original derivation of Bowlerbut can be assigned values different from unity to reduce (rQ rarr 0) or emphasize (rQ gt 1) the effectSince rQ multiplies the heavy-quark mass (squared) it can also be viewed as an effective rescalingof the mass value The net result is a suppression of the region z rarr 1 hence a relative softening ofthe fragmentation spectrum for heavy flavours (relative since the presence of m2

perp in the exponent ofeq (3) still implies an overall harder fragmentation for higher hadron masses)

We emphasize that this is the only fragmentation function that is self-consistent within the string-fragmentation model [33 62] Although a few alternative forms of the fragmentation functions formassive quarks are available in the code we therefore here work only with the Bowler type As forthe massless function the proportionality sign in eq (6) indicates that the function is normalized tounity

In PYTHIA separate rQ parameters are provided for c and b quarks We consider the one for bquarks first Its default value is rb = 067 but this appears to give too hard b fragmentation spectrawhen compared to LEP and SLD data see below For the Monash tune we instead use

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (DELPHI)weak

Bx

Pythia 8181Data from EurPhysJ C71 (2011) 1557

DELPHI PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn16

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (SLD)weak

Bx

Pythia 8181HepData5111d1-x1-y1

SLDPY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn07

00plusmn15

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a06

08

1

12

14

Figure 8 Hadronic Z decays atradics = 912 GeV Momentum (xB) spectra of weakly decaying B

hadrons compared to data from DELPHI [63] (left) and SLD [64] (right)

StringZrFactB = 0855

which produces softer B spectra and simultaneously agrees better with the theoretically preferredvalue (rb = 1)

A comparison to the scaled-momentum spectra (xB = 2|pB|Ecm) of weakly decayingB hadronsfrom both DELPHI [63] and SLD [64] is given in fig 8 (due to small differences between the twomeasured results we choose to show both) The dampening of the hardest part of the spectrum causedby the increase in the rb parameter is visible in the right-most two bins of the distributions and in thesmaller χ2

5 values for the Monash tune The effects of the modification can be further emphasizedby an analysis of the moments of the distribution in which the higher moments are increasinglydominated by the region xB rarr 1 A comparison to a combined LEP analysis of the moments of thexB distribution [63] is given in fig 9 further emphasizing that the high-xB part of the distribution isnow under better control

The reason we have not increased the rb parameter further is that it comes at a price If theB hadrons are taking less energy then there is more energy left over to produce other particlesand the generated multiplicity distribution in b events already exhibits a slightly high tail towardslarge multiplicities Nonetheless since the revised light-flavour fragmentation parameters produce anoverall narrower fragmentation function the end result is still a slight improvement in the multiplicitydistribution also for b events This is illustrated together with the inclusive momentum distributionfor b-tagged events in fig 10 compared to measurements by L3 [26] Interestingly the multiplicitydistribution still appears to be too wide but within the constraints of the present study we were unableto obtain further improvements As a point of speculation we note that the distribution of the numberof partons before hadronization is also quite wide in PYTHIA and this may be playing a role ineffectively setting a lower limit on the width that can be achieved for the hadron-level distribution

Comparisons to L3 event shapes in b-tagged events are collected in appendix B1 (the left columnof plots contains light-flavour tagged event shapes the right column b-tagged ones) In particular the

15

0 10 20 30 40

Mom

ent

0

02

04

06

08 (moments)weakBx

Pythia 8181Data from Eur Phys J C71 (2011) 1557

LEP (combined)PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn10

00plusmn103

00plusmn129

V I

N C

I A

R O

O T

N0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

Figure 9 Hadronic Z decays atradics = 912 GeV Moments of the B fragmentation function com-

pared to a combined analysis of LEP+SLD data by DELPHI [63]

0 20 40

)ch

Pro

babi

lity(

n

-610

-510

-410

-310

-210

-110

1

10

210 Charged Multiplicity (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

06plusmn45

08plusmn64

13plusmn110

V I

N C

I A

R O

O T

(b)chn0 20 40

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

ch d

nch

1n

-510

-410

-310

-210

-110

1

10

210 Charged Momentum Fraction (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn08

00plusmn06 V

I N

C I

A R

O O

T

)| (b)p

|Ln(x0 2 4 6 8

The

ory

Dat

a

06

08

1

12

14

Figure 10 HadronicZ decays atradics = 912 GeV Charged-hadron multiplicity (left) and momentum-

fraction (right) spectra in b-tagged events

16

0 02 04 06 08 1

dx

Dgt

dn

D1

ltn

0

05

1

15

2

25gt01)

E) (x

plusmnx(D

Pythia 8183Data from EurPhysJ C16 (2000) 597

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn14

02plusmn28

02plusmn32

V I

N C

I A

R O

O T

Ex0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

EX02 04 06 08 1

E)

dX

dN

(DZ

had

1N

0

0002

0004

0006

0008

001

0012

0014

0016

ALEPHHerwig++Sherpa

91 GeV ee Z (hadronic)

mcp

lots

cer

nch

41

M e

vent

sge

Riv

et 1

82

Herwig++ 261a Sherpa 141

ALEPH_1999_S4193598

spectrum (particle-level)+-D

02 04 06 08 105

1

15Ratio to ALEPH

Figure 11 The inclusive Dlowast spectrum in hadronic Z decays [55] Left Monash 2013 tune com-pared with default PYTHIA 8 and the Fischer tune Right comparison with HERWIG (dashed) andSHERPA (dotted) from MCPLOTS [25] Note that the plot in the left-hand pane is normalized tounity while the one in the right-hand pane is normalized to the number of hadronic Z decays

Monash tune gives a significant improvement in the soft region of the jet-broadening parameters inb-tagged events while no significant changes are observed for the other event shapes These smallimprovements are presumably a direct consequence of the softening of the b fragmentation functionit is now less likely to find an isolated ultra-hard B hadron

We round off the discussion of heavy-quark fragmentation by noting that a similarly comprehen-sive study of charm-quark fragmentation would be desirable However charm-quark tagged multi-plicity and event-shape data is not available to our knowledge and most of the D meson spectra onHEPDATA concern only specific decay chains (hence depend on the decay modeling) andor are lim-ited to restricted fiducial regions (limiting their generality) Experimentally the cleanest measurementis obtained from Dlowast decays and an inclusive momentum spectrum for Dlowast mesons has been measuredby ALEPH [55] From this distribution shown in fig 11 we determine a value for rc of

StringZrFactC = 132

We note that the low-x part of the Dlowast spectrum originates from g rarr cc shower splittings whilethe high-x tail represents prompt Dlowast production from leading charm in Z rarr cc (see [55] for a nicefigure illustrating this) The intermediate range contains a large component of feed-down from brarr cdecays hence this distribution is also indirectly sensitive to the b-quark sector The previous defaulttune had a harder spectrum for both b- and c-fragmentation leading to an overestimate of the high-xpart of the Dlowast distribution The undershooting at low xDlowast values which remains unchanged in theMonash tune most likely indicates an underproduction of g rarr cc branchings in the shower We notethat such an underproduction may also be reflected in the LHC data on Dlowast production see eg [65]We return to this issue in the discussion of identified particles at LHC section 35

17

Charm Our Reference Our〈n〉 or BR Value Source

D+ +Dminus 0251 plusmn0047 AD0 + D0 0518 plusmn0063 ADlowast+ +Dlowastminus 0194 plusmn00057 PD+

s +Dminuss 0131 plusmn0021 PBR(Z rarr Λ+

c X) 00220 plusmn00047 ZBR(Z rarr X + cc) 00306 plusmn00047 AOJψ 00052 plusmn00004 Pχc1 00041 plusmn00011 Pψprime 00023 plusmn00004 P

Beauty Our Reference Our〈n〉 or BR Value Source

BR(Z rarr B+X) 0087 plusmn0002 ZB+ +B0 + B0 +Bminus 0330 plusmn0052 PBlowastu +Blowastd +Blowasts 0288 plusmn0026 PBR(Z rarr B0

sX) 00227 plusmn00019 ZBR(Z rarr BbaryonX) 00197 plusmn00032 ZBR(Z rarr X + bb) 000288 plusmn000061 ADSBR(Z rarr bbbbX) 000051 plusmn000019 ZΥ (times10) 00014 plusmn00007 P

Table 2 Hadronic Z decays atradics = MZ Measured rates and inclusive branching fractions of

particles containing c and b quarks as used in this work Note the branching fractions are normalizedto Z rarr hadrons and hence should be interpreted as eg BR(Z rarr B+X)BR(Z rarr hadrons)Note 2 the sum over Blowast states includes both particles and anti-particles Note 3 the Υ rate ismultiplied by a factor 10 Source labels indicate A (ALEPH) D (DELPHI) O (OPAL) P (PDGsection 46) S (SLD) Z (PDG Z Boson Summary Table)

boson summary table We find these two numbers difficult to reconcile and choose to use theinclusive BR(Z rarr B0

sX)BR(Z rarr hadrons) branching fraction as our main constraint

bull We also include the inclusive branching fractions for B-baryons (summed over baryons andantibaryons) the rate of g rarr bb splittings obtained by combining ALEPH [59] DELPHI [60]and SLD [61] measurements (including an additional 10 systematic to account for largerpossible mismodeling effects in the correction factors [57 58]) and the rate of Z rarr bbbb fromthe PDG Z boson summary table [39]

Our constraints on the heavy-quark particle rates are summarized in tab 2 Comparisons to these ratesare shown in fig 7 now without normalizing to the average charged-particle multiplicity Given thatmost of the c and b quarks come directly from Z rarr cc and Z rarr bb decays there is not a lot of roomfor tuning to these numbers apart from the relative rates of vector mesons vs pseudoscalars which iscontrolled by the parameters

Heavy MesonsStringFlavmesonCvector = 088StringFlavmesonBvector = 22

Our parameters are slightly smaller than the current default values leading to slightly smaller Dlowast

and Blowast rates as can be seen from the plots in fig 7 Note also that the increased overall amount ofstrangeness in the fragmentation leads to slightly higherDs andBs fractions in better agreement withthe data Uncertainties are however large and some exotic onium states like χc1 ψprime and Υ are notwell described by the default modeling (It is encouraging that at least the multiplicity of Jψ mesonsis well described though a substantial fraction of this likely owes to the feed-down from B decaysand hence does not depend directly on the string-fragmentation model itself)

We also note that it would be desirable to reduce the rate of g rarr bb and Z rarr bbbb events whilethe g rarr cc one appears consistent with the LEP constraints We suspect that this issue may be tiedto the fixed choice of using pperp as the renormalization scale for both gluon emissions and for g rarr qq

13

plusmnD 0D plusmnD plusmns

D X+

cΛ

ccrarrg ψJ c1χ

3685

ψ

X)

rarrlt

ngt o

r B

R(Z

-410

-310

-210

-110

1

10Charm Rates

Pythia 8185Data from HEPDATAPDG

LEP

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn15

00plusmn18

00plusmn17

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

plusmnD 0Dplusmn

D plusmnsD X+

cΛ ccrarrg ψJ c1χ

3685ψ

The

ory

Dat

a

0

05

1

15

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

X)

rarrlt

ngt o

r B

R(Z

-510

-410

-310

-210

-110

1

10Beauty Rates

Pythia 8185Data from HEPDATAPDG

LEP+SLD

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn17

00plusmn23

00plusmn23

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

The

ory

Dat

a0

05

1

15

Figure 7 Hadronic Z decays atradics = 912 GeV Rates and inclusive Z rarr X branching fractions

(normalized to Z rarr hadrons) of particles containing c and b quarks

splittings in the current version of PYTHIA A more natural choice for g rarr qq could be microR prop mqqas used eg in the VINCIA shower model [29]

We now turn to the dynamics of heavy-quark fragmentation focusing mainly on the b quarkFor heavy quarks the Lund fragmentation function is modified due to the (massive) endpoints not

moving along straight lightcones as the string pulls on them they slow down resulting in the stringtracing out a smaller space-time area than it would for massless quarks This modifies the implicationsof the string area law in a manner captured by the so-called Bowler modification of the fragmentationfunction [62]

fmassive(zmQ) prop f(z)

zbrQm2Q

(6)

with mQ the heavy-quark mass b the same universal parameter that appears in the massless fragmen-tation function eq (3) and rQ a tuning parameter which is unity in the original derivation of Bowlerbut can be assigned values different from unity to reduce (rQ rarr 0) or emphasize (rQ gt 1) the effectSince rQ multiplies the heavy-quark mass (squared) it can also be viewed as an effective rescalingof the mass value The net result is a suppression of the region z rarr 1 hence a relative softening ofthe fragmentation spectrum for heavy flavours (relative since the presence of m2

perp in the exponent ofeq (3) still implies an overall harder fragmentation for higher hadron masses)

We emphasize that this is the only fragmentation function that is self-consistent within the string-fragmentation model [33 62] Although a few alternative forms of the fragmentation functions formassive quarks are available in the code we therefore here work only with the Bowler type As forthe massless function the proportionality sign in eq (6) indicates that the function is normalized tounity

In PYTHIA separate rQ parameters are provided for c and b quarks We consider the one for bquarks first Its default value is rb = 067 but this appears to give too hard b fragmentation spectrawhen compared to LEP and SLD data see below For the Monash tune we instead use

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (DELPHI)weak

Bx

Pythia 8181Data from EurPhysJ C71 (2011) 1557

DELPHI PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn16

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (SLD)weak

Bx

Pythia 8181HepData5111d1-x1-y1

SLDPY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn07

00plusmn15

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a06

08

1

12

14

Figure 8 Hadronic Z decays atradics = 912 GeV Momentum (xB) spectra of weakly decaying B

hadrons compared to data from DELPHI [63] (left) and SLD [64] (right)

StringZrFactB = 0855

which produces softer B spectra and simultaneously agrees better with the theoretically preferredvalue (rb = 1)

A comparison to the scaled-momentum spectra (xB = 2|pB|Ecm) of weakly decayingB hadronsfrom both DELPHI [63] and SLD [64] is given in fig 8 (due to small differences between the twomeasured results we choose to show both) The dampening of the hardest part of the spectrum causedby the increase in the rb parameter is visible in the right-most two bins of the distributions and in thesmaller χ2

5 values for the Monash tune The effects of the modification can be further emphasizedby an analysis of the moments of the distribution in which the higher moments are increasinglydominated by the region xB rarr 1 A comparison to a combined LEP analysis of the moments of thexB distribution [63] is given in fig 9 further emphasizing that the high-xB part of the distribution isnow under better control

The reason we have not increased the rb parameter further is that it comes at a price If theB hadrons are taking less energy then there is more energy left over to produce other particlesand the generated multiplicity distribution in b events already exhibits a slightly high tail towardslarge multiplicities Nonetheless since the revised light-flavour fragmentation parameters produce anoverall narrower fragmentation function the end result is still a slight improvement in the multiplicitydistribution also for b events This is illustrated together with the inclusive momentum distributionfor b-tagged events in fig 10 compared to measurements by L3 [26] Interestingly the multiplicitydistribution still appears to be too wide but within the constraints of the present study we were unableto obtain further improvements As a point of speculation we note that the distribution of the numberof partons before hadronization is also quite wide in PYTHIA and this may be playing a role ineffectively setting a lower limit on the width that can be achieved for the hadron-level distribution

Comparisons to L3 event shapes in b-tagged events are collected in appendix B1 (the left columnof plots contains light-flavour tagged event shapes the right column b-tagged ones) In particular the

15

0 10 20 30 40

Mom

ent

0

02

04

06

08 (moments)weakBx

Pythia 8181Data from Eur Phys J C71 (2011) 1557

LEP (combined)PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn10

00plusmn103

00plusmn129

V I

N C

I A

R O

O T

N0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

Figure 9 Hadronic Z decays atradics = 912 GeV Moments of the B fragmentation function com-

pared to a combined analysis of LEP+SLD data by DELPHI [63]

0 20 40

)ch

Pro

babi

lity(

n

-610

-510

-410

-310

-210

-110

1

10

210 Charged Multiplicity (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

06plusmn45

08plusmn64

13plusmn110

V I

N C

I A

R O

O T

(b)chn0 20 40

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

ch d

nch

1n

-510

-410

-310

-210

-110

1

10

210 Charged Momentum Fraction (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn08

00plusmn06 V

I N

C I

A R

O O

T

)| (b)p

|Ln(x0 2 4 6 8

The

ory

Dat

a

06

08

1

12

14

Figure 10 HadronicZ decays atradics = 912 GeV Charged-hadron multiplicity (left) and momentum-

fraction (right) spectra in b-tagged events

16

0 02 04 06 08 1

dx

Dgt

dn

D1

ltn

0

05

1

15

2

25gt01)

E) (x

plusmnx(D

Pythia 8183Data from EurPhysJ C16 (2000) 597

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn14

02plusmn28

02plusmn32

V I

N C

I A

R O

O T

Ex0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

EX02 04 06 08 1

E)

dX

dN

(DZ

had

1N

0

0002

0004

0006

0008

001

0012

0014

0016

ALEPHHerwig++Sherpa

91 GeV ee Z (hadronic)

mcp

lots

cer

nch

41

M e

vent

sge

Riv

et 1

82

Herwig++ 261a Sherpa 141

ALEPH_1999_S4193598

spectrum (particle-level)+-D

02 04 06 08 105

1

15Ratio to ALEPH

Figure 11 The inclusive Dlowast spectrum in hadronic Z decays [55] Left Monash 2013 tune com-pared with default PYTHIA 8 and the Fischer tune Right comparison with HERWIG (dashed) andSHERPA (dotted) from MCPLOTS [25] Note that the plot in the left-hand pane is normalized tounity while the one in the right-hand pane is normalized to the number of hadronic Z decays

Monash tune gives a significant improvement in the soft region of the jet-broadening parameters inb-tagged events while no significant changes are observed for the other event shapes These smallimprovements are presumably a direct consequence of the softening of the b fragmentation functionit is now less likely to find an isolated ultra-hard B hadron

We round off the discussion of heavy-quark fragmentation by noting that a similarly comprehen-sive study of charm-quark fragmentation would be desirable However charm-quark tagged multi-plicity and event-shape data is not available to our knowledge and most of the D meson spectra onHEPDATA concern only specific decay chains (hence depend on the decay modeling) andor are lim-ited to restricted fiducial regions (limiting their generality) Experimentally the cleanest measurementis obtained from Dlowast decays and an inclusive momentum spectrum for Dlowast mesons has been measuredby ALEPH [55] From this distribution shown in fig 11 we determine a value for rc of

StringZrFactC = 132

We note that the low-x part of the Dlowast spectrum originates from g rarr cc shower splittings whilethe high-x tail represents prompt Dlowast production from leading charm in Z rarr cc (see [55] for a nicefigure illustrating this) The intermediate range contains a large component of feed-down from brarr cdecays hence this distribution is also indirectly sensitive to the b-quark sector The previous defaulttune had a harder spectrum for both b- and c-fragmentation leading to an overestimate of the high-xpart of the Dlowast distribution The undershooting at low xDlowast values which remains unchanged in theMonash tune most likely indicates an underproduction of g rarr cc branchings in the shower We notethat such an underproduction may also be reflected in the LHC data on Dlowast production see eg [65]We return to this issue in the discussion of identified particles at LHC section 35

17

plusmnD 0D plusmnD plusmns

D X+

cΛ

ccrarrg ψJ c1χ

3685

ψ

X)

rarrlt

ngt o

r B

R(Z

-410

-310

-210

-110

1

10Charm Rates

Pythia 8185Data from HEPDATAPDG

LEP

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn15

00plusmn18

00plusmn17

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

plusmnD 0Dplusmn

D plusmnsD X+

cΛ ccrarrg ψJ c1χ

3685ψ

The

ory

Dat

a

0

05

1

15

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

X)

rarrlt

ngt o

r B

R(Z

-510

-410

-310

-210

-110

1

10Beauty Rates

Pythia 8185Data from HEPDATAPDG

LEP+SLD

PY8 Monash 13

PY8 Default

PY8 Fischer

binsN2

5χ

00plusmn17

00plusmn23

00plusmn23

V I

N C

I A

R O

O T

hadronsrarree 912 GeV

X+B 0plusmnB

uds

B X0

sB Xbqq

Bbbrarrg 4b 10)times(Υ

The

ory

Dat

a0

05

1

15

Figure 7 Hadronic Z decays atradics = 912 GeV Rates and inclusive Z rarr X branching fractions

(normalized to Z rarr hadrons) of particles containing c and b quarks

splittings in the current version of PYTHIA A more natural choice for g rarr qq could be microR prop mqqas used eg in the VINCIA shower model [29]

We now turn to the dynamics of heavy-quark fragmentation focusing mainly on the b quarkFor heavy quarks the Lund fragmentation function is modified due to the (massive) endpoints not

moving along straight lightcones as the string pulls on them they slow down resulting in the stringtracing out a smaller space-time area than it would for massless quarks This modifies the implicationsof the string area law in a manner captured by the so-called Bowler modification of the fragmentationfunction [62]

fmassive(zmQ) prop f(z)

zbrQm2Q

(6)

with mQ the heavy-quark mass b the same universal parameter that appears in the massless fragmen-tation function eq (3) and rQ a tuning parameter which is unity in the original derivation of Bowlerbut can be assigned values different from unity to reduce (rQ rarr 0) or emphasize (rQ gt 1) the effectSince rQ multiplies the heavy-quark mass (squared) it can also be viewed as an effective rescalingof the mass value The net result is a suppression of the region z rarr 1 hence a relative softening ofthe fragmentation spectrum for heavy flavours (relative since the presence of m2

perp in the exponent ofeq (3) still implies an overall harder fragmentation for higher hadron masses)

We emphasize that this is the only fragmentation function that is self-consistent within the string-fragmentation model [33 62] Although a few alternative forms of the fragmentation functions formassive quarks are available in the code we therefore here work only with the Bowler type As forthe massless function the proportionality sign in eq (6) indicates that the function is normalized tounity

In PYTHIA separate rQ parameters are provided for c and b quarks We consider the one for bquarks first Its default value is rb = 067 but this appears to give too hard b fragmentation spectrawhen compared to LEP and SLD data see below For the Monash tune we instead use

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (DELPHI)weak

Bx

Pythia 8181Data from EurPhysJ C71 (2011) 1557

DELPHI PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn16

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (SLD)weak

Bx

Pythia 8181HepData5111d1-x1-y1

SLDPY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn07

00plusmn15

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a06

08

1

12

14

Figure 8 Hadronic Z decays atradics = 912 GeV Momentum (xB) spectra of weakly decaying B

hadrons compared to data from DELPHI [63] (left) and SLD [64] (right)

StringZrFactB = 0855

which produces softer B spectra and simultaneously agrees better with the theoretically preferredvalue (rb = 1)

A comparison to the scaled-momentum spectra (xB = 2|pB|Ecm) of weakly decayingB hadronsfrom both DELPHI [63] and SLD [64] is given in fig 8 (due to small differences between the twomeasured results we choose to show both) The dampening of the hardest part of the spectrum causedby the increase in the rb parameter is visible in the right-most two bins of the distributions and in thesmaller χ2

5 values for the Monash tune The effects of the modification can be further emphasizedby an analysis of the moments of the distribution in which the higher moments are increasinglydominated by the region xB rarr 1 A comparison to a combined LEP analysis of the moments of thexB distribution [63] is given in fig 9 further emphasizing that the high-xB part of the distribution isnow under better control

The reason we have not increased the rb parameter further is that it comes at a price If theB hadrons are taking less energy then there is more energy left over to produce other particlesand the generated multiplicity distribution in b events already exhibits a slightly high tail towardslarge multiplicities Nonetheless since the revised light-flavour fragmentation parameters produce anoverall narrower fragmentation function the end result is still a slight improvement in the multiplicitydistribution also for b events This is illustrated together with the inclusive momentum distributionfor b-tagged events in fig 10 compared to measurements by L3 [26] Interestingly the multiplicitydistribution still appears to be too wide but within the constraints of the present study we were unableto obtain further improvements As a point of speculation we note that the distribution of the numberof partons before hadronization is also quite wide in PYTHIA and this may be playing a role ineffectively setting a lower limit on the width that can be achieved for the hadron-level distribution

Comparisons to L3 event shapes in b-tagged events are collected in appendix B1 (the left columnof plots contains light-flavour tagged event shapes the right column b-tagged ones) In particular the

15

0 10 20 30 40

Mom

ent

0

02

04

06

08 (moments)weakBx

Pythia 8181Data from Eur Phys J C71 (2011) 1557

LEP (combined)PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn10

00plusmn103

00plusmn129

V I

N C

I A

R O

O T

N0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

Figure 9 Hadronic Z decays atradics = 912 GeV Moments of the B fragmentation function com-

pared to a combined analysis of LEP+SLD data by DELPHI [63]

0 20 40

)ch

Pro

babi

lity(

n

-610

-510

-410

-310

-210

-110

1

10

210 Charged Multiplicity (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

06plusmn45

08plusmn64

13plusmn110

V I

N C

I A

R O

O T

(b)chn0 20 40

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

ch d

nch

1n

-510

-410

-310

-210

-110

1

10

210 Charged Momentum Fraction (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn08

00plusmn06 V

I N

C I

A R

O O

T

)| (b)p

|Ln(x0 2 4 6 8

The

ory

Dat

a

06

08

1

12

14

Figure 10 HadronicZ decays atradics = 912 GeV Charged-hadron multiplicity (left) and momentum-

fraction (right) spectra in b-tagged events

16

0 02 04 06 08 1

dx

Dgt

dn

D1

ltn

0

05

1

15

2

25gt01)

E) (x

plusmnx(D

Pythia 8183Data from EurPhysJ C16 (2000) 597

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn14

02plusmn28

02plusmn32

V I

N C

I A

R O

O T

Ex0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

EX02 04 06 08 1

E)

dX

dN

(DZ

had

1N

0

0002

0004

0006

0008

001

0012

0014

0016

ALEPHHerwig++Sherpa

91 GeV ee Z (hadronic)

mcp

lots

cer

nch

41

M e

vent

sge

Riv

et 1

82

Herwig++ 261a Sherpa 141

ALEPH_1999_S4193598

spectrum (particle-level)+-D

02 04 06 08 105

1

15Ratio to ALEPH

Figure 11 The inclusive Dlowast spectrum in hadronic Z decays [55] Left Monash 2013 tune com-pared with default PYTHIA 8 and the Fischer tune Right comparison with HERWIG (dashed) andSHERPA (dotted) from MCPLOTS [25] Note that the plot in the left-hand pane is normalized tounity while the one in the right-hand pane is normalized to the number of hadronic Z decays

Monash tune gives a significant improvement in the soft region of the jet-broadening parameters inb-tagged events while no significant changes are observed for the other event shapes These smallimprovements are presumably a direct consequence of the softening of the b fragmentation functionit is now less likely to find an isolated ultra-hard B hadron

We round off the discussion of heavy-quark fragmentation by noting that a similarly comprehen-sive study of charm-quark fragmentation would be desirable However charm-quark tagged multi-plicity and event-shape data is not available to our knowledge and most of the D meson spectra onHEPDATA concern only specific decay chains (hence depend on the decay modeling) andor are lim-ited to restricted fiducial regions (limiting their generality) Experimentally the cleanest measurementis obtained from Dlowast decays and an inclusive momentum spectrum for Dlowast mesons has been measuredby ALEPH [55] From this distribution shown in fig 11 we determine a value for rc of

StringZrFactC = 132

We note that the low-x part of the Dlowast spectrum originates from g rarr cc shower splittings whilethe high-x tail represents prompt Dlowast production from leading charm in Z rarr cc (see [55] for a nicefigure illustrating this) The intermediate range contains a large component of feed-down from brarr cdecays hence this distribution is also indirectly sensitive to the b-quark sector The previous defaulttune had a harder spectrum for both b- and c-fragmentation leading to an overestimate of the high-xpart of the Dlowast distribution The undershooting at low xDlowast values which remains unchanged in theMonash tune most likely indicates an underproduction of g rarr cc branchings in the shower We notethat such an underproduction may also be reflected in the LHC data on Dlowast production see eg [65]We return to this issue in the discussion of identified particles at LHC section 35

17

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (DELPHI)weak

Bx

Pythia 8181Data from EurPhysJ C71 (2011) 1557

DELPHI PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn16

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

pd

xB

dn

B1

n

-110

1

10 (SLD)weak

Bx

Pythia 8181HepData5111d1-x1-y1

SLDPY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn07

00plusmn15

00plusmn21

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a06

08

1

12

14

Figure 8 Hadronic Z decays atradics = 912 GeV Momentum (xB) spectra of weakly decaying B

hadrons compared to data from DELPHI [63] (left) and SLD [64] (right)

StringZrFactB = 0855

which produces softer B spectra and simultaneously agrees better with the theoretically preferredvalue (rb = 1)

A comparison to the scaled-momentum spectra (xB = 2|pB|Ecm) of weakly decayingB hadronsfrom both DELPHI [63] and SLD [64] is given in fig 8 (due to small differences between the twomeasured results we choose to show both) The dampening of the hardest part of the spectrum causedby the increase in the rb parameter is visible in the right-most two bins of the distributions and in thesmaller χ2

5 values for the Monash tune The effects of the modification can be further emphasizedby an analysis of the moments of the distribution in which the higher moments are increasinglydominated by the region xB rarr 1 A comparison to a combined LEP analysis of the moments of thexB distribution [63] is given in fig 9 further emphasizing that the high-xB part of the distribution isnow under better control

The reason we have not increased the rb parameter further is that it comes at a price If theB hadrons are taking less energy then there is more energy left over to produce other particlesand the generated multiplicity distribution in b events already exhibits a slightly high tail towardslarge multiplicities Nonetheless since the revised light-flavour fragmentation parameters produce anoverall narrower fragmentation function the end result is still a slight improvement in the multiplicitydistribution also for b events This is illustrated together with the inclusive momentum distributionfor b-tagged events in fig 10 compared to measurements by L3 [26] Interestingly the multiplicitydistribution still appears to be too wide but within the constraints of the present study we were unableto obtain further improvements As a point of speculation we note that the distribution of the numberof partons before hadronization is also quite wide in PYTHIA and this may be playing a role ineffectively setting a lower limit on the width that can be achieved for the hadron-level distribution

Comparisons to L3 event shapes in b-tagged events are collected in appendix B1 (the left columnof plots contains light-flavour tagged event shapes the right column b-tagged ones) In particular the

15

0 10 20 30 40

Mom

ent

0

02

04

06

08 (moments)weakBx

Pythia 8181Data from Eur Phys J C71 (2011) 1557

LEP (combined)PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn10

00plusmn103

00plusmn129

V I

N C

I A

R O

O T

N0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

Figure 9 Hadronic Z decays atradics = 912 GeV Moments of the B fragmentation function com-

pared to a combined analysis of LEP+SLD data by DELPHI [63]

0 20 40

)ch

Pro

babi

lity(

n

-610

-510

-410

-310

-210

-110

1

10

210 Charged Multiplicity (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

06plusmn45

08plusmn64

13plusmn110

V I

N C

I A

R O

O T

(b)chn0 20 40

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

ch d

nch

1n

-510

-410

-310

-210

-110

1

10

210 Charged Momentum Fraction (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn08

00plusmn06 V

I N

C I

A R

O O

T

)| (b)p

|Ln(x0 2 4 6 8

The

ory

Dat

a

06

08

1

12

14

Figure 10 HadronicZ decays atradics = 912 GeV Charged-hadron multiplicity (left) and momentum-

fraction (right) spectra in b-tagged events

16

0 02 04 06 08 1

dx

Dgt

dn

D1

ltn

0

05

1

15

2

25gt01)

E) (x

plusmnx(D

Pythia 8183Data from EurPhysJ C16 (2000) 597

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn14

02plusmn28

02plusmn32

V I

N C

I A

R O

O T

Ex0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

EX02 04 06 08 1

E)

dX

dN

(DZ

had

1N

0

0002

0004

0006

0008

001

0012

0014

0016

ALEPHHerwig++Sherpa

91 GeV ee Z (hadronic)

mcp

lots

cer

nch

41

M e

vent

sge

Riv

et 1

82

Herwig++ 261a Sherpa 141

ALEPH_1999_S4193598

spectrum (particle-level)+-D

02 04 06 08 105

1

15Ratio to ALEPH

Figure 11 The inclusive Dlowast spectrum in hadronic Z decays [55] Left Monash 2013 tune com-pared with default PYTHIA 8 and the Fischer tune Right comparison with HERWIG (dashed) andSHERPA (dotted) from MCPLOTS [25] Note that the plot in the left-hand pane is normalized tounity while the one in the right-hand pane is normalized to the number of hadronic Z decays

Monash tune gives a significant improvement in the soft region of the jet-broadening parameters inb-tagged events while no significant changes are observed for the other event shapes These smallimprovements are presumably a direct consequence of the softening of the b fragmentation functionit is now less likely to find an isolated ultra-hard B hadron

We round off the discussion of heavy-quark fragmentation by noting that a similarly comprehen-sive study of charm-quark fragmentation would be desirable However charm-quark tagged multi-plicity and event-shape data is not available to our knowledge and most of the D meson spectra onHEPDATA concern only specific decay chains (hence depend on the decay modeling) andor are lim-ited to restricted fiducial regions (limiting their generality) Experimentally the cleanest measurementis obtained from Dlowast decays and an inclusive momentum spectrum for Dlowast mesons has been measuredby ALEPH [55] From this distribution shown in fig 11 we determine a value for rc of

StringZrFactC = 132

We note that the low-x part of the Dlowast spectrum originates from g rarr cc shower splittings whilethe high-x tail represents prompt Dlowast production from leading charm in Z rarr cc (see [55] for a nicefigure illustrating this) The intermediate range contains a large component of feed-down from brarr cdecays hence this distribution is also indirectly sensitive to the b-quark sector The previous defaulttune had a harder spectrum for both b- and c-fragmentation leading to an overestimate of the high-xpart of the Dlowast distribution The undershooting at low xDlowast values which remains unchanged in theMonash tune most likely indicates an underproduction of g rarr cc branchings in the shower We notethat such an underproduction may also be reflected in the LHC data on Dlowast production see eg [65]We return to this issue in the discussion of identified particles at LHC section 35

17

0 10 20 30 40

Mom

ent

0

02

04

06

08 (moments)weakBx

Pythia 8181Data from Eur Phys J C71 (2011) 1557

LEP (combined)PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn10

00plusmn103

00plusmn129

V I

N C

I A

R O

O T

N0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

Figure 9 Hadronic Z decays atradics = 912 GeV Moments of the B fragmentation function com-

pared to a combined analysis of LEP+SLD data by DELPHI [63]

0 20 40

)ch

Pro

babi

lity(

n

-610

-510

-410

-310

-210

-110

1

10

210 Charged Multiplicity (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

06plusmn45

08plusmn64

13plusmn110

V I

N C

I A

R O

O T

(b)chn0 20 40

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8

)|p

d|L

n(x

ch d

nch

1n

-510

-410

-310

-210

-110

1

10

210 Charged Momentum Fraction (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn12

00plusmn08

00plusmn06 V

I N

C I

A R

O O

T

)| (b)p

|Ln(x0 2 4 6 8

The

ory

Dat

a

06

08

1

12

14

Figure 10 HadronicZ decays atradics = 912 GeV Charged-hadron multiplicity (left) and momentum-

fraction (right) spectra in b-tagged events

16

0 02 04 06 08 1

dx

Dgt

dn

D1

ltn

0

05

1

15

2

25gt01)

E) (x

plusmnx(D

Pythia 8183Data from EurPhysJ C16 (2000) 597

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn14

02plusmn28

02plusmn32

V I

N C

I A

R O

O T

Ex0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

EX02 04 06 08 1

E)

dX

dN

(DZ

had

1N

0

0002

0004

0006

0008

001

0012

0014

0016

ALEPHHerwig++Sherpa

91 GeV ee Z (hadronic)

mcp

lots

cer

nch

41

M e

vent

sge

Riv

et 1

82

Herwig++ 261a Sherpa 141

ALEPH_1999_S4193598

spectrum (particle-level)+-D

02 04 06 08 105

1

15Ratio to ALEPH

Figure 11 The inclusive Dlowast spectrum in hadronic Z decays [55] Left Monash 2013 tune com-pared with default PYTHIA 8 and the Fischer tune Right comparison with HERWIG (dashed) andSHERPA (dotted) from MCPLOTS [25] Note that the plot in the left-hand pane is normalized tounity while the one in the right-hand pane is normalized to the number of hadronic Z decays

Monash tune gives a significant improvement in the soft region of the jet-broadening parameters inb-tagged events while no significant changes are observed for the other event shapes These smallimprovements are presumably a direct consequence of the softening of the b fragmentation functionit is now less likely to find an isolated ultra-hard B hadron

We round off the discussion of heavy-quark fragmentation by noting that a similarly comprehen-sive study of charm-quark fragmentation would be desirable However charm-quark tagged multi-plicity and event-shape data is not available to our knowledge and most of the D meson spectra onHEPDATA concern only specific decay chains (hence depend on the decay modeling) andor are lim-ited to restricted fiducial regions (limiting their generality) Experimentally the cleanest measurementis obtained from Dlowast decays and an inclusive momentum spectrum for Dlowast mesons has been measuredby ALEPH [55] From this distribution shown in fig 11 we determine a value for rc of

StringZrFactC = 132

We note that the low-x part of the Dlowast spectrum originates from g rarr cc shower splittings whilethe high-x tail represents prompt Dlowast production from leading charm in Z rarr cc (see [55] for a nicefigure illustrating this) The intermediate range contains a large component of feed-down from brarr cdecays hence this distribution is also indirectly sensitive to the b-quark sector The previous defaulttune had a harder spectrum for both b- and c-fragmentation leading to an overestimate of the high-xpart of the Dlowast distribution The undershooting at low xDlowast values which remains unchanged in theMonash tune most likely indicates an underproduction of g rarr cc branchings in the shower We notethat such an underproduction may also be reflected in the LHC data on Dlowast production see eg [65]We return to this issue in the discussion of identified particles at LHC section 35

17

0 02 04 06 08 1

dx

Dgt

dn

D1

ltn

0

05

1

15

2

25gt01)

E) (x

plusmnx(D

Pythia 8183Data from EurPhysJ C16 (2000) 597

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn14

02plusmn28

02plusmn32

V I

N C

I A

R O

O T

Ex0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

EX02 04 06 08 1

E)

dX

dN

(DZ

had

1N

0

0002

0004

0006

0008

001

0012

0014

0016

ALEPHHerwig++Sherpa

91 GeV ee Z (hadronic)

mcp

lots

cer

nch

41

M e

vent

sge

Riv

et 1

82

Herwig++ 261a Sherpa 141

ALEPH_1999_S4193598

spectrum (particle-level)+-D

02 04 06 08 105

1

15Ratio to ALEPH

Figure 11 The inclusive Dlowast spectrum in hadronic Z decays [55] Left Monash 2013 tune com-pared with default PYTHIA 8 and the Fischer tune Right comparison with HERWIG (dashed) andSHERPA (dotted) from MCPLOTS [25] Note that the plot in the left-hand pane is normalized tounity while the one in the right-hand pane is normalized to the number of hadronic Z decays

Monash tune gives a significant improvement in the soft region of the jet-broadening parameters inb-tagged events while no significant changes are observed for the other event shapes These smallimprovements are presumably a direct consequence of the softening of the b fragmentation functionit is now less likely to find an isolated ultra-hard B hadron

We round off the discussion of heavy-quark fragmentation by noting that a similarly comprehen-sive study of charm-quark fragmentation would be desirable However charm-quark tagged multi-plicity and event-shape data is not available to our knowledge and most of the D meson spectra onHEPDATA concern only specific decay chains (hence depend on the decay modeling) andor are lim-ited to restricted fiducial regions (limiting their generality) Experimentally the cleanest measurementis obtained from Dlowast decays and an inclusive momentum spectrum for Dlowast mesons has been measuredby ALEPH [55] From this distribution shown in fig 11 we determine a value for rc of

StringZrFactC = 132

We note that the low-x part of the Dlowast spectrum originates from g rarr cc shower splittings whilethe high-x tail represents prompt Dlowast production from leading charm in Z rarr cc (see [55] for a nicefigure illustrating this) The intermediate range contains a large component of feed-down from brarr cdecays hence this distribution is also indirectly sensitive to the b-quark sector The previous defaulttune had a harder spectrum for both b- and c-fragmentation leading to an overestimate of the high-xpart of the Dlowast distribution The undershooting at low xDlowast values which remains unchanged in theMonash tune most likely indicates an underproduction of g rarr cc branchings in the shower We notethat such an underproduction may also be reflected in the LHC data on Dlowast production see eg [65]We return to this issue in the discussion of identified particles at LHC section 35

17

xshy6

10shy5

10 shy410shy3

10 shy210 shy110 1

0

5

10

15

20 = 0119sαNNPDF23QED LO

= 0119sαNNPDF23QED NLO

= 0119sαNNPDF23QED NNLO

)2 = 2 GeV2xg(xQ

Figure 12 Comparison of the gluon PDF at Q2 = 2 GeV2 between the LO NLO and NNLO fits ofthe NNPDF23QED family

For completeness the right-hand pane of fig 11 shows the Dlowast spectra from the two other general-purpose MC models HERWIG [66] and SHERPA [67] The HERWIG spectrum (dashed lines) issimilar to the default PYTHIA one with a deficit in the g rarr cc dominated region at low xE and asignificant overshooting in the hard leading-charm region xE rarr 1 Interestingly the Dlowast spectrum inSHERPA (dotted lines) exhibits an excess at small xE values suggesting relatively larger contributionsfrom b decays and from g rarr cc splittings

3 Hadron Collisions

We discuss PDFs in section 31 the choice of strong coupling (and total cross sections) in section 32initial-state radiation (and primordial kT ) in section 33 minimum-bias and underlying event in sec-tion 34 and finally identified-particle spectra in section 35 Energy scaling is discussed separatelyin section 4

31 Parton Distributions

In the context of MC models a highly important role is played by the small-x gluon PDF which hasa strikingly different behavior between LO and NLONNLO fits This effect is illustrated in Fig 12obtained from the NNPDF23QED PDF sets [19] (see also the useful plot of colour-weighted partonfluxes fig 2 in [13]) The origin of this different small-x behavior is the missing large higher-ordercorrections to the DIS splitting functions and matrix elements (represented by cofficient functions)in the LO fit Another source of the differences between LO and N(N)LO is related to the positivityof PDFs Indeed while at LO PDFs have a probabilistic interpretation and are thus positive-definitestarting from NLO they are scheme-dependent quantities and thus can become negative [68] (Ofcourse physical observables like structure functions are positive-definite to all orders in the perturba-tive expansion)

18

In recent years there has been some discussion about possible modifications of the vanilla LOPDFs that could lead to improved predictions from LO event generators Some possibilities for theseimprovements that have been explored include the use of the LO value of αs but with two-loop run-ning or relaxing the momentum sum rules constraint from the LO fits These and other related ideasunderlie recent attempts to produce modified LO PDFs such as MRST2007lomod PDFs [69] and theCT09MC1MC2 [70] PDFs The claim was that such improved LO (also called LO) PDFs lead toa better agreement between data and theory in the LO fit and that their predictions for some impor-tant collider observables are closer to the results using the full NLO calculation We note howeverthat in the context of earlier multi-parton-interaction-model tuning studies undertaken by us [8] andby ATLAS [13] the large gluon component in LO PDFs has been problematic (driving very highinclusive-jet and MPI rates)

In the context of the NNPDF fits which we shall use for the Monash 2013 tune the above modifi-cations were also studied In particular in the study of the NNPDF21LO fits in Ref [18] it was foundthat from the point of view of the agreement between data and theory the standard LO PDFs providedas good a description as the other possible variations including a different value of αs(MZ) using theone- or two-loop running or relaxing the momentum sum rule The different results found by previousstudies could be related to the limited flexibility in the input gluon PDFs in the CTEQMSRT LO fitsindeed with a flexible enough parametrization such as that used in the NNPDF fits the differencesbetween these theory choices can always be absorbed into the initial condition

Therefore we have settled on an unmodified LO PDF set for the Monash 2013 tune the NNPDF23LO set [19 20] which combines the NNPDF21 LO PDFs with a determination of the photon PDFand a combined QCD+QED evolution [19 71] The relevant parameter in the code is

Choice of PDF set (NNPDF23 LO alphaS(mZ)=013)PDFpSet = 13

Note that the NNPDF23 LO sets are provided for two values of the strong coupling αs(MZ) =0119 and 0130 we use the latter here The sets have also been extended in order to have a widervalidity range in particular they are valid down to x = 10minus9 and Q = 1 GeV2 precisely with themotivation of using them in LO event generators

In Fig 13 we compare the gluon PDF xg(xQ2) for the two NNPDF23 LO fits (central valuesonly) with other recent LO and LO PDFs There is a significant spread between the various LOLOPDF determinations reflecting the substantial theoretical uncertainties in LO fits These differencesare further enhanced at small x due to the lack of experimental constraints in this region For instancethe CTEQ LO sets have a smaller gluon at small x than the other sets The NNPDF23 LO PDF set forαs(MZ) = 0130 is the largest at small x beginning in x sim 5 times 10minus6 and is smaller than the othersets in the middle-x region These differences will translate into different phase-space populations forthe multi-parton-interaction processes relevant for the tuning of event generators

32 The Strong Coupling and Total Cross Sections

For hard QCD matrix elements in PYTHIA (including those for MPI) we use the same strong-coupling value as in the PDF set11 αs(MZ) = 0130

SigmaProcessalphaSvalue = 0130MultipartonInteractionsalphaSvalue = 0130

11The difference between this αs value and that used for ISRFSR will be discussed in section 33

19

x shy6

10shy5

10 shy410shy3

10 shy210 shy110

1

10

210

)2 = 2 GeV2x g ( x Q

=0130S

αNNPDF23LO

=0119S

αNNPDF23LO

CTEQ6L

MRST07lomod

CT09MC2

CT09MCS

)2 = 2 GeV2x g ( x Q

Figure 13 Comparison of the gluon PDF at Q2 = 2 GeV2 between recent LO and LO PDF determinationsFor NNPDF23LO results for both αs(MZ) = 0130 and αs(MZ) = 0119 are shown

This is slightly lower than the current default value of αs(MZ) = 0135 which however tends toproduce too high inclusive jet rates cf the MCPLOTS web site [25] Reducing the αs value also forMPI seems a reasonable first assumption it should result in a slightly less ldquojettyrdquo underlying eventwith activity shifted to lower pperp scales

Already at this level before considering any details of the MPI modelling we can show one ofthe main theoretical reference distributions for multi-parton interactions the integrated partonic QCD2 rarr 2 cross section (integrated above some pTmin scale) as a function of pTmin All that is requiredto compute this are the PDFs the value of αs(MZ) and the simple QCD LO dσ2rarr2 differential crosssections There is no dependence on other model parameters at this stage Due to the 1p4

T singularityof the differential Rutherford cross section12 this distribution diverges at low pTmin an effect whichis further amplified by the running of αs (which blows up at low scales) and the PDFs (which becomelarge at low x) MPI models reconcile the calculated divergent parton-parton cross section with themeasured (or parametrized) total inelastic hadron-hadron cross section by interpreting the divergenceas a consequence of each hadron-hadron collision containing several parton-parton ones with

〈n〉MPI (pT ge pTmin) asymp σ2rarr2(pT ge pTmin)

σinel (7)

Note that there is some ambiguity whether to normalize to the total inelastic cross section or to adiffraction-subtracted smaller number To be conservative we show a comparison to the full σinel infig 14 We compare two different αs and PDF settings corresponding to the choices made in theMonash 2013 tune (filled blue dots) and the current default 4C tune (open red squares) to the highlyprecise measurement of the total inelastic cross section at 8 TeV by the TOTEM collaboration [72]

σinel(8 TeV) = (747plusmn 17) mb (8)

For reference the value obtained from the default Donnachie-Landshoff and Schuler-Sjostrand parametriza-tions currently used in PYTHIA (prop s00808 at high energies [73 74]) is 73 mb consistent with the

12 t-channel gluon exchange gives an amplitude squared proportional to 1t2 which for small pT goes to 1p4T

20

In recent years there has been some discussion about possible modifications of the vanilla LOPDFs that could lead to improved predictions from LO event generators Some possibilities for theseimprovements that have been explored include the use of the LO value of αs but with two-loop run-ning or relaxing the momentum sum rules constraint from the LO fits These and other related ideasunderlie recent attempts to produce modified LO PDFs such as MRST2007lomod PDFs [69] and theCT09MC1MC2 [70] PDFs The claim was that such improved LO (also called LO) PDFs lead toa better agreement between data and theory in the LO fit and that their predictions for some impor-tant collider observables are closer to the results using the full NLO calculation We note howeverthat in the context of earlier multi-parton-interaction-model tuning studies undertaken by us [8] andby ATLAS [13] the large gluon component in LO PDFs has been problematic (driving very highinclusive-jet and MPI rates)

In the context of the NNPDF fits which we shall use for the Monash 2013 tune the above modifi-cations were also studied In particular in the study of the NNPDF21LO fits in Ref [18] it was foundthat from the point of view of the agreement between data and theory the standard LO PDFs providedas good a description as the other possible variations including a different value of αs(MZ) using theone- or two-loop running or relaxing the momentum sum rule The different results found by previousstudies could be related to the limited flexibility in the input gluon PDFs in the CTEQMSRT LO fitsindeed with a flexible enough parametrization such as that used in the NNPDF fits the differencesbetween these theory choices can always be absorbed into the initial condition

Therefore we have settled on an unmodified LO PDF set for the Monash 2013 tune the NNPDF23LO set [19 20] which combines the NNPDF21 LO PDFs with a determination of the photon PDFand a combined QCD+QED evolution [19 71] The relevant parameter in the code is

Choice of PDF set (NNPDF23 LO alphaS(mZ)=013)PDFpSet = 13

Note that the NNPDF23 LO sets are provided for two values of the strong coupling αs(MZ) =0119 and 0130 we use the latter here The sets have also been extended in order to have a widervalidity range in particular they are valid down to x = 10minus9 and Q = 1 GeV2 precisely with themotivation of using them in LO event generators

In Fig 13 we compare the gluon PDF xg(xQ2) for the two NNPDF23 LO fits (central valuesonly) with other recent LO and LO PDFs There is a significant spread between the various LOLOPDF determinations reflecting the substantial theoretical uncertainties in LO fits These differencesare further enhanced at small x due to the lack of experimental constraints in this region For instancethe CTEQ LO sets have a smaller gluon at small x than the other sets The NNPDF23 LO PDF set forαs(MZ) = 0130 is the largest at small x beginning in x sim 5 times 10minus6 and is smaller than the othersets in the middle-x region These differences will translate into different phase-space populations forthe multi-parton-interaction processes relevant for the tuning of event generators

32 The Strong Coupling and Total Cross Sections

For hard QCD matrix elements in PYTHIA (including those for MPI) we use the same strong-coupling value as in the PDF set11 αs(MZ) = 0130

SigmaProcessalphaSvalue = 0130MultipartonInteractionsalphaSvalue = 0130

11The difference between this αs value and that used for ISRFSR will be discussed in section 33

19

x shy6

10shy5

10 shy410shy3

10 shy210 shy110

1

10

210

)2 = 2 GeV2x g ( x Q

=0130S

αNNPDF23LO

=0119S

αNNPDF23LO

CTEQ6L

MRST07lomod

CT09MC2

CT09MCS

)2 = 2 GeV2x g ( x Q

Figure 13 Comparison of the gluon PDF at Q2 = 2 GeV2 between recent LO and LO PDF determinationsFor NNPDF23LO results for both αs(MZ) = 0130 and αs(MZ) = 0119 are shown

This is slightly lower than the current default value of αs(MZ) = 0135 which however tends toproduce too high inclusive jet rates cf the MCPLOTS web site [25] Reducing the αs value also forMPI seems a reasonable first assumption it should result in a slightly less ldquojettyrdquo underlying eventwith activity shifted to lower pperp scales

Already at this level before considering any details of the MPI modelling we can show one ofthe main theoretical reference distributions for multi-parton interactions the integrated partonic QCD2 rarr 2 cross section (integrated above some pTmin scale) as a function of pTmin All that is requiredto compute this are the PDFs the value of αs(MZ) and the simple QCD LO dσ2rarr2 differential crosssections There is no dependence on other model parameters at this stage Due to the 1p4

T singularityof the differential Rutherford cross section12 this distribution diverges at low pTmin an effect whichis further amplified by the running of αs (which blows up at low scales) and the PDFs (which becomelarge at low x) MPI models reconcile the calculated divergent parton-parton cross section with themeasured (or parametrized) total inelastic hadron-hadron cross section by interpreting the divergenceas a consequence of each hadron-hadron collision containing several parton-parton ones with

〈n〉MPI (pT ge pTmin) asymp σ2rarr2(pT ge pTmin)

σinel (7)

Note that there is some ambiguity whether to normalize to the total inelastic cross section or to adiffraction-subtracted smaller number To be conservative we show a comparison to the full σinel infig 14 We compare two different αs and PDF settings corresponding to the choices made in theMonash 2013 tune (filled blue dots) and the current default 4C tune (open red squares) to the highlyprecise measurement of the total inelastic cross section at 8 TeV by the TOTEM collaboration [72]

σinel(8 TeV) = (747plusmn 17) mb (8)

For reference the value obtained from the default Donnachie-Landshoff and Schuler-Sjostrand parametriza-tions currently used in PYTHIA (prop s00808 at high energies [73 74]) is 73 mb consistent with the

12 t-channel gluon exchange gives an amplitude squared proportional to 1t2 which for small pT goes to 1p4T

20

x shy6

10shy5

10 shy410shy3

10 shy210 shy110

1

10

210

)2 = 2 GeV2x g ( x Q

=0130S

αNNPDF23LO

=0119S

αNNPDF23LO

CTEQ6L

MRST07lomod

CT09MC2

CT09MCS

)2 = 2 GeV2x g ( x Q

Figure 13 Comparison of the gluon PDF at Q2 = 2 GeV2 between recent LO and LO PDF determinationsFor NNPDF23LO results for both αs(MZ) = 0130 and αs(MZ) = 0119 are shown

This is slightly lower than the current default value of αs(MZ) = 0135 which however tends toproduce too high inclusive jet rates cf the MCPLOTS web site [25] Reducing the αs value also forMPI seems a reasonable first assumption it should result in a slightly less ldquojettyrdquo underlying eventwith activity shifted to lower pperp scales

Already at this level before considering any details of the MPI modelling we can show one ofthe main theoretical reference distributions for multi-parton interactions the integrated partonic QCD2 rarr 2 cross section (integrated above some pTmin scale) as a function of pTmin All that is requiredto compute this are the PDFs the value of αs(MZ) and the simple QCD LO dσ2rarr2 differential crosssections There is no dependence on other model parameters at this stage Due to the 1p4

T singularityof the differential Rutherford cross section12 this distribution diverges at low pTmin an effect whichis further amplified by the running of αs (which blows up at low scales) and the PDFs (which becomelarge at low x) MPI models reconcile the calculated divergent parton-parton cross section with themeasured (or parametrized) total inelastic hadron-hadron cross section by interpreting the divergenceas a consequence of each hadron-hadron collision containing several parton-parton ones with

〈n〉MPI (pT ge pTmin) asymp σ2rarr2(pT ge pTmin)

σinel (7)

Note that there is some ambiguity whether to normalize to the total inelastic cross section or to adiffraction-subtracted smaller number To be conservative we show a comparison to the full σinel infig 14 We compare two different αs and PDF settings corresponding to the choices made in theMonash 2013 tune (filled blue dots) and the current default 4C tune (open red squares) to the highlyprecise measurement of the total inelastic cross section at 8 TeV by the TOTEM collaboration [72]

σinel(8 TeV) = (747plusmn 17) mb (8)

For reference the value obtained from the default Donnachie-Landshoff and Schuler-Sjostrand parametriza-tions currently used in PYTHIA (prop s00808 at high energies [73 74]) is 73 mb consistent with the

12 t-channel gluon exchange gives an amplitude squared proportional to 1t2 which for small pT goes to 1p4T

20

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

8 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 14 Integrated LO QCD 2 rarr 2 cross section vs pTmin for 8 TeV pp collisions with twodifferent αs and PDF choices compared with the measured σinel

TOTEM measurement13 The fact that the curves cross each other at a value of pTmin sim 5 GeVmeans that we can make a relatively model-independent statement that every inelastic event will onaverage contain at least one 5-GeV partonic subprocess (This value agrees with that found by earlieranalyses [76 77 87]) The corresponding pTmin scales at

radics = 200 or 900 GeV are just 1 ndash 2 GeV

(see plots included appendix B3) hence the expected presence of ldquosemi-hardrdquo partonic substructureat a scale of 5 GeV in min-bias events is a qualitatively new feature at LHC energies for completenessthe corresponding scale at the Tevatron was about 25 GeV [76] The plots in appendix B3 also showextrapolations to higher energies At 100 TeV we expect the partonic cross section to saturate thetotal inelastic one at a pT scale of 10 GeV

33 Initial-State Radiation and Primordial kT

We follow the approach of the Perugia tunes of PYTHIA 6 [6 8] and use the same αs(Mz) valuefor initial-state radiation as that obtained for final-state radiation That is we use one-loop runningwith αs(MZ) = 01365 for both FSR and ISR This choice is made essentially to facilitate matchingapplications see eg [21] Nonetheless we emphasize that we do not regard this choice as mandatoryfor the following reasons

Firstly since each collinear direction is associated with its own singular (set of) diagram(s) onecan consistently associate at least the collinear radiation components with separate well-defined αsvalues without violating gauge invariance Secondly while the LO splitting functions for ISR andFSR are identical they differ at higher orders (beyond the shower accuracy) and there are impor-

13We note however that the value obtained for the 8-TeV elastic cross section in PYTHIA is 20 mb whereas the valuemeasured by TOTEM is 271 plusmn 14 mb [72] While this discrepancy does not influence the normalization or modelling ofinelastic events and hence is a non-issue in that context an update of the total cross-section expressions in PYTHIA maybe timely in the near future eg using the updated Donnachie-Landsgoff analysis in [75] We also note that the decom-position of the inelastic cross section into individual non-diffractive and diffractive components which follows Schuler-Sjostrand [74] may also be due for an update

21

tant differences between the collinear (DGLAP) evolution performed in PDF fits and the (coherentmomentum-conserving) evolution performed by parton showers these differences could well be de-sired to be reflected in slightly different effective scale choices for ISR with respect to FSR onepossibility then being to absorb this in a redefinition of the effective value of αs(MZ) Thirdly andperhaps most importantly while we agree that maintaining separate αs values (equivalent to mak-ing slightly different effective scale choices) for ISR and FSR is ambiguous for wide-angle radiationwe emphasize that merely using the same αs(MZ) value for the two algorithms does not removethis fundamental ambiguity This is because in the context of a shower algorithm the value of therenormalization scale depends upon which parton is branching and that assignment is fundamentallyambiguous outside the collinear limit For instance an emitted gluon with a certain momentum willhave a different pperp with respect to the beam (ISR) than it will with respect to a final-state parton(FSR) and hence the argument of αs typically taken to be proportional to some measure of pperp willbe different depending on who the emitter was This effect is present in all parton-based shower algo-rithms and is not cured by arbitrarily setting αs(MZ) to be the same for ISR and FSR Using the sameαs(MZ) for both ISR and FSR (as we do here) should therefore not be perceived of as being morerigorous than not doing so it is a choice we make purely for convenience (The situation is slightlybetter in antenna-based showers [78ndash80] where there is no distinction between radiator and recoilerin the soft limit hence the renormalization-scale choice is unique at leading colour)

The difference between the value αs(MZ) = 0130 used for QCD matrix elements (and in thePDF evolution) and that used for ISRFSR may be interpreted as follows The former is specifiedin the MS scheme while the effective ISRFSR one should presumably be interpreted in somethingcloser to the so-called MC (CMW) scheme [28] Taking the translation into account (correspondingroughly to a factor 16 on the value of ΛQCD) the PDF value comes out slightly lower than theshower one Given the ambiguities caused by the non-identical nature of PDF and shower evolutionshowever we nonetheless regard this small difference as acceptable in particular since the showerevolution is intrinsically somewhat slower than the PDF one due to coherence effects and a morerestrictive phase space that are not taken into account in the PDF evolution For completeness wenote that the renormalization scale for ISR in PYTHIA is [27]

ISR micro2R = p2

perpevol = (1minus z)Q2 (9)

with Q2 = minusp2 the virtuality of the (spacelike) emitting parton (defined so that Q2 is positive notethat Q2 = minusp2 + m2

0 is used for g rarr QQ splittings) and z the energy fraction appearing in theDGLAP splitting kernels P (z) which in PYTHIA is defined as the ratio of s values before andafter the branching in question (To estimate the shower uncertainties associated with this choice ofrenormalization scale we recommend using ln(micro2

R) plusmn ln(2) corresponding to a factorradic

2 variationof microR similarly to what was recommended for final-state radiation in section 2)

The remaining settings for the ISR evolution are taken over from the previous default tune Therelevant parameters in the code are

ISR Strong Coupling (same as FSR)SpaceShoweralphaSvalue = 01365SpaceShoweralphaSuseCMW = offSpaceShoweralphaSorder = 1

ISR Infrared Cutoff (fixed value at 20 GeV)SpaceShowersamePTasMPI = offSpaceShowerpT0Ref = 20SpaceShowerecmRef = 70000SpaceShowerecmPow = 00

22

ISR Coherence and Spin CorrelationsSpaceShowerrapidityOrder = onSpaceShowerphiPolAsym = onSpaceShowerphiIntAsym = on

We choose a fixed ISR cutoff rather than one that scales with CM energy in order to maintain a corre-spondence between the ISR cutoff and the ldquoprimordial kT rdquo component which parametrizes additionalnon-perturbative andor unresolved motion in the beam remnant This latter component does not scalewith the CM energy (though it may depend on the Q2 scale of the hard process) hence we believeit is most consistent to keep the ISR cutoff fixed as well Since we choose an ISR cutoff of 2 GeV(see the ISR parameter list above) there are no perturbative (ISR) corrections generated below thatscale and soft processes involving momentum transfers less than 2 GeV do not receive any perturba-tive corrections at all To represent the combined effects of unresolved radiation and non-perturbativeFermi motion we add a Gaussian-distributed primordial-kT component to the partons extracted fromthe proton at the low-Q end of the ISR cascade In the Monash tune the width of the Gaussian startsat 09 GeV for an infinitely soft process and gradually rises to an asymptotic value of 18 GeV witha characteristic ldquohalf-scalerdquo of Q = 15 GeV

BeamRemnantsprimordialKTsoft = 09BeamRemnantsprimordialKThard = 18BeamRemnantshalfScaleForKT = 15

The half-scale of Q = 15 GeV was chosen in order to prevent the primordial-kT component fromgenerating momentum kicks larger than that of the ldquohardrdquo process for low-scale processes Theasymptotic value of 18 GeV was chosen by comparing to the pperp spectrum of the lepton pair in pprarrZ rarr `+`minus events measured by the ATLAS and CDF experiments [81 83] Note that PYTHIArsquosparton shower is automatically corrected to reproduce the full LO Z + jet matrix element [27 84]in a manner highly similar to (but predating) that of POWHEG [85] Our value for primordial kT(18 GeV) is slightly lower than the current default (2 GeV) and gives a better agreement with thelow-pperp part of the lepton-pair pperp spectrum as is illustrated in fig 15 for 7 TeV (top row) and 1800GeV (bottom row) pp (pp) collisions Note that the left-hand panes show a ldquocloseuprdquo of the peakregion at low pperp while the right-hand panes show the full spectrum (Note also that these pperp spectraare normalized to unity so the normalization of the inclusive Z cross section drops out)

In the ATLAS spectra the feature around pmicromicroperp sim 35 GeV is repeated by all MCs in the compar-isons shown on the MCPLOTS web site [25] hence we regard it as an artifact of the data We notehowever that there is a tendency for PYTHIA to overshoot the data between pperp values of roughly20 GeV to 100 GeV at both CM energies This is an interesting region intermediate between low-pperpbremsstrahlung and high-pperp Z+jet processes which will be particularly relevant to reconsider in thecontext of matrix-element corrections at the O(α2

s) level and beyond [86]

34 Minimum Bias and Underlying Event

The Monash 2013 tune has been constructed to give a reasonable description of both soft-inclusive(ldquominimum-biasrdquo) physics as well as underlying-event (UE) type observables The difference betweenthe two is sensitive to the shape of the hadron-hadron overlap profile in impact-parameter space (theUE probes the most ldquocentralrdquo collisions while min-bias (MB) is more inclusive) and to the modeling ofcolour reconnections (CR) Most previous tunes including the current default Tune 4C [9] have useda Gaussian assumption [87] for the transverse matter distribution but this appears to give a slightlytoo low UE level (for a given average MB level)

23

tant differences between the collinear (DGLAP) evolution performed in PDF fits and the (coherentmomentum-conserving) evolution performed by parton showers these differences could well be de-sired to be reflected in slightly different effective scale choices for ISR with respect to FSR onepossibility then being to absorb this in a redefinition of the effective value of αs(MZ) Thirdly andperhaps most importantly while we agree that maintaining separate αs values (equivalent to mak-ing slightly different effective scale choices) for ISR and FSR is ambiguous for wide-angle radiationwe emphasize that merely using the same αs(MZ) value for the two algorithms does not removethis fundamental ambiguity This is because in the context of a shower algorithm the value of therenormalization scale depends upon which parton is branching and that assignment is fundamentallyambiguous outside the collinear limit For instance an emitted gluon with a certain momentum willhave a different pperp with respect to the beam (ISR) than it will with respect to a final-state parton(FSR) and hence the argument of αs typically taken to be proportional to some measure of pperp willbe different depending on who the emitter was This effect is present in all parton-based shower algo-rithms and is not cured by arbitrarily setting αs(MZ) to be the same for ISR and FSR Using the sameαs(MZ) for both ISR and FSR (as we do here) should therefore not be perceived of as being morerigorous than not doing so it is a choice we make purely for convenience (The situation is slightlybetter in antenna-based showers [78ndash80] where there is no distinction between radiator and recoilerin the soft limit hence the renormalization-scale choice is unique at leading colour)

The difference between the value αs(MZ) = 0130 used for QCD matrix elements (and in thePDF evolution) and that used for ISRFSR may be interpreted as follows The former is specifiedin the MS scheme while the effective ISRFSR one should presumably be interpreted in somethingcloser to the so-called MC (CMW) scheme [28] Taking the translation into account (correspondingroughly to a factor 16 on the value of ΛQCD) the PDF value comes out slightly lower than theshower one Given the ambiguities caused by the non-identical nature of PDF and shower evolutionshowever we nonetheless regard this small difference as acceptable in particular since the showerevolution is intrinsically somewhat slower than the PDF one due to coherence effects and a morerestrictive phase space that are not taken into account in the PDF evolution For completeness wenote that the renormalization scale for ISR in PYTHIA is [27]

ISR micro2R = p2

perpevol = (1minus z)Q2 (9)

with Q2 = minusp2 the virtuality of the (spacelike) emitting parton (defined so that Q2 is positive notethat Q2 = minusp2 + m2

0 is used for g rarr QQ splittings) and z the energy fraction appearing in theDGLAP splitting kernels P (z) which in PYTHIA is defined as the ratio of s values before andafter the branching in question (To estimate the shower uncertainties associated with this choice ofrenormalization scale we recommend using ln(micro2

R) plusmn ln(2) corresponding to a factorradic

2 variationof microR similarly to what was recommended for final-state radiation in section 2)

The remaining settings for the ISR evolution are taken over from the previous default tune Therelevant parameters in the code are

ISR Strong Coupling (same as FSR)SpaceShoweralphaSvalue = 01365SpaceShoweralphaSuseCMW = offSpaceShoweralphaSorder = 1

ISR Infrared Cutoff (fixed value at 20 GeV)SpaceShowersamePTasMPI = offSpaceShowerpT0Ref = 20SpaceShowerecmRef = 70000SpaceShowerecmPow = 00

22

ISR Coherence and Spin CorrelationsSpaceShowerrapidityOrder = onSpaceShowerphiPolAsym = onSpaceShowerphiIntAsym = on

We choose a fixed ISR cutoff rather than one that scales with CM energy in order to maintain a corre-spondence between the ISR cutoff and the ldquoprimordial kT rdquo component which parametrizes additionalnon-perturbative andor unresolved motion in the beam remnant This latter component does not scalewith the CM energy (though it may depend on the Q2 scale of the hard process) hence we believeit is most consistent to keep the ISR cutoff fixed as well Since we choose an ISR cutoff of 2 GeV(see the ISR parameter list above) there are no perturbative (ISR) corrections generated below thatscale and soft processes involving momentum transfers less than 2 GeV do not receive any perturba-tive corrections at all To represent the combined effects of unresolved radiation and non-perturbativeFermi motion we add a Gaussian-distributed primordial-kT component to the partons extracted fromthe proton at the low-Q end of the ISR cascade In the Monash tune the width of the Gaussian startsat 09 GeV for an infinitely soft process and gradually rises to an asymptotic value of 18 GeV witha characteristic ldquohalf-scalerdquo of Q = 15 GeV

BeamRemnantsprimordialKTsoft = 09BeamRemnantsprimordialKThard = 18BeamRemnantshalfScaleForKT = 15

The half-scale of Q = 15 GeV was chosen in order to prevent the primordial-kT component fromgenerating momentum kicks larger than that of the ldquohardrdquo process for low-scale processes Theasymptotic value of 18 GeV was chosen by comparing to the pperp spectrum of the lepton pair in pprarrZ rarr `+`minus events measured by the ATLAS and CDF experiments [81 83] Note that PYTHIArsquosparton shower is automatically corrected to reproduce the full LO Z + jet matrix element [27 84]in a manner highly similar to (but predating) that of POWHEG [85] Our value for primordial kT(18 GeV) is slightly lower than the current default (2 GeV) and gives a better agreement with thelow-pperp part of the lepton-pair pperp spectrum as is illustrated in fig 15 for 7 TeV (top row) and 1800GeV (bottom row) pp (pp) collisions Note that the left-hand panes show a ldquocloseuprdquo of the peakregion at low pperp while the right-hand panes show the full spectrum (Note also that these pperp spectraare normalized to unity so the normalization of the inclusive Z cross section drops out)

In the ATLAS spectra the feature around pmicromicroperp sim 35 GeV is repeated by all MCs in the compar-isons shown on the MCPLOTS web site [25] hence we regard it as an artifact of the data We notehowever that there is a tendency for PYTHIA to overshoot the data between pperp values of roughly20 GeV to 100 GeV at both CM energies This is an interesting region intermediate between low-pperpbremsstrahlung and high-pperp Z+jet processes which will be particularly relevant to reconsider in thecontext of matrix-element corrections at the O(α2

s) level and beyond [86]

34 Minimum Bias and Underlying Event

The Monash 2013 tune has been constructed to give a reasonable description of both soft-inclusive(ldquominimum-biasrdquo) physics as well as underlying-event (UE) type observables The difference betweenthe two is sensitive to the shape of the hadron-hadron overlap profile in impact-parameter space (theUE probes the most ldquocentralrdquo collisions while min-bias (MB) is more inclusive) and to the modeling ofcolour reconnections (CR) Most previous tunes including the current default Tune 4C [9] have useda Gaussian assumption [87] for the transverse matter distribution but this appears to give a slightlytoo low UE level (for a given average MB level)

23

ISR Coherence and Spin CorrelationsSpaceShowerrapidityOrder = onSpaceShowerphiPolAsym = onSpaceShowerphiIntAsym = on

We choose a fixed ISR cutoff rather than one that scales with CM energy in order to maintain a corre-spondence between the ISR cutoff and the ldquoprimordial kT rdquo component which parametrizes additionalnon-perturbative andor unresolved motion in the beam remnant This latter component does not scalewith the CM energy (though it may depend on the Q2 scale of the hard process) hence we believeit is most consistent to keep the ISR cutoff fixed as well Since we choose an ISR cutoff of 2 GeV(see the ISR parameter list above) there are no perturbative (ISR) corrections generated below thatscale and soft processes involving momentum transfers less than 2 GeV do not receive any perturba-tive corrections at all To represent the combined effects of unresolved radiation and non-perturbativeFermi motion we add a Gaussian-distributed primordial-kT component to the partons extracted fromthe proton at the low-Q end of the ISR cascade In the Monash tune the width of the Gaussian startsat 09 GeV for an infinitely soft process and gradually rises to an asymptotic value of 18 GeV witha characteristic ldquohalf-scalerdquo of Q = 15 GeV

BeamRemnantsprimordialKTsoft = 09BeamRemnantsprimordialKThard = 18BeamRemnantshalfScaleForKT = 15

The half-scale of Q = 15 GeV was chosen in order to prevent the primordial-kT component fromgenerating momentum kicks larger than that of the ldquohardrdquo process for low-scale processes Theasymptotic value of 18 GeV was chosen by comparing to the pperp spectrum of the lepton pair in pprarrZ rarr `+`minus events measured by the ATLAS and CDF experiments [81 83] Note that PYTHIArsquosparton shower is automatically corrected to reproduce the full LO Z + jet matrix element [27 84]in a manner highly similar to (but predating) that of POWHEG [85] Our value for primordial kT(18 GeV) is slightly lower than the current default (2 GeV) and gives a better agreement with thelow-pperp part of the lepton-pair pperp spectrum as is illustrated in fig 15 for 7 TeV (top row) and 1800GeV (bottom row) pp (pp) collisions Note that the left-hand panes show a ldquocloseuprdquo of the peakregion at low pperp while the right-hand panes show the full spectrum (Note also that these pperp spectraare normalized to unity so the normalization of the inclusive Z cross section drops out)

In the ATLAS spectra the feature around pmicromicroperp sim 35 GeV is repeated by all MCs in the compar-isons shown on the MCPLOTS web site [25] hence we regard it as an artifact of the data We notehowever that there is a tendency for PYTHIA to overshoot the data between pperp values of roughly20 GeV to 100 GeV at both CM energies This is an interesting region intermediate between low-pperpbremsstrahlung and high-pperp Z+jet processes which will be particularly relevant to reconsider in thecontext of matrix-element corrections at the O(α2

s) level and beyond [86]

34 Minimum Bias and Underlying Event

The Monash 2013 tune has been constructed to give a reasonable description of both soft-inclusive(ldquominimum-biasrdquo) physics as well as underlying-event (UE) type observables The difference betweenthe two is sensitive to the shape of the hadron-hadron overlap profile in impact-parameter space (theUE probes the most ldquocentralrdquo collisions while min-bias (MB) is more inclusive) and to the modeling ofcolour reconnections (CR) Most previous tunes including the current default Tune 4C [9] have useda Gaussian assumption [87] for the transverse matter distribution but this appears to give a slightlytoo low UE level (for a given average MB level)

23

0 10 20 30

Td

pσ

dσ

1

0

002

004

006

|lt24)micro

ηgt20 |microT

Peak (66ltmlt116 pmicromicroT

barep

Pythia 8181Data from PhysLett B705 (2011) 415

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn04

01plusmn13

01plusmn13

V I

N C

I A

R O

O T

7000 GeV pp

[GeV]T

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 100 200 300

Td

pσ

dσ

1-610

-510

-410

-310

-210

-110 |lt24)micro

ηgt20 |microT

Peak (66ltmlt116 pmicromicroT

barep

Pythia 8181Data from PhysLett B705 (2011) 415

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn07

00plusmn14

00plusmn13

V I

N C

I A

R O

O T

7000 GeV pp

[GeV]T

p0 100 200 300

The

ory

Dat

a

06

08

1

12

14

0 10 20 30

Td

pσ

dσ

1

0

002

004

006

008

01

012 (66ltmlt116)

TZp

Pythia 8181Data from PhysRevLett 84 (2000) 845

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn08

00plusmn12

00plusmn10

V I

N C

I A

R O

O T

1800 GeV ppbar

[GeV]T

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 50 100 150 200

Td

pσ

dσ

1

-610

-510

-410

-310

-210

-110 (66ltmlt116)TZ

p

Pythia 8181Data from PhysRevLett 84 (2000) 845

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn12

00plusmn15

00plusmn13

V I

N C

I A

R O

O T

1800 GeV ppbar

[GeV]T

p0 50 100 150 200

The

ory

Dat

a

06

08

1

12

14

Figure 15 The peak (left) and tail (right) of the Z pperp distribution as measured at 7 TeV (using ldquobarerdquomuon pairs) [81] and 18 TeV (corrected to unphysical generator-level see [82]) [83]

24

0 10 20

)M

PI

Pro

b(n

-510

-410

-310

-210

-110

1 number of interactions

Pythia 8185

PY8 (Monash 13)PY8 (4C)PY8 (2C)

V I

N C

I A

R O

O T

pp 7000 GeV

MPIn0 10 20

Rat

io

06

08

1

12

14

Figure 16 pp collisions at 7 TeV Number of MPI in inelastic events

For the Monash tune we have chosen a slightly more peaked transverse matter profile [27]thus generating a relatively larger UE for the same average MB quantities We note however thatthere are still several indications that the dynamics are not well understood in particular when itcomes to very low multiplicities (overlapping with diffraction) very high multiplicities (eg the so-called CMS ldquoridgerdquo effect [88]) and to identified-particle spectra (eg possible modifications byre-scattering [89] string boosts from colour reconnections [90] or other collective effects)

For the 7-TeV reference energy we focus on here (energy scaling will be studied in the followingsubsection) the relevant parameters in the code are

Hadron transverse mass overlap density profileMultipartonInteractionsbProfile = 3MultipartonInteractionsexpPow = 185

IR regularization scale for MPI and energy scalingMultipartonInteractionspT0Ref = 228MultipartonInteractionsecmRef = 7000MultipartonInteractionsecmPow = 0215

The slightly more peaked matter distribution combined with a relatively low pperp0 value producesan intrinsically broader distribution in the number of parton-parton interactions (MPI) illustrated bythe theory-level plot in fig 16

The sampling of the PDFs by MPI initiators (including also the hardest scattering in our definitionof ldquoMPIrdquo) as a function of parton x values is illustrated in fig 17 for the three tunes considered in thispaper The top left-hand pane shows the most inclusive quantity simply the probability distribution ofthe x value of all MPI initiators (again we emphasize that we include the hardest-interaction initiatorsin our definition of ldquoMPIrdquo here) on a logarithmic x axis Here we see that the NNPDF tune hasa harder distribution both at large and small x as compared to the CTEQ6L1 tunes The effect isparticularly marked at small x Since MPI is dominated by the low-Q gluon PDF cf fig 12 thisis precisely what we expect the shape of the distribution of sampled x values follows that of the

25

-8 -6 -4 -2 0

(x)

101

n dn

dLo

g

-510

-410

-310

-210

-110

1

10(x) including MPI

10Log

Pythia 8185

PY8 (Monash 13)PY8 (4C)PY8 (2C)

V I

N C

I A

R O

O T

pp 7000 GeV

(x)10

Log-8 -6 -4 -2 0

Rat

io

06

08

1

12

14

-8 -6 -4 -2 0

Rat

io0

05

1

15Gluon Fraction including MPI

Pythia 8185

PY8 (Monash 13)PY8 (4C)PY8 (2C)

V I

N C

I A

R O

O T

pp 7000 GeV

(x)10

Log-8 -6 -4 -2 0

Rat

io

06

08

1

12

14

-8 -6 -4 -2 0

Rat

io

-310

-210

-110

1

10

210u including MPIu

Pythia 8185

PY8 (Monash 13)PY8 (4C)PY8 (2C)

V I

N C

I A

R O

O T

pp 7000 GeV

(x)10

Log-8 -6 -4 -2 0

Rat

io

06

08

1

12

14

0 02 04 06 08 1

1n

dnd

X

-510

-410

-310

-210

-110

1

10

210MPIxΣBeam Remnant X = 1 -

Pythia 8185

PY8 (Monash 13)PY8 (4C)PY8 (2C)

V I

N C

I A

R O

O T

pp 7000 GeV

RemnantX0 02 04 06 08 1

Rat

io

06

08

1

12

14

Figure 17 PDF sampling by MPIs in inelastic non-diffractive pp collisions at 7 TeV Top Left thex distribution of all MPI initiators (including the hardest scattering) Top Right the fraction of MPIinitiators which are gluons as a function of x Bottom Left the uu ratio Bottom Right thedistribution of the amount of x left in the beam remnant after MPI (note linear scale in x)

26

PDFs themselves Indeed the NNPDF23 gluon is harder than the CTEQ6L one for x gt 02 and forx lt 10minus5

The relative dominance of the gluon PDF is illustrated by the bottom right-hand pane of fig 17showing the gluon fraction (relative to all MPI initiators) as a function of log10(x) Below x sim 01the NNPPDF sampling is 80 gluon-dominated and the gluon fraction is higher than in CTEQ6L1for both very small x lt 10minus5 as well as for very large x gt 02

A further consistency check is provided by the uu ratio shown in the bottom left-hand pane offig 17 This is consistent with unity (as expected for sea quarks) in the entire small-x region x lt 10minus2The valence bump appears to be slightly more pronounced in the NNPDF tune (relative to the sea)since the uu ratio drops off more quickly above 10minus2 This trend persists until the very highest binat x sim 1 where the experimental uncertainties are extremely large The CTEQ6L1 parametrizationthere forces the u PDF to zero while the NNPDF parametrization allows for a small amount of u toremain even at the largest x values though we note that they are still outnumbered by u quarks at alevel of hundred-to-one

The last pane of fig 17 shows the amount of x remaining in the beam remnant after all MPI(including both the hardest interaction and additional MPI) have been considered ie

Xrem = 1minussumiisinMPI

xi (10)

Note the linear scale in x on this plot and the highly logaritmic axis In the vast majority of casesthe beam remnant thus still retains over 90 of the initial hadron energy But there is a class ofevents at the level of 10minus4 or 10minus5 of the total cross section (depending on the tune) in whichthe beam remnant retains less than 10 of the incoming hadron energy Experiments studying theamount and distribution of forward scattered energy in particular may be able to tell us about whetherthis class of events which we term ldquoCatastrophic Energy Lossrdquo events really exists and at whatlevel Note that these events are typically not caused by a single hard partonic scattering processdue to the high penalty associated with accessing PDFs in the region x gt 05 Rather they arean intrinsic consequence of MPI A straightforward extrapolation requiring a catastrophic energyloss on both sides of the event mdash more than 90 of the energy scattered out of both beams whichwe term ldquoTotal Inelastic Scatteringrdquo mdash may occur at a level of 10minus10 minus 10minus8 of the cross sectionor between 10 - 1000 pb (though we of course only have PYTHIArsquos word for it) This would bean extremely interesting part of hadron-hadron collision physics to study very far from the single-interaction dominated limit and hence potentially very sensitive to the existence of possible collectiveeffects Designing efficient triggers for this class of events would be a great accomplishment

Turning now to physics distributions in min-bias events the broader MPI distribution in theMonash tune translates to a broader charged-multiplicity spectrum though the effect is modulatedby the colour-reconnection model The resulting multiplicity and pperp spectra are shown in fig 18for ldquostandardrdquo fiducial cuts (top row pperp ge 500 MeV |η| lt 25 nCh ge 1) and ldquosoftrdquo fiducial cuts(bottom row pperp ge 100 MeV |η| lt 25 nCh ge 2) with the latter representing the most inclusivephase-space region accessible with the ATLAS detector For both of the nCh distributions we notethat a significant ldquodouble-crested waverdquo pattern is still present in the ratio panes though it has beendampened slightly The pperp spectra in the right-hand panes are a bit below the data for the standardfiducial cuts and above it for the soft cuts hence we regard the Monash tune as a reasonable compro-mise

Pseudorapidity distributions are shown in fig 19 However due to the complicated interplaybetween diffractive contributions at low multiplicity and high-multiplicity multi-parton interactions(with associated questions of transverse matter density profile and colour reconnections) the average

27

0 50 100

)C

hP

rob(

n

-710

-610

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn27

00plusmn27

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

Chn0 50 100

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20

Td

pC

h d

nT

)p

π(

2C

h1

n

-810

-710

-610

-510

-410

-310

-210

-110

1

10|lt25)ηgt05 |

T 1 pge

Ch (n

Tp

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLAS PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn15

00plusmn08

01plusmn58

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 5 10 15 20

The

ory

Dat

a

06

08

1

12

14

0 50 100 150 200

)C

hP

rob(

n

-610

-510

-410

-310

-210

-110

1|lt25)ηgt01 |

T 2 pge

ChSoft Chg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn45

00plusmn49

01plusmn197

V I

N C

I A

R O

O T

pp 7000 GeV

Chn0 50 100 150 200

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20

Td

pC

h d

nT

)p

π(

2C

h1

n

-910

-710

-510

-310

-110

10|lt25)ηgt01 |

T 2 pge

Ch (n

Tp

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn43

01plusmn73

02plusmn155

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 5 10 15 20

The

ory

Dat

a

06

08

1

12

14

Figure 18 Min-bias pp collisions at 7 TeV Charged-multiplicity and pperp distributions with standard(top row) and soft (bottom row) fiducial cuts compared to ATLAS data [91]

28

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from PhysRevLett 105 (2010) 022002

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn00

00plusmn03

00plusmn71

V I

N C

I A

R O

O T

pp 7000 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

55 6 65

gtηd

Ch

ltdn

Tot

em1

n

0

1

2

3

4

5

6|lt65)ηgt004 53lt|

T1 pge

chgt (nηd

Chltdn

Pythia 8185Data from EurophysLett 98 (2012) 31002

TOTEMPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn01

00plusmn27

00plusmn62

V I

N C

I A

R O

O T

pp 7000 GeV

η55 6 65

The

ory

Dat

a

06

08

1

12

14

3 35 4 45 5

gtηlt

dEd

0

100

200

300

400

500|lt465)η1 in both 323lt|ge

chMB Fwd E Flow (n

Pythia 8185Data from JHEP 11 (2011) 148

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn01

00plusmn04

00plusmn22

V I

N C

I A

R O

O T

pp 7000 GeV

η3 35 4 45 5

The

ory

Dat

a

06

08

1

12

14

Figure 19 Charged-particle pseudorapidity distributions and forward energy flow in min-bias ppcollisions at 7 TeV compared to CMS [92 93] and TOTEM [94] data

29

0 50 100

0

05

1

15

2

25|lt25)ηgt05 |

T) (p

Chgt(n

Tltp

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn05

01plusmn01

05plusmn07

V I

N C

I A

R O

O T

pp 7000 GeV

0 50 100

The

ory

Dat

a

06

08

1

12

14

0 50 100 150 200

0

05

1

15|lt25)ηgt01 |

T 2 pge

Ch) (n

Chgt(n

TSoft ltp

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn06

00plusmn08

03plusmn40

V I

N C

I A

R O

O T

pp 7000 GeV

0 50 100 150 200

The

ory

Dat

a06

08

1

12

14

Figure 20 Average-pperp vs charged-multiplicity distributions in min-bias pp collisions at 7 TeV withstandard (left) and soft (right) fiducial cuts compared to ATLAS data [91]

multiplicity by itself is a very difficult quantity to extract reliable conclusions from Note also that theCMS measurement [92] shown in the top pane of fig 19 was corrected to an unphysical ldquonon-singlediffractiverdquo event definition which essentially amounts to switching off single-diffractive contributionsin the MC generator (We note that later CMS measurements instead use a physical observable relatedto the diffractive mass to define NSD) For the comparisons to CMS NSD data shown here the single-diffractive contributions were switched off in the generator With these caveats in mind we note thatboth the 4C and Monash 2013 tunes are in good agreement with the CMS measurement with theMonash one giving a slightly lower central charged-track density (by about 5) This is closer to thevalues observed in data though as already noted in section 11 we do not regard differences at the 5level as significant

In the bottom two panes of fig 19 we focus on the forward region (with physical event selections)In particular we see that the NNPDF set [20] generates a broader rapidity spectrum so that while theactivity in the central region (top pane) is reduced slightly the activity in the very forward regionactually increases and comes into agreement with the TOTEM measurement [94] covering the range53 lt |η| lt 64 The bottom right-hand pane shows the forward energy flow measured by CMS [93]in the intermediate region 323 lt |η| lt 465 The dependence on η is a bit steeper in the Monashtune than in the previous one and more similar to that seen in the data

A complementary observable which is highly sensitive to interconnection effects between theMPI (and hence eg to the effects of ldquocolour reconnectionsrdquo [95]) is the average charged-particlepperp as a function of the number of charged particles In a strict leading-colour picture each MPIwould cause one or two new strings to be stretched between the remnants but each such string wouldbe independent (modulo endpoint effects) therefore (modulo jets) the pperp spectrum of the hadronsproduced by each of these strings would be independent of the number of strings The result would bea flat 〈pperp〉 (nCh) spectrum Jets and colour reconnections both produce a rising spectrum The spectraobserved by ATLAS [91] are compared to the Monash 2C and 4C tunes in fig 20 for standard

30

0 1 2 3

gtφ|dη

d|

Ch

n2

ltd

0

02

04

06

08

1gt01)

T|lt25 pηgt1 (|

Tlead| wrt pφ∆|

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn16

00plusmn19

00plusmn56

V I

N C

I A

R O

O T

pp 7000 GeV

| [rad]φ∆|0 1 2 3

The

ory

Dat

a

06

08

1

12

14

0 1 2 3

gtφ|dη

d|

Ch

n2

ltd

0

05

1

15

2

gt05)T

|lt25 pηgt5 (|Tlead

| wrt pφ∆|

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn05

00plusmn05

00plusmn70

V I

N C

I A

R O

O T

pp 7000 GeV

| [rad]φ∆|0 1 2 3

The

ory

Dat

a06

08

1

12

14

Figure 21 pp collisions at 7 TeV ∆φ of charged particles with respect to the hardest track for twodifferent hardest-track triggers compared with ATLAS data [98]

(left) and soft (right) fiducial cuts Both of the Monash and 4C tunes reproduce the data quite wellwith χ2

5 lt 1 while the older tune 2C had a higher CR strength optimized to describe Tevatrondata [96] We certainly consider the energy scaling of the effective CR strength among the mostuncertain parameters of the current min-biasunderlying-event modelling (a similar conclusion wasreached for the CR modelling in PYTHIA 6 in [97]) and intend to study the physics aspects of thisissue more closely in a forthcoming paper

For a more differential look at the event structure we consider the charged-track ∆φ distributionswith respect to the azimuthal angle of the leading track in fig 21 compared with ATLAS data [98]The plot in the left-hand pane corresponds to a requirement of pperplead ge 1 GeV while the one in theright-hand pane is for a harder trigger pperplead ge 5 GeV The former can roughly be taken as charac-teristic of min-bias events while the latter is related to the differential distribution of the underlyingevent In both cases the activity in the wide-angle region near π2 is significantly better described bythe 4C and Monash 2013 tunes (which agrees with their improved description of the overall activity)while there is a too strong peaking at low ∆φ especially for the lowest pperplead cut (left) possibly indi-cating that the structure of the min-bias events is still slightly too ldquolumpyrdquo (ie jetty) For the higherpperplead cut (right) the overcounting at very low ∆φ is already significantly milder and we observe agood agreement with the data

Turning now to the underlying event (UE) what matters most for high-pperp jet studies is that theMC models describe the UE contamination per ∆R jet area The most important UE observable fromthis perspective is thus the pperp sum density in the UE and its fluctuations For charged particles atLHC typically a pperp cut of 500 MeV is relevant since softer tracks will form helices and hence notcontribute to calorimetric jet energies Neutral particles are of course relevant across all pperp scalesIn fig 22 we show the charged pperp sum density (left with the lowest possible pperp cut of 100 MeV)and the charged-track density (right with a pperp cut of 500 MeV) in the so-called ldquoTransverse Regionrdquo(defined by 60 lt ∆φ lt 120 with respect to the leading track) inside the ATLAS acceptance of

31

0 5 10 15 20

)φ∆η

∆gt

(T

psum

lt

0

05

1

15

2

25gt01)

T|lt25 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn03

01plusmn09

02plusmn112

V I

N C

I A

R O

O T

pp 7000 GeV

(hardest track) [GeV]T1

p0 5 10 15 20

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20

)φ∆η

∆gt

(C

hlt

n

0

05

1

15

2

25gt05)

T|lt25 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn02

00plusmn04

02plusmn104

V I

N C

I A

R O

O T

pp 7000 GeV

(hardest track) [GeV]T1

p0 5 10 15 20

The

ory

Dat

a06

08

1

12

14

Figure 22 pp collisions at 7 TeV UE (ldquoTransverse regionrdquo) transverse-momentum sum density (left)and charged-track density (right) compared with ATLAS data [98]

|η| lt 25 [98] As is now well known the Tevatron extrapolations (represented here by Tune 2C)predicted a UE level which was 10 ndash 20 below the LHC data Both the current default tune 4C(which included LHC data) and the Monash 2013 tune exhibit significantly better agreement with theLHC measurements with the Monash one giving a slight additional improvement in the χ2

5 valuesWe conclude that the Monash 2013 tune parameters are appropriate for both min-bias and UE studies

35 Identified Particles at LHC

While the description of inclusive charged particles discussed in the previous section is acceptablelarger discrepancies emerge when we consider the spectra of identified particles We here focus onstrange particles in particular K0

S mesons and Λ0 hyperons in figs 23 and 24 respectively Theexperimental measurements come from CMS [99] Additional comparisons to strange-particle spectra(Klowast φ and Ξ) are collected in appendix B2

In the K0S rapidity distribution shown in the left-hand pane of fig 23 we observe that tune 4C

exhibits a mild underproduction of about 10 Though it might be tempting to speculate whether thiscould indicate some small reduction of strangeness suppression in pp collisions however we alreadynoted in section 21 that the strangeness production in ee collisions also needed to be increased byabout 10 After this adjustment we see that the overall K0

S yield in the Monash 2013 tune is fullyconsistent with the CMS measurement Nonetheless we note that the momentum distribution is stillnot satisfactorily described as shown in the right-hand pane of fig 23 Our current best guess istherefore that the overall rate of strange quarks is consistent at least in the average min-bias collision(dedicated comparisons in high-multiplicity samples would still be interesting) but that the phase-space distribution of strange hadrons needs more work Similarly to the case in ee collisions cf fig 6the model predicts too many very soft kaons though we do not currently know whether there is adynamic link between the ee and pp observations

For strange baryons we note that the increase in the Λ0 fraction in ee collisions (cf fig 5) does

32

0 05 1 15 2

dygt

K lt

dnN

SD

1n

0

02

04

06

08)d|y|gt Rapidity (NSD)

S

0ltdn(K

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn01

00plusmn09

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8 10

Td

pK

dn

NS

D1

N

-510

-410

-310

-210

-110

1

10 (|y|lt20 NSD)

T pS

0K

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn78

01plusmn34

02plusmn22

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6 8 10

The

ory

Dat

a06

08

1

12

14

Figure 23 pp collisions at 7 TeV K0S rapidity and pperp spectrum compared with CMS data [99]

0 05 1 15 2

dygt

Λ lt

dnN

SD

1N

0

01

02

03

04)d|y|gt (NSD)0Λltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn64

00plusmn78

01plusmn147

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8 10

Td

pΛ

dn

Λ1

n

-510

-410

-310

-210

-110

1

10 (|y|lt20 NSD)

T p0Λ

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn59

03plusmn66

05plusmn105

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6 8 10

The

ory

Dat

a

06

08

1

12

14

Figure 24 pp collisions at 7 TeV Λ0 rapidity and pperp spectrum compared with CMS data [99]

not result in an equivalent improvement of the Λ0 rate in pp collisions shown in fig 24 The Monash2013 tune still produces only about 23 of the observed Λ0 rate (and just over half of the observedΞminus rate cf appendix B2) We therefore believe it to be likely that an additional source of net baryonproduction is needed (at least within the limited context of the current PYTHIA modelling) in orderto describe the LHC data The momentum spectrum is likewise quite discrepant exhibiting an excessat very low momenta (stronger than that for kaons) a dip between 1ndash4 GeV and then an excess of veryhard Λ0 production The latter hard tail is somewhat milder in the Monash 2013 tune than previously

33

and it may be consistent with the trend also seen in the Λ0 spectrum at LEP cf fig 6 We concludethat baryon production still requires further modelling and tuning efforts

4 Energy Scaling

Though energy scaling these days mostly refers to the scaling of pp collisions (see eg [97]) animportant first step is to consider the scaling of observables in ee rarr γlowastZ rarr hadrons This scalingcontains information on the relative contributions of perturbative and non-perturbative fragmentationThus at low ee energies the non-perturbative components of the fragmentation model dominatewhile perturbative bremsstrahlung increases in importance towards higher ee energies In fig 25we consider the scaling of the average charged-particle multiplicity and that of charged Kaons andLambda baryons from CM energies of 14 GeV to 200 GeV obtained from measurements availableat HEPDATA Below the Z pole the measurements we include mostly come from TASSO [100]though a few points on 〈nCh〉 come from HRS (at 29 GeV [101]) and TOPAZ (at 578 GeV [102]) Atthe Z pole the data come from the four LEP experiments [38 51ndash53] with the latter extending alsoto energies above MZ [103ndash108] For completeness and as reference for future ee collider studiesmodel extrapolations for CM energies up to 1000 GeV are also shown (though still only including theeerarr γlowastZ rarr hadrons component as usual with photon ISR switched off)

From the plots in fig 25 it is clear that there are no significant differences between the energyscaling of the three ee tunes considered here (mainly reflecting that they have been tuned to samereference point at 912 GeV and that their scaling is dictated by the same underlying physics model)and that their energy dependence closely matches that observed in data However the increasedamount of non-perturbative strangeness production in the Monash tune leads to a better agreementwith the overall normalization of the Kplusmn and Λ rates at all energies

Moving to pp collisions the plots in fig 26 show the scaling of the average charged multiplicity(left column) and multiplicity distributions (right column) in min-bias collisions from 7000 GeV (toprow) to 900 GeV (middle row) and 200 GeV (bottom row) compared with data from CMS [92 109]ATLAS [91] and UA5 [110 111] We regret the omission of additional relevant min-bias measure-ments from the Tevatron and RHIC experiments here but have chosen to focus in this paper mainlyon the LHC The comparisons at 7 TeV were already discussed in the main section on pp collisionssection 3 At 900 GeV the Monash 2013 tune again gives a roughly 5 lower average central chargedmultiplicity than the 4C one with a better description of the tail towards high multiplicities At 200GeV the UA5 measurement we include here extends over the full rapidity and pperp range hence the in-terplay between diffraction and low-multiplicity non-diffractive processes is presumably (much) moreimportant We believe imperfections in this modelling to be the likely cause of the significant discrep-ancies observed at high η and for nCh le 20 at these energies Since a dedicated study of this interplayis beyond the scope of this study we limit ourselves merely to stating this observation as a point forfuture studies to help clarify

Finally in fig 27 we compare to the underlying event measured in the highly useful energyscan that was performed at the Tevatron in the last days before its shutdown [22 23] during whichextremely high min-bias statistics were collected at 300 and 900 GeV CM energy over a period of afew days As was already noted in section 3 the UE at 7 TeV is slightly larger in the Monash 2013tune than in tune 4C As can be seen from the plots here the two tunes give comparable results for allthe Tevatron energies Interestingly the UE plateau region at 900 and 1960 GeV is reached sooner inthese models than in the data translating to a roughly 10 - 20 too low UE level for leading-trackpperp values in the neighbourhood of the transition from the rise to the plateau (roughly for leading-

34

14 22 29 35 44 58 91 91 91 91 133 161 183 189 200 250 350 500 1000

gtC

hlt

n

0

20

40

60

Average Charged Multiplicity vs ECM

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN25

χ00plusmn03 00plusmn02 00plusmn02

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 22 29 35 44 58 91 91 91 91 133 161 183 189 200 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

14 22 35 44 91 91 133 161 183 189 250 350 500 1000

gtK

ltn

0

2

4

6 Multiplicity vs ECM+-Average K

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN25

χ00plusmn06 00plusmn20

00plusmn18

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 22 35 44 91 91 133 161 183 189 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

14 35 91 91 91 91 133 200 250 350 500 1000

gtΛ

ltn

0

02

04

06

08

1

12 Multiplicity vs ECM0ΛAverage

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn06

01plusmn22

01plusmn18

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 35 91 91 91 91 133 200 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

Figure 25 e+eminus rarr hadrons Energy scaling of 〈nCh〉 〈nKplusmn〉 and 〈nΛ〉 in e+eminus rarr qq eventsincluding comparisons to measurements from HEPDATA for CM energies from 14 GeV to 200 GeVAlso shown are model extrapolations up to 1000 GeV

35

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from PhysRevLett 105 (2010) 022002

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn00

00plusmn03

00plusmn71

V I

N C

I A

R O

O T

pp 7000 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

0 50 100

)C

hP

rob(

n

-710

-610

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn27

00plusmn27

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

Chn0 50 100

The

ory

Dat

a

06

08

1

12

14

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from JHEP 1002 (2010) 041

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn03

00plusmn05

00plusmn29

V I

N C

I A

R O

O T

pp 900 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

0 10 20 30 40

)C

hP

rob(

n

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn17

01plusmn25

02plusmn127

V I

N C

I A

R O

O T

pp 900 GeV

Chn0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

0 1 2 3 4 5

gtηd

ch lt

dnN

SD

1n

0

1

2

3

4

5gt (NSD)ηd

chltdn

Pythia 8185Data from ZPhys C33 (1986) 1-6

UA5PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn36

00plusmn24

00plusmn16

V I

N C

I A

R O

O T

ppbar 200 GeV

η0 1 2 3 4 5

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)C

hP

rob(

n

-410

-310

-210

-110

1

)T

|lt05 all pηChg Mult (NSD |

Pythia 8185Data from ZPhys C43 (1989) 357

UA5PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn24

00plusmn24

00plusmn08

V I

N C

I A

R O

O T

ppbar 200 GeV

Chn0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 26 Min-bias pp events from 200 to 7000 GeV Energy scaling of 〈dnChdη〉 (left) andP (nCh) (right)

36

0 10 20 30

)φ∆η

∆gt

(T

psum

lt

0

05

1

15gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn24

26plusmn33

12plusmn143

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 10 20 30

)φ∆η

∆gt

(C

hlt

n

0

05

1

15gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

04plusmn05

13plusmn08

14plusmn100

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn58

06plusmn53

08plusmn193

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn16

15plusmn20

06plusmn114

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

gt05)T

|lt10 pη (|T1

)gt vs pT

TRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn10

02plusmn07

05plusmn22

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

gt05)T

|lt10 pη (|T1

gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn20

02plusmn11

03plusmn08

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 27 The Tevatron energy scan The underlying event (left average summed-pperp density andright average track density in the transverse region as function of leading-track pperp) for pp collisionsat 300 (bottom row) 900 GeV (middle row) and 1960 GeV (top row)

37

track pperp values 2 lt pT1 lt 10 GeV) This indicates that the energy scaling of the UE modeling and inparticular the details of its transition between central and peripheral collisions is still not satisfactorilyunderstood

5 Conclusions and Exhortation

We have presented a reanalysis of the constraints on fragmentation in ee collisions and applied theresults to update the final-state fragmentation parameters in PYTHIA 8 We combine these parameterswith a tune to hadron-collider data using a new NNPDF 23 LO QCD+QED PDF set which has beenencoded so it is available as an internal PDF set in PYTHIA 8 independently of LHAPDF [112]

In this PDF set as well as in our tune the value of the strong coupling for hard-scattering matrixelements is fixed to be αs(MZ) = 013 consistent with other LO determinations of it For initial-and final-state radiation our tune uses the effective value αs(MZ) = 01365 The difference isconsistent with an effective translation between the MS and CMW schemes We note that alternative(LO NLO and NNLO) NNPDF 23 QCD+QED sets with αs(MZ) = 0119 are also available inthe code for people who want to check the impact of using a different αs(MZ) value andor higher-order PDF sets on hard-scattering events For the purpose of such studies we point out that it ispossible in PYTHIA 8 to preserve most of the features of the shower- and underlying-event tuningby changing only the PDF for the hard-scattering matrix elements leaving the PDF choice for theshower evolution and MPI framework unaltered (see the PYTHIA 8 HTML manualrsquos PDF sectionunder PDFuseHard)

The updated parameters are available as an option starting from PYTHIA 8185 by setting

Tuneee = 7 and Tunepp = 14

By no means do we claim that this should be regarded as the final word in tuning the PYTHIA 8Monte Carlo model First of all the model continues to evolve For instance developments foreseenfor the near future include updates of colour reconnections diffraction and the treatment of g rarr qqsplittings Any of these should in principle be accompanied by a reevaluation of the model constraints

Moreover despite the comprehensive view of collider data we have attempted to take in thisstudy there still remains several issues that were not addressed including initial-final interferenceand coherence effects [113 114] (probably more a modelling issue than a tuning one) reliable esti-mates of theoretical uncertainties [8 17 24 29 97 115] diffraction14 [74 116 117] and other colour-singlet phenomena such as onium production long-distance (eg forward-backward forward-centraland ldquoridgerdquo-type) correlations [88 118ndash123] B-hadron decays [124] and tuning in the presence ofmatrix-element matching at LO and NLO (see [21 29 115 125 126] for recent phenomenologi-cal studies) Especially in the latter context of matrix-element matching we expect that in manycases PYTHIA 8 will be used together with codes such as ALPGEN [127] MADGRAPH [128]aMCatNLO [129] or POWHEG [130] either using the matching algorithms of those programs them-selves or via any of PYTHIArsquos several internal (LHEF-based [131]) implementations of matchingschemes (POWHEG [85] CKKW-L [132ndash134] MLM [135 136] UMEPS [137] NL3 [138] UN-LOPS [139]) The impact of such corrections on MC tuning depends on the details of the matchingscheme (especially its treatment of unitarity) and there is in general a non-negligible possibility ofldquomis-tuningrdquo when combining a stand-alone tune with ME corrections A simple example illustrating

14In particular the constraints on fragmentation mainly come from SLD and LEP where the non-perturbative parametersare clearly defined at the shower cutoff scaleQhad whereas diffraction is dominated by soft physics for which the definitionof the effective hadronization scale is less clear The amount of MPI in hard diffractive events also requires tuning

38

this is the effective value of αs(MZ) which for a leading-order tune is typically of order 013 whilea consistent NLO correction scheme should be compatible with values closer to 012 [29] There isalso the question of the running order of αs The propagation of such changes from the level of hardmatrix elements through the shower and hadronization tuning process are still not fully explored andhence we advise users to perform simple cross-checks such as checking the distributions presented inthis paper before and after applying matrix-element corrections Parameters that appear on both sidesof the matching such as αs should also be checked for consistency [21]

We noted several issues concerning the ee data used to constrain the fragmentation modelling thatit would be good to resolve In particular we find some tensions between the identified-particle ratesextracted from 1) HEDPATA 2) Sec 46 of the PDG and 3) the Z boson summary table in the PDGas discussed in more detail in section 2 and concerning which we made some (subjective) decisionsto arrive at a set of hopefully self-consistent constraints for this work We also note that the overallprecision of the fragmentation constraints could likely be significantly improved by an FCC-ee typemachine such as Tera-Z a possibility we hope to see more fully explored in the context of future eeQCD phenomenology studies

We conclude that the new parameter set does improve significantly on the previous default valuesin several respects including better agreement with data on

1 the net strangeness fraction (has been increased by 10 reflected not only in improved kaonand hyperon yields but also in the Ds and Bs fractions)

2 the ultra-hard fragmentation tail (has been softened especially for leading baryons and for Dand B hadrons)

3 the pTZ spectrum (softened at low pTZ)

4 the minimum-bias charged multiplicity in the forward region (has increased by 10)

5 the underlying event at 7 TeV (is very slightly higher than before)

Some questions that remain open include the following We see a roughly 20 excess of verysoft kaons in both ee and pp environments cf figs 6 and 23 despite the overall kaon yields beingwell described and the overall baryon yields at LHC appear to be underestimated by at least 30despite good agreement at LEP The momentum spectra of heavier strange particles are also poorlyreproduced in particular at LHC It is interesting and exciting that some of the LHC spectra appearto be better described by allowing collective flow in a fraction of events (cf the EPOS model [140])though we believe the jury is still out on whether this accurately reflects the underlying physics Forinstance it has been argued that colour reconnections can mimick flow effects [90] and they may alsobe able to modify the yield of baryons if the creationdestruction of string junctions is allowed [141]We look forward to future discussions on these issues

We round off with an exhortation for follow-ups on this study to provide

bull Not only central tunes experiments and other user-end colleagues need more than central de-scriptions of data there is an increasing need for serious uncertainty estimates In the contextof tune variations it is important to keep in mind that the modelling uncertainties are often in-trinsically non-universal Therefore the constraints obtained by considering data uncertaintiesonly (eg in the spirit of PROFESSORrsquos eigentunes [17]) can at most constitute a lower boundon the theoretical uncertainty (similarly to the case for PDFs) A serious uncertainty estimateincludes some systematic modelling variation irrespectively of and in addition to what data

39

allows (eg in the spirit of the Perugia set of tunes for PYTHIA 6 [8]) We therefore hope thefuture will see more elaborate combinations of data- and theory-driven approaches to systematictune uncertainties

bull Not only global tunes the power of MC models lies in their ability to simultaneously describea large variety of data hence we do not mean to imply that one should give up on universalityand tune to increasingly specific corners of phase space disregarding (or de-emphasizing withlower weights) all others However as proposed in [97] one can obtain useful explicit tests ofthe universality of the underlying physics model by performing independent tunes on separateldquophysics windowsrdquo say in the forward vs central regions for different event-selection crite-ria at different collider energies or even for different collider types In this connection justmaking one global ldquobest-fitrdquo tune may obscure tensions between the descriptions of differentcomplementary data sets By performing independent tunes to each data set separately andchecking the degree of universality of the resulting parameters one obtains a powerful crosscheck on the underlying physics model If all sets produce the same or similar parameters thenuniversality is OK hence a global tune makes very good sense and the remaining uncertain-ties can presumably be reliably estimated from data alone If instead some data sets resultin significantly different tune parameters one has a powerful indication that the universality ofthe underlying modeling is breaking down which can lead to several productive actions 1) itcan be taken into account in the context of uncertainty variations 2) the nature of the data setsfor which non-universal tune parameters are obtained can implicitly indicate the nature of theproblem leading to more robust conclusions about the underlying model than merely whether atune cancannot fit the data and 3) the observations can be communicated to the model authorsin a more unambiguous way hopefully resulting in a speedier cycle of model improvements

We hope that the Monash 2013 tune parameters may serve as a useful starting point for phe-nomenology studies and for future PYTHIA 8 tuning efforts

Acknowledgments

We thank S Mrenna M Ritzmann and T Sjostrand for comments on the manuscript and L de Nooijfor pointing us to the ALICE Klowast and φ measurements [142] and to the ATLAS φ measurementsin [143] The work of J R is supported by an STFC Rutherford Fellowship STK0052271 Thiswork was supported in part by the Research Executive Agency (REA) of the European Commissionunder the Grant Agreements PITN-GA-2012-315877 (MCnet)

A Monash 2013 Tune Parameters

In tabs 3 ndash 7 we list the FSR fragmentation parameters for the Monash tune of PYTHIA Forreference we compare them to the current default parameters

40

FSR Parameters Monash 13 (Default) CommentTimeShoweralphaSvalue = 01365 = 01383 Effective alphaS(mZ) valueTimeShoweralphaSorder = 1 = 1 Running orderTimeShoweralphaSuseCMW = off = off Translation from MS to CMWTimeShowerpTmin = 050 = 040 Cutoff for QCD radiationTimeShowerpTminChgQ = 050 = 040 Cutoff for QED radiationTimeShowerphiPolAsym = on = on Asymmetric azimuth distributions

Table 3 Final-state radiation (FSR) parameters

HAD Parameters Monash 13 (Default) Comment String breaks pT and z distributionsStringPTsigma = 0335 = 0304 Soft pT in string breaks (in GeV)StringPTenhancedFraction = 001 = 001 Fraction of breakups with enhanced pTStringPTenhancedWidth = 20 = 20 Enhancement factorStringZaLund = 068 = 03 Lund FF a (hard fragmentation supp)StringZbLund = 098 = 08 Lund FF b (soft fragmentation supp)StringZaExtraSquark = 00 = 00 Extra a when picking up an s quarkStringZaExtraDiquark = 097 = 050 Extra a when picking up a diquarkStringZrFactC = 132 = 100 Lund-Bowler c-quark parameterStringZrFactB = 0855 = 067 Lund-Bowler b-quark parameter Flavour composition mesonsStringFlavProbStoUD = 0217 = 019 Strangeness-to-UD ratioStringFlavmesonUDvector = 05 = 062 Light-flavour vector suppressionStringFlavmesonSvector = 055 = 0725 Strange vector suppressionStringFlavmesonCvector = 088 = 106 Charm vector suppressionStringFlavmesonBvector = 22 = 30 Bottom vector suppressionStringFlavetaSup = 060 = 063 Suppression of eta mesonsStringFlavetaPrimeSup = 012 = 012 Suppression of etarsquo mesons Flavour composition baryonsStringFlavprobQQtoQ = 0081 = 009 Diquark rate (for baryon production)StringFlavprobSQtoQQ = 0915 = 1000 Strange-diquark suppressionStringFlavprobQQ1toQQ0 = 00275 = 0027 Vector diquark suppressionStringFlavdecupletSup = 10 = 10 Spin-32 baryon suppressionStringFlavsuppressLeadingB = off = off Optional leading-baryon suppressionStringFlavpopcornSpair = 09 = 05 StringFlavpopcornSmeson = 05 = 05

Table 4 String-breaking parameters

PDF and ME Parameters Monash 13 (Default) CommentPDFpSet = 13 = 8 PDF set for the protonSigmaProcessalphaSvalue = 0130 0135 alphaS(MZ) for matrix elementsMultiPartonInteractionsalphaSvalue = 0130 0135 alphaS(MZ) for MPI

Table 5 Parton-distribution (PDF) and Matrix-Element (ME) parameters

41

ISR Parameters Monash 13 (Default) CommentSpaceShoweralphaSvalue = 01365 = 0137 Effective alphaS(mZ) valueSpaceShoweralphaSorder = 1 = 1 Running orderSpaceShoweralphaSuseCMW = off = off Translation from MS to CMWSpaceShowersamePTasMPI = off = off ISR cutoff typeSpaceShowerpT0Ref = 20 = 20 ISR pT0 cutoffSpaceShowerecmRef = 70000 = 18000 ISR pT0 reference ECM scaleSpaceShowerecmPow = 00 = 00 ISR pT0 scaling powerSpaceShowerrapidityOrder = on = on Approx coherence via y-orderingSpaceShowerphiPolAsym = on = on Azimuth asymmetries from gluon polSpaceShowerphiIntAsym = on = on Azimuth asymmetries from interferenceTimeShowerdampenBeamRecoil = on = on Recoil dampening in final-initial dipolesBeamRemnantsprimordialKTsoft = 09 = 05 Primordial kT for soft procsBeamRemnantsprimordialKThard = 18 = 20 Primordial kT for hard procsBeamRemnantshalfScaleForKT = 15 = 10 Primordial kT softhard boundaryBeamRemnantshalfMassForKT = 10 = 10 Primordial kT softhard mass boundary

Table 6 Initial-state radiation (ISR) and primordial-kT parameters

MPI Parameters Monash 13 (Default) CommentMultipartonInteractionspT0Ref = 228 = 2085 MPI pT0 IR regularization scaleMultipartonInteractionsecmRef = 70000 = 18000 MPI pT0 reference ECM scaleMultipartonInteractionsecmPow = 0215 = 019 MPI pT0 scaling powerMultipartonInteractionsbProfile = 3 = 3 Transverse matter overlap profileMultipartonInteractionsexpPow = 185 = 20 Shape parameterBeamRemnantsreconnectRange = 18 = 15 Colour ReconnectionsSigmaTotalzeroAXB = on = on Carried over from 4CSigmaDiffractivedampen = on = on Carried over from 4CSigmaDiffractivemaxXB = 650 = 650 Carried over from 4CSigmaDiffractivemaxAX = 650 = 650 Carried over from 4CSigmaDiffractivemaxXX = 650 = 650 Carried over from 4CDiffractionlargeMassSuppress = 40 = 20 High-mass diffraction suppression power

Table 7 Multi-Parton-Interaction (MPI) Colour-Reconnection (CR) and Diffractive parameters

42

B Additional Plots

B1 LEP Event-Shape Distributions

To keep the main body of the paper as uncluttered as possible we collect various plots of event-shapedistributions in figs 28 and 29 separated into light-flavour and b-tagged events on the left and rightrespectively

The experimental results come from the L3 experiment [26] However since the data points areonly available with 3-digit precision some of the least populated bins contain artifacts like uncertain-ties being reported as exactly zero etc Thus we have been forced to make the following modificationsto the data set

The statistical uncertainty was reported as zero for the last two bins of light-flavour Thrust as wellas for the last bin of the C D and BT parameters Uncertainties lt 10minus3 were derived using anapproximate statistical scaling based on the contents and uncertainties of the other bins Likewise thesystematical uncertainty for the last bin of Thrust was given as zero which we have replaced by theupper limit 5times 10minus4 The last bin of BT quoted a measured y value of zero removed in this study

For the heavy-flavour tagged event shapes more significant rounding issues were present Thusseveral of the first and last bins of each distribution either quoted zero (statistical andor systematic)uncertainties or ones with only a single digit of precision (such as 0001 for which the rounding errorcould be up to sim 50) We have interpreted all such values conservatively inserting by hand a fourthdigit on the uncertainties as large as could be consistent with rounding

B2 Additional Particle Spectra

In addition to the K and Λ spectra shown in the main body of the paper (sections 22 and 35) wehere include for reference the x spectra of φ mesons protons and Ξ baryons at LEP in figs 30 and 31the pT spectrum of Klowast mesons and the rapidity and pT spectra of φ mesons at LHC in fig 32 (withabsolute normalizations to the number of inelastic events) and the rapidity spectrum of Ξ baryons atLHC in fig 33

The transverse-momentum spectra of Klowast and φ mesons in fig 32 exhibit the same qualitativebehaviour as that of the KS mesons (fig 23) namely an excess at very soft momenta below sim 500MeV and a depletion at slightly higher momenta between 1 and 2 GeV As discussed in section 35we did not find a way to remove these undesirable features in the Monash 2013 tune suggesting thatthis is an issue that further theoretical modeling will be needed to resolve

The rapidity spectrum of Ξ baryons fig 33 shows that although the Monash tune does producemore Ξ baryons overall (as expected also from the relative increase of Ξ production at LEP cf fig 5)there is still a significant deficit of Ξ baryons at the LHC almost a factor 2 compared with the dataThis is qualitatively similar to the situation for Λ baryons (fig 24) discussed in section 35 Sincenew physics mechanisms may be required to ldquoexplainrdquo the missing baryons we conclude that furthermeasurements and better precision on both the Λ and Ξ sectors (in addition to any other baryonsthat may be accessible) would be highly interesting More explicit recommendations can be found insections 35 and 5

43

0 01 02 03 04

d(1

-T)

σ d

σ1

-310

-210

-110

1

10

2101-Thrust (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn03

01plusmn04

02plusmn05

V I

N C

I A

R O

O T

1-T (udsc)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

d(1

-T)

σ dσ

1

-310

-210

-110

1

10

2101-T (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn13

02plusmn12

02plusmn14

V I

N C

I A

R O

O T

1-T (b)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210

310C Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn03

00plusmn04

01plusmn04

V I

N C

I A

R O

O T

C0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210 C parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn17

01plusmn24

01plusmn27

V I

N C

I A

R O

O T

C (b)0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn06

01plusmn06

V I

N C

I A

R O

O T

D0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn24

02plusmn21

02plusmn26

V I

N C

I A

R O

O T

D (b)0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

Figure 28 Hadronic Z decays atradics = 912 GeV The T C and D event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

44

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn02

01plusmn03

01plusmn04

V I

N C

I A

R O

O T

WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn05

01plusmn12

01plusmn17

V I

N C

I A

R O

O T

(b)WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn02

00plusmn02

01plusmn03

V I

N C

I A

R O

O T

TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

04plusmn24

08plusmn49

08plusmn55

V I

N C

I A

R O

O T

(b)TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

Figure 29 Hadronic Z decays atradics = 912 GeV The BW and BT event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

45

0 02 04 06 08 1

dx

φgt

dn

φ1

ltn

-210

-110

1

10 )φx(

Pythia 8183Data from ALEPH_1996_S3486095d40-x01-y01

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn37

02plusmn53

03plusmn62

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

0608

112141618

Figure 30 Hadronic Z decays atradics = 912 GeV φ meson x spectrum

-5 -4 -3 -2 -1 0

dx

pgt

dn

p1

ltn

-410

-310

-210

-110

1

10

210) (Combined)px(p+

Pythia 8183Data from Zeit Phys C66 (1995) 355 PhysRev D59 (1998) 052001

ALEPH+SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn08

00plusmn09

00plusmn08

V I

N C

I A

R O

O T

px-5 -4 -3 -2 -1 0

The

ory

Dat

a

06

08

1

12

14

0 02 04

dx

Ξgt

dn

Ξ1

ltn

-110

1

10

)plusmnΞx(

Pythia 8183Data from Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn11

02plusmn13

02plusmn14

V I

N C

I A

R O

O T

Ex0 02 04

The

ory

Dat

a

06

08

1

12

14

Figure 31 Hadronic Z decays atradics = 912 GeV pplusmn and Ξplusmn x spectra

46

0 2 4 6

Td

pK

d

nIN

EL

1N

-510

-410

-310

-210

-110

(INEL |y|lt05)T

p0K

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn35

01plusmn26

01plusmn29

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 2 4 6

Td

pφ

dn

INE

L1

N-510

-410

-310

-210

-110

gt04)T

(INEL |y|lt05 pT

pφ

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn88

03plusmn84

04plusmn173

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

)dy

[mb]

-K

+K

rarrφ(σd

0

05

1

15

2 Rapidity (INEL ATLAS cuts)φ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn14

01plusmn19

01plusmn34

V I

N C

I A

R O

O T

pp 7000 GeV

|y|0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

06 08 1 12

[mb

GeV

]φ

T)

dp-

K+

Krarrφ(

σd

0

05

1

15

2

25 (INEL ATLAS cuts)

T pφ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn21

01plusmn30

02plusmn53

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p06 08 1 12

The

ory

Dat

a

06

08

1

12

14

Figure 32 pp collisions at 7 TeV Top row Klowast and φ pperp spectra compared with ALICE data [142]Bottom row φ rapidity and pperp spectrum compared with ATLAS data [143] The ATLAS cuts areφrarr K+Kminus pperpφ isin [05 12] GeV |y(φ)| lt 08 pperpK gt 023 GeV |pK | lt 08 GeV

47

0 05 1 15 2

dygt

Ξ lt

dnN

SD

1N

0

001

002

003

004)d|y|gt (NSD)Ξltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn89

01plusmn129

01plusmn192

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

0

05

1

15

2

Figure 33 pp collisions at 7 TeV Ξminus rapidity spectrum compared with CMS data [99]

48

B3 Energy Scaling of σ2rarr2(pTmin) vs σinel from 200 GeV to 100 TeV

In fig 34 we show the LO QCD 2rarr 2 cross section integrated above pTmin as a function of pTminin pp collisions at 4 different CM energies complementing and expanding on the 8-TeV CM energyshown in the main body of the paper We compare two different αs and PDF choices correspondingto those made in tunes Monash 13 (blue filled dots) and 4C (red open squares) respectively As areference for the total inelastic cross section at each energy we base ourselves on the best-fit curvein the TOTEM cross-section measurement paper [72] which in turn represents a fit produced by theCOMPETE collaboration [144] Uncertainties are rough conservative estimates based on the plot inthe TOTEM paper but they are in any case too small to significantly affect conclusions about the scaleat which the partonic cross section saturates the hadronic one

We observe that the pTmin value for which the LO QCD 2 rarr 2 partonic cross section formallybecomes equal to the total inelastic cross section (strongly suggesting that every event has at leastone such mini-jet pair) rises from values around 1 ndash 2 GeV at energies

radics lt 1 TeV to 5 GeV atradic

s = 13 TeV and finally 10 GeV atradics = 100 TeV

49

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

0 10 20

)M

PI

Pro

b(n

-510

-410

-310

-210

-110

1 number of interactions

Pythia 8185

PY8 (Monash 13)PY8 (4C)PY8 (2C)

V I

N C

I A

R O

O T

pp 7000 GeV

MPIn0 10 20

Rat

io

06

08

1

12

14

Figure 16 pp collisions at 7 TeV Number of MPI in inelastic events

For the Monash tune we have chosen a slightly more peaked transverse matter profile [27]thus generating a relatively larger UE for the same average MB quantities We note however thatthere are still several indications that the dynamics are not well understood in particular when itcomes to very low multiplicities (overlapping with diffraction) very high multiplicities (eg the so-called CMS ldquoridgerdquo effect [88]) and to identified-particle spectra (eg possible modifications byre-scattering [89] string boosts from colour reconnections [90] or other collective effects)

For the 7-TeV reference energy we focus on here (energy scaling will be studied in the followingsubsection) the relevant parameters in the code are

Hadron transverse mass overlap density profileMultipartonInteractionsbProfile = 3MultipartonInteractionsexpPow = 185

IR regularization scale for MPI and energy scalingMultipartonInteractionspT0Ref = 228MultipartonInteractionsecmRef = 7000MultipartonInteractionsecmPow = 0215

The slightly more peaked matter distribution combined with a relatively low pperp0 value producesan intrinsically broader distribution in the number of parton-parton interactions (MPI) illustrated bythe theory-level plot in fig 16

The sampling of the PDFs by MPI initiators (including also the hardest scattering in our definitionof ldquoMPIrdquo) as a function of parton x values is illustrated in fig 17 for the three tunes considered in thispaper The top left-hand pane shows the most inclusive quantity simply the probability distribution ofthe x value of all MPI initiators (again we emphasize that we include the hardest-interaction initiatorsin our definition of ldquoMPIrdquo here) on a logarithmic x axis Here we see that the NNPDF tune hasa harder distribution both at large and small x as compared to the CTEQ6L1 tunes The effect isparticularly marked at small x Since MPI is dominated by the low-Q gluon PDF cf fig 12 thisis precisely what we expect the shape of the distribution of sampled x values follows that of the

25

-8 -6 -4 -2 0

(x)

101

n dn

dLo

g

-510

-410

-310

-210

-110

1

10(x) including MPI

10Log

Pythia 8185

PY8 (Monash 13)PY8 (4C)PY8 (2C)

V I

N C

I A

R O

O T

pp 7000 GeV

(x)10

Log-8 -6 -4 -2 0

Rat

io

06

08

1

12

14

-8 -6 -4 -2 0

Rat

io0

05

1

15Gluon Fraction including MPI

Pythia 8185

PY8 (Monash 13)PY8 (4C)PY8 (2C)

V I

N C

I A

R O

O T

pp 7000 GeV

(x)10

Log-8 -6 -4 -2 0

Rat

io

06

08

1

12

14

-8 -6 -4 -2 0

Rat

io

-310

-210

-110

1

10

210u including MPIu

Pythia 8185

PY8 (Monash 13)PY8 (4C)PY8 (2C)

V I

N C

I A

R O

O T

pp 7000 GeV

(x)10

Log-8 -6 -4 -2 0

Rat

io

06

08

1

12

14

0 02 04 06 08 1

1n

dnd

X

-510

-410

-310

-210

-110

1

10

210MPIxΣBeam Remnant X = 1 -

Pythia 8185

PY8 (Monash 13)PY8 (4C)PY8 (2C)

V I

N C

I A

R O

O T

pp 7000 GeV

RemnantX0 02 04 06 08 1

Rat

io

06

08

1

12

14

Figure 17 PDF sampling by MPIs in inelastic non-diffractive pp collisions at 7 TeV Top Left thex distribution of all MPI initiators (including the hardest scattering) Top Right the fraction of MPIinitiators which are gluons as a function of x Bottom Left the uu ratio Bottom Right thedistribution of the amount of x left in the beam remnant after MPI (note linear scale in x)

26

PDFs themselves Indeed the NNPDF23 gluon is harder than the CTEQ6L one for x gt 02 and forx lt 10minus5

The relative dominance of the gluon PDF is illustrated by the bottom right-hand pane of fig 17showing the gluon fraction (relative to all MPI initiators) as a function of log10(x) Below x sim 01the NNPPDF sampling is 80 gluon-dominated and the gluon fraction is higher than in CTEQ6L1for both very small x lt 10minus5 as well as for very large x gt 02

A further consistency check is provided by the uu ratio shown in the bottom left-hand pane offig 17 This is consistent with unity (as expected for sea quarks) in the entire small-x region x lt 10minus2The valence bump appears to be slightly more pronounced in the NNPDF tune (relative to the sea)since the uu ratio drops off more quickly above 10minus2 This trend persists until the very highest binat x sim 1 where the experimental uncertainties are extremely large The CTEQ6L1 parametrizationthere forces the u PDF to zero while the NNPDF parametrization allows for a small amount of u toremain even at the largest x values though we note that they are still outnumbered by u quarks at alevel of hundred-to-one

The last pane of fig 17 shows the amount of x remaining in the beam remnant after all MPI(including both the hardest interaction and additional MPI) have been considered ie

Xrem = 1minussumiisinMPI

xi (10)

Note the linear scale in x on this plot and the highly logaritmic axis In the vast majority of casesthe beam remnant thus still retains over 90 of the initial hadron energy But there is a class ofevents at the level of 10minus4 or 10minus5 of the total cross section (depending on the tune) in whichthe beam remnant retains less than 10 of the incoming hadron energy Experiments studying theamount and distribution of forward scattered energy in particular may be able to tell us about whetherthis class of events which we term ldquoCatastrophic Energy Lossrdquo events really exists and at whatlevel Note that these events are typically not caused by a single hard partonic scattering processdue to the high penalty associated with accessing PDFs in the region x gt 05 Rather they arean intrinsic consequence of MPI A straightforward extrapolation requiring a catastrophic energyloss on both sides of the event mdash more than 90 of the energy scattered out of both beams whichwe term ldquoTotal Inelastic Scatteringrdquo mdash may occur at a level of 10minus10 minus 10minus8 of the cross sectionor between 10 - 1000 pb (though we of course only have PYTHIArsquos word for it) This would bean extremely interesting part of hadron-hadron collision physics to study very far from the single-interaction dominated limit and hence potentially very sensitive to the existence of possible collectiveeffects Designing efficient triggers for this class of events would be a great accomplishment

Turning now to physics distributions in min-bias events the broader MPI distribution in theMonash tune translates to a broader charged-multiplicity spectrum though the effect is modulatedby the colour-reconnection model The resulting multiplicity and pperp spectra are shown in fig 18for ldquostandardrdquo fiducial cuts (top row pperp ge 500 MeV |η| lt 25 nCh ge 1) and ldquosoftrdquo fiducial cuts(bottom row pperp ge 100 MeV |η| lt 25 nCh ge 2) with the latter representing the most inclusivephase-space region accessible with the ATLAS detector For both of the nCh distributions we notethat a significant ldquodouble-crested waverdquo pattern is still present in the ratio panes though it has beendampened slightly The pperp spectra in the right-hand panes are a bit below the data for the standardfiducial cuts and above it for the soft cuts hence we regard the Monash tune as a reasonable compro-mise

Pseudorapidity distributions are shown in fig 19 However due to the complicated interplaybetween diffractive contributions at low multiplicity and high-multiplicity multi-parton interactions(with associated questions of transverse matter density profile and colour reconnections) the average

27

0 50 100

)C

hP

rob(

n

-710

-610

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn27

00plusmn27

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

Chn0 50 100

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20

Td

pC

h d

nT

)p

π(

2C

h1

n

-810

-710

-610

-510

-410

-310

-210

-110

1

10|lt25)ηgt05 |

T 1 pge

Ch (n

Tp

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLAS PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn15

00plusmn08

01plusmn58

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 5 10 15 20

The

ory

Dat

a

06

08

1

12

14

0 50 100 150 200

)C

hP

rob(

n

-610

-510

-410

-310

-210

-110

1|lt25)ηgt01 |

T 2 pge

ChSoft Chg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn45

00plusmn49

01plusmn197

V I

N C

I A

R O

O T

pp 7000 GeV

Chn0 50 100 150 200

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20

Td

pC

h d

nT

)p

π(

2C

h1

n

-910

-710

-510

-310

-110

10|lt25)ηgt01 |

T 2 pge

Ch (n

Tp

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn43

01plusmn73

02plusmn155

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 5 10 15 20

The

ory

Dat

a

06

08

1

12

14

Figure 18 Min-bias pp collisions at 7 TeV Charged-multiplicity and pperp distributions with standard(top row) and soft (bottom row) fiducial cuts compared to ATLAS data [91]

28

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from PhysRevLett 105 (2010) 022002

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn00

00plusmn03

00plusmn71

V I

N C

I A

R O

O T

pp 7000 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

55 6 65

gtηd

Ch

ltdn

Tot

em1

n

0

1

2

3

4

5

6|lt65)ηgt004 53lt|

T1 pge

chgt (nηd

Chltdn

Pythia 8185Data from EurophysLett 98 (2012) 31002

TOTEMPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn01

00plusmn27

00plusmn62

V I

N C

I A

R O

O T

pp 7000 GeV

η55 6 65

The

ory

Dat

a

06

08

1

12

14

3 35 4 45 5

gtηlt

dEd

0

100

200

300

400

500|lt465)η1 in both 323lt|ge

chMB Fwd E Flow (n

Pythia 8185Data from JHEP 11 (2011) 148

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn01

00plusmn04

00plusmn22

V I

N C

I A

R O

O T

pp 7000 GeV

η3 35 4 45 5

The

ory

Dat

a

06

08

1

12

14

Figure 19 Charged-particle pseudorapidity distributions and forward energy flow in min-bias ppcollisions at 7 TeV compared to CMS [92 93] and TOTEM [94] data

29

0 50 100

0

05

1

15

2

25|lt25)ηgt05 |

T) (p

Chgt(n

Tltp

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn05

01plusmn01

05plusmn07

V I

N C

I A

R O

O T

pp 7000 GeV

0 50 100

The

ory

Dat

a

06

08

1

12

14

0 50 100 150 200

0

05

1

15|lt25)ηgt01 |

T 2 pge

Ch) (n

Chgt(n

TSoft ltp

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn06

00plusmn08

03plusmn40

V I

N C

I A

R O

O T

pp 7000 GeV

0 50 100 150 200

The

ory

Dat

a06

08

1

12

14

Figure 20 Average-pperp vs charged-multiplicity distributions in min-bias pp collisions at 7 TeV withstandard (left) and soft (right) fiducial cuts compared to ATLAS data [91]

multiplicity by itself is a very difficult quantity to extract reliable conclusions from Note also that theCMS measurement [92] shown in the top pane of fig 19 was corrected to an unphysical ldquonon-singlediffractiverdquo event definition which essentially amounts to switching off single-diffractive contributionsin the MC generator (We note that later CMS measurements instead use a physical observable relatedto the diffractive mass to define NSD) For the comparisons to CMS NSD data shown here the single-diffractive contributions were switched off in the generator With these caveats in mind we note thatboth the 4C and Monash 2013 tunes are in good agreement with the CMS measurement with theMonash one giving a slightly lower central charged-track density (by about 5) This is closer to thevalues observed in data though as already noted in section 11 we do not regard differences at the 5level as significant

In the bottom two panes of fig 19 we focus on the forward region (with physical event selections)In particular we see that the NNPDF set [20] generates a broader rapidity spectrum so that while theactivity in the central region (top pane) is reduced slightly the activity in the very forward regionactually increases and comes into agreement with the TOTEM measurement [94] covering the range53 lt |η| lt 64 The bottom right-hand pane shows the forward energy flow measured by CMS [93]in the intermediate region 323 lt |η| lt 465 The dependence on η is a bit steeper in the Monashtune than in the previous one and more similar to that seen in the data

A complementary observable which is highly sensitive to interconnection effects between theMPI (and hence eg to the effects of ldquocolour reconnectionsrdquo [95]) is the average charged-particlepperp as a function of the number of charged particles In a strict leading-colour picture each MPIwould cause one or two new strings to be stretched between the remnants but each such string wouldbe independent (modulo endpoint effects) therefore (modulo jets) the pperp spectrum of the hadronsproduced by each of these strings would be independent of the number of strings The result would bea flat 〈pperp〉 (nCh) spectrum Jets and colour reconnections both produce a rising spectrum The spectraobserved by ATLAS [91] are compared to the Monash 2C and 4C tunes in fig 20 for standard

30

0 1 2 3

gtφ|dη

d|

Ch

n2

ltd

0

02

04

06

08

1gt01)

T|lt25 pηgt1 (|

Tlead| wrt pφ∆|

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn16

00plusmn19

00plusmn56

V I

N C

I A

R O

O T

pp 7000 GeV

| [rad]φ∆|0 1 2 3

The

ory

Dat

a

06

08

1

12

14

0 1 2 3

gtφ|dη

d|

Ch

n2

ltd

0

05

1

15

2

gt05)T

|lt25 pηgt5 (|Tlead

| wrt pφ∆|

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn05

00plusmn05

00plusmn70

V I

N C

I A

R O

O T

pp 7000 GeV

| [rad]φ∆|0 1 2 3

The

ory

Dat

a06

08

1

12

14

Figure 21 pp collisions at 7 TeV ∆φ of charged particles with respect to the hardest track for twodifferent hardest-track triggers compared with ATLAS data [98]

(left) and soft (right) fiducial cuts Both of the Monash and 4C tunes reproduce the data quite wellwith χ2

5 lt 1 while the older tune 2C had a higher CR strength optimized to describe Tevatrondata [96] We certainly consider the energy scaling of the effective CR strength among the mostuncertain parameters of the current min-biasunderlying-event modelling (a similar conclusion wasreached for the CR modelling in PYTHIA 6 in [97]) and intend to study the physics aspects of thisissue more closely in a forthcoming paper

For a more differential look at the event structure we consider the charged-track ∆φ distributionswith respect to the azimuthal angle of the leading track in fig 21 compared with ATLAS data [98]The plot in the left-hand pane corresponds to a requirement of pperplead ge 1 GeV while the one in theright-hand pane is for a harder trigger pperplead ge 5 GeV The former can roughly be taken as charac-teristic of min-bias events while the latter is related to the differential distribution of the underlyingevent In both cases the activity in the wide-angle region near π2 is significantly better described bythe 4C and Monash 2013 tunes (which agrees with their improved description of the overall activity)while there is a too strong peaking at low ∆φ especially for the lowest pperplead cut (left) possibly indi-cating that the structure of the min-bias events is still slightly too ldquolumpyrdquo (ie jetty) For the higherpperplead cut (right) the overcounting at very low ∆φ is already significantly milder and we observe agood agreement with the data

Turning now to the underlying event (UE) what matters most for high-pperp jet studies is that theMC models describe the UE contamination per ∆R jet area The most important UE observable fromthis perspective is thus the pperp sum density in the UE and its fluctuations For charged particles atLHC typically a pperp cut of 500 MeV is relevant since softer tracks will form helices and hence notcontribute to calorimetric jet energies Neutral particles are of course relevant across all pperp scalesIn fig 22 we show the charged pperp sum density (left with the lowest possible pperp cut of 100 MeV)and the charged-track density (right with a pperp cut of 500 MeV) in the so-called ldquoTransverse Regionrdquo(defined by 60 lt ∆φ lt 120 with respect to the leading track) inside the ATLAS acceptance of

31

0 5 10 15 20

)φ∆η

∆gt

(T

psum

lt

0

05

1

15

2

25gt01)

T|lt25 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn03

01plusmn09

02plusmn112

V I

N C

I A

R O

O T

pp 7000 GeV

(hardest track) [GeV]T1

p0 5 10 15 20

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20

)φ∆η

∆gt

(C

hlt

n

0

05

1

15

2

25gt05)

T|lt25 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn02

00plusmn04

02plusmn104

V I

N C

I A

R O

O T

pp 7000 GeV

(hardest track) [GeV]T1

p0 5 10 15 20

The

ory

Dat

a06

08

1

12

14

Figure 22 pp collisions at 7 TeV UE (ldquoTransverse regionrdquo) transverse-momentum sum density (left)and charged-track density (right) compared with ATLAS data [98]

|η| lt 25 [98] As is now well known the Tevatron extrapolations (represented here by Tune 2C)predicted a UE level which was 10 ndash 20 below the LHC data Both the current default tune 4C(which included LHC data) and the Monash 2013 tune exhibit significantly better agreement with theLHC measurements with the Monash one giving a slight additional improvement in the χ2

5 valuesWe conclude that the Monash 2013 tune parameters are appropriate for both min-bias and UE studies

35 Identified Particles at LHC

While the description of inclusive charged particles discussed in the previous section is acceptablelarger discrepancies emerge when we consider the spectra of identified particles We here focus onstrange particles in particular K0

S mesons and Λ0 hyperons in figs 23 and 24 respectively Theexperimental measurements come from CMS [99] Additional comparisons to strange-particle spectra(Klowast φ and Ξ) are collected in appendix B2

In the K0S rapidity distribution shown in the left-hand pane of fig 23 we observe that tune 4C

exhibits a mild underproduction of about 10 Though it might be tempting to speculate whether thiscould indicate some small reduction of strangeness suppression in pp collisions however we alreadynoted in section 21 that the strangeness production in ee collisions also needed to be increased byabout 10 After this adjustment we see that the overall K0

S yield in the Monash 2013 tune is fullyconsistent with the CMS measurement Nonetheless we note that the momentum distribution is stillnot satisfactorily described as shown in the right-hand pane of fig 23 Our current best guess istherefore that the overall rate of strange quarks is consistent at least in the average min-bias collision(dedicated comparisons in high-multiplicity samples would still be interesting) but that the phase-space distribution of strange hadrons needs more work Similarly to the case in ee collisions cf fig 6the model predicts too many very soft kaons though we do not currently know whether there is adynamic link between the ee and pp observations

For strange baryons we note that the increase in the Λ0 fraction in ee collisions (cf fig 5) does

32

0 05 1 15 2

dygt

K lt

dnN

SD

1n

0

02

04

06

08)d|y|gt Rapidity (NSD)

S

0ltdn(K

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn01

00plusmn09

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8 10

Td

pK

dn

NS

D1

N

-510

-410

-310

-210

-110

1

10 (|y|lt20 NSD)

T pS

0K

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn78

01plusmn34

02plusmn22

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6 8 10

The

ory

Dat

a06

08

1

12

14

Figure 23 pp collisions at 7 TeV K0S rapidity and pperp spectrum compared with CMS data [99]

0 05 1 15 2

dygt

Λ lt

dnN

SD

1N

0

01

02

03

04)d|y|gt (NSD)0Λltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn64

00plusmn78

01plusmn147

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8 10

Td

pΛ

dn

Λ1

n

-510

-410

-310

-210

-110

1

10 (|y|lt20 NSD)

T p0Λ

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn59

03plusmn66

05plusmn105

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6 8 10

The

ory

Dat

a

06

08

1

12

14

Figure 24 pp collisions at 7 TeV Λ0 rapidity and pperp spectrum compared with CMS data [99]

not result in an equivalent improvement of the Λ0 rate in pp collisions shown in fig 24 The Monash2013 tune still produces only about 23 of the observed Λ0 rate (and just over half of the observedΞminus rate cf appendix B2) We therefore believe it to be likely that an additional source of net baryonproduction is needed (at least within the limited context of the current PYTHIA modelling) in orderto describe the LHC data The momentum spectrum is likewise quite discrepant exhibiting an excessat very low momenta (stronger than that for kaons) a dip between 1ndash4 GeV and then an excess of veryhard Λ0 production The latter hard tail is somewhat milder in the Monash 2013 tune than previously

33

and it may be consistent with the trend also seen in the Λ0 spectrum at LEP cf fig 6 We concludethat baryon production still requires further modelling and tuning efforts

4 Energy Scaling

Though energy scaling these days mostly refers to the scaling of pp collisions (see eg [97]) animportant first step is to consider the scaling of observables in ee rarr γlowastZ rarr hadrons This scalingcontains information on the relative contributions of perturbative and non-perturbative fragmentationThus at low ee energies the non-perturbative components of the fragmentation model dominatewhile perturbative bremsstrahlung increases in importance towards higher ee energies In fig 25we consider the scaling of the average charged-particle multiplicity and that of charged Kaons andLambda baryons from CM energies of 14 GeV to 200 GeV obtained from measurements availableat HEPDATA Below the Z pole the measurements we include mostly come from TASSO [100]though a few points on 〈nCh〉 come from HRS (at 29 GeV [101]) and TOPAZ (at 578 GeV [102]) Atthe Z pole the data come from the four LEP experiments [38 51ndash53] with the latter extending alsoto energies above MZ [103ndash108] For completeness and as reference for future ee collider studiesmodel extrapolations for CM energies up to 1000 GeV are also shown (though still only including theeerarr γlowastZ rarr hadrons component as usual with photon ISR switched off)

From the plots in fig 25 it is clear that there are no significant differences between the energyscaling of the three ee tunes considered here (mainly reflecting that they have been tuned to samereference point at 912 GeV and that their scaling is dictated by the same underlying physics model)and that their energy dependence closely matches that observed in data However the increasedamount of non-perturbative strangeness production in the Monash tune leads to a better agreementwith the overall normalization of the Kplusmn and Λ rates at all energies

Moving to pp collisions the plots in fig 26 show the scaling of the average charged multiplicity(left column) and multiplicity distributions (right column) in min-bias collisions from 7000 GeV (toprow) to 900 GeV (middle row) and 200 GeV (bottom row) compared with data from CMS [92 109]ATLAS [91] and UA5 [110 111] We regret the omission of additional relevant min-bias measure-ments from the Tevatron and RHIC experiments here but have chosen to focus in this paper mainlyon the LHC The comparisons at 7 TeV were already discussed in the main section on pp collisionssection 3 At 900 GeV the Monash 2013 tune again gives a roughly 5 lower average central chargedmultiplicity than the 4C one with a better description of the tail towards high multiplicities At 200GeV the UA5 measurement we include here extends over the full rapidity and pperp range hence the in-terplay between diffraction and low-multiplicity non-diffractive processes is presumably (much) moreimportant We believe imperfections in this modelling to be the likely cause of the significant discrep-ancies observed at high η and for nCh le 20 at these energies Since a dedicated study of this interplayis beyond the scope of this study we limit ourselves merely to stating this observation as a point forfuture studies to help clarify

Finally in fig 27 we compare to the underlying event measured in the highly useful energyscan that was performed at the Tevatron in the last days before its shutdown [22 23] during whichextremely high min-bias statistics were collected at 300 and 900 GeV CM energy over a period of afew days As was already noted in section 3 the UE at 7 TeV is slightly larger in the Monash 2013tune than in tune 4C As can be seen from the plots here the two tunes give comparable results for allthe Tevatron energies Interestingly the UE plateau region at 900 and 1960 GeV is reached sooner inthese models than in the data translating to a roughly 10 - 20 too low UE level for leading-trackpperp values in the neighbourhood of the transition from the rise to the plateau (roughly for leading-

34

14 22 29 35 44 58 91 91 91 91 133 161 183 189 200 250 350 500 1000

gtC

hlt

n

0

20

40

60

Average Charged Multiplicity vs ECM

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN25

χ00plusmn03 00plusmn02 00plusmn02

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 22 29 35 44 58 91 91 91 91 133 161 183 189 200 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

14 22 35 44 91 91 133 161 183 189 250 350 500 1000

gtK

ltn

0

2

4

6 Multiplicity vs ECM+-Average K

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN25

χ00plusmn06 00plusmn20

00plusmn18

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 22 35 44 91 91 133 161 183 189 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

14 35 91 91 91 91 133 200 250 350 500 1000

gtΛ

ltn

0

02

04

06

08

1

12 Multiplicity vs ECM0ΛAverage

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn06

01plusmn22

01plusmn18

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 35 91 91 91 91 133 200 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

Figure 25 e+eminus rarr hadrons Energy scaling of 〈nCh〉 〈nKplusmn〉 and 〈nΛ〉 in e+eminus rarr qq eventsincluding comparisons to measurements from HEPDATA for CM energies from 14 GeV to 200 GeVAlso shown are model extrapolations up to 1000 GeV

35

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from PhysRevLett 105 (2010) 022002

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn00

00plusmn03

00plusmn71

V I

N C

I A

R O

O T

pp 7000 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

0 50 100

)C

hP

rob(

n

-710

-610

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn27

00plusmn27

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

Chn0 50 100

The

ory

Dat

a

06

08

1

12

14

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from JHEP 1002 (2010) 041

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn03

00plusmn05

00plusmn29

V I

N C

I A

R O

O T

pp 900 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

0 10 20 30 40

)C

hP

rob(

n

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn17

01plusmn25

02plusmn127

V I

N C

I A

R O

O T

pp 900 GeV

Chn0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

0 1 2 3 4 5

gtηd

ch lt

dnN

SD

1n

0

1

2

3

4

5gt (NSD)ηd

chltdn

Pythia 8185Data from ZPhys C33 (1986) 1-6

UA5PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn36

00plusmn24

00plusmn16

V I

N C

I A

R O

O T

ppbar 200 GeV

η0 1 2 3 4 5

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)C

hP

rob(

n

-410

-310

-210

-110

1

)T

|lt05 all pηChg Mult (NSD |

Pythia 8185Data from ZPhys C43 (1989) 357

UA5PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn24

00plusmn24

00plusmn08

V I

N C

I A

R O

O T

ppbar 200 GeV

Chn0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 26 Min-bias pp events from 200 to 7000 GeV Energy scaling of 〈dnChdη〉 (left) andP (nCh) (right)

36

0 10 20 30

)φ∆η

∆gt

(T

psum

lt

0

05

1

15gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn24

26plusmn33

12plusmn143

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 10 20 30

)φ∆η

∆gt

(C

hlt

n

0

05

1

15gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

04plusmn05

13plusmn08

14plusmn100

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn58

06plusmn53

08plusmn193

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn16

15plusmn20

06plusmn114

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

gt05)T

|lt10 pη (|T1

)gt vs pT

TRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn10

02plusmn07

05plusmn22

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

gt05)T

|lt10 pη (|T1

gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn20

02plusmn11

03plusmn08

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 27 The Tevatron energy scan The underlying event (left average summed-pperp density andright average track density in the transverse region as function of leading-track pperp) for pp collisionsat 300 (bottom row) 900 GeV (middle row) and 1960 GeV (top row)

37

track pperp values 2 lt pT1 lt 10 GeV) This indicates that the energy scaling of the UE modeling and inparticular the details of its transition between central and peripheral collisions is still not satisfactorilyunderstood

5 Conclusions and Exhortation

We have presented a reanalysis of the constraints on fragmentation in ee collisions and applied theresults to update the final-state fragmentation parameters in PYTHIA 8 We combine these parameterswith a tune to hadron-collider data using a new NNPDF 23 LO QCD+QED PDF set which has beenencoded so it is available as an internal PDF set in PYTHIA 8 independently of LHAPDF [112]

In this PDF set as well as in our tune the value of the strong coupling for hard-scattering matrixelements is fixed to be αs(MZ) = 013 consistent with other LO determinations of it For initial-and final-state radiation our tune uses the effective value αs(MZ) = 01365 The difference isconsistent with an effective translation between the MS and CMW schemes We note that alternative(LO NLO and NNLO) NNPDF 23 QCD+QED sets with αs(MZ) = 0119 are also available inthe code for people who want to check the impact of using a different αs(MZ) value andor higher-order PDF sets on hard-scattering events For the purpose of such studies we point out that it ispossible in PYTHIA 8 to preserve most of the features of the shower- and underlying-event tuningby changing only the PDF for the hard-scattering matrix elements leaving the PDF choice for theshower evolution and MPI framework unaltered (see the PYTHIA 8 HTML manualrsquos PDF sectionunder PDFuseHard)

The updated parameters are available as an option starting from PYTHIA 8185 by setting

Tuneee = 7 and Tunepp = 14

By no means do we claim that this should be regarded as the final word in tuning the PYTHIA 8Monte Carlo model First of all the model continues to evolve For instance developments foreseenfor the near future include updates of colour reconnections diffraction and the treatment of g rarr qqsplittings Any of these should in principle be accompanied by a reevaluation of the model constraints

Moreover despite the comprehensive view of collider data we have attempted to take in thisstudy there still remains several issues that were not addressed including initial-final interferenceand coherence effects [113 114] (probably more a modelling issue than a tuning one) reliable esti-mates of theoretical uncertainties [8 17 24 29 97 115] diffraction14 [74 116 117] and other colour-singlet phenomena such as onium production long-distance (eg forward-backward forward-centraland ldquoridgerdquo-type) correlations [88 118ndash123] B-hadron decays [124] and tuning in the presence ofmatrix-element matching at LO and NLO (see [21 29 115 125 126] for recent phenomenologi-cal studies) Especially in the latter context of matrix-element matching we expect that in manycases PYTHIA 8 will be used together with codes such as ALPGEN [127] MADGRAPH [128]aMCatNLO [129] or POWHEG [130] either using the matching algorithms of those programs them-selves or via any of PYTHIArsquos several internal (LHEF-based [131]) implementations of matchingschemes (POWHEG [85] CKKW-L [132ndash134] MLM [135 136] UMEPS [137] NL3 [138] UN-LOPS [139]) The impact of such corrections on MC tuning depends on the details of the matchingscheme (especially its treatment of unitarity) and there is in general a non-negligible possibility ofldquomis-tuningrdquo when combining a stand-alone tune with ME corrections A simple example illustrating

14In particular the constraints on fragmentation mainly come from SLD and LEP where the non-perturbative parametersare clearly defined at the shower cutoff scaleQhad whereas diffraction is dominated by soft physics for which the definitionof the effective hadronization scale is less clear The amount of MPI in hard diffractive events also requires tuning

38

this is the effective value of αs(MZ) which for a leading-order tune is typically of order 013 whilea consistent NLO correction scheme should be compatible with values closer to 012 [29] There isalso the question of the running order of αs The propagation of such changes from the level of hardmatrix elements through the shower and hadronization tuning process are still not fully explored andhence we advise users to perform simple cross-checks such as checking the distributions presented inthis paper before and after applying matrix-element corrections Parameters that appear on both sidesof the matching such as αs should also be checked for consistency [21]

We noted several issues concerning the ee data used to constrain the fragmentation modelling thatit would be good to resolve In particular we find some tensions between the identified-particle ratesextracted from 1) HEDPATA 2) Sec 46 of the PDG and 3) the Z boson summary table in the PDGas discussed in more detail in section 2 and concerning which we made some (subjective) decisionsto arrive at a set of hopefully self-consistent constraints for this work We also note that the overallprecision of the fragmentation constraints could likely be significantly improved by an FCC-ee typemachine such as Tera-Z a possibility we hope to see more fully explored in the context of future eeQCD phenomenology studies

We conclude that the new parameter set does improve significantly on the previous default valuesin several respects including better agreement with data on

1 the net strangeness fraction (has been increased by 10 reflected not only in improved kaonand hyperon yields but also in the Ds and Bs fractions)

2 the ultra-hard fragmentation tail (has been softened especially for leading baryons and for Dand B hadrons)

3 the pTZ spectrum (softened at low pTZ)

4 the minimum-bias charged multiplicity in the forward region (has increased by 10)

5 the underlying event at 7 TeV (is very slightly higher than before)

Some questions that remain open include the following We see a roughly 20 excess of verysoft kaons in both ee and pp environments cf figs 6 and 23 despite the overall kaon yields beingwell described and the overall baryon yields at LHC appear to be underestimated by at least 30despite good agreement at LEP The momentum spectra of heavier strange particles are also poorlyreproduced in particular at LHC It is interesting and exciting that some of the LHC spectra appearto be better described by allowing collective flow in a fraction of events (cf the EPOS model [140])though we believe the jury is still out on whether this accurately reflects the underlying physics Forinstance it has been argued that colour reconnections can mimick flow effects [90] and they may alsobe able to modify the yield of baryons if the creationdestruction of string junctions is allowed [141]We look forward to future discussions on these issues

We round off with an exhortation for follow-ups on this study to provide

bull Not only central tunes experiments and other user-end colleagues need more than central de-scriptions of data there is an increasing need for serious uncertainty estimates In the contextof tune variations it is important to keep in mind that the modelling uncertainties are often in-trinsically non-universal Therefore the constraints obtained by considering data uncertaintiesonly (eg in the spirit of PROFESSORrsquos eigentunes [17]) can at most constitute a lower boundon the theoretical uncertainty (similarly to the case for PDFs) A serious uncertainty estimateincludes some systematic modelling variation irrespectively of and in addition to what data

39

allows (eg in the spirit of the Perugia set of tunes for PYTHIA 6 [8]) We therefore hope thefuture will see more elaborate combinations of data- and theory-driven approaches to systematictune uncertainties

bull Not only global tunes the power of MC models lies in their ability to simultaneously describea large variety of data hence we do not mean to imply that one should give up on universalityand tune to increasingly specific corners of phase space disregarding (or de-emphasizing withlower weights) all others However as proposed in [97] one can obtain useful explicit tests ofthe universality of the underlying physics model by performing independent tunes on separateldquophysics windowsrdquo say in the forward vs central regions for different event-selection crite-ria at different collider energies or even for different collider types In this connection justmaking one global ldquobest-fitrdquo tune may obscure tensions between the descriptions of differentcomplementary data sets By performing independent tunes to each data set separately andchecking the degree of universality of the resulting parameters one obtains a powerful crosscheck on the underlying physics model If all sets produce the same or similar parameters thenuniversality is OK hence a global tune makes very good sense and the remaining uncertain-ties can presumably be reliably estimated from data alone If instead some data sets resultin significantly different tune parameters one has a powerful indication that the universality ofthe underlying modeling is breaking down which can lead to several productive actions 1) itcan be taken into account in the context of uncertainty variations 2) the nature of the data setsfor which non-universal tune parameters are obtained can implicitly indicate the nature of theproblem leading to more robust conclusions about the underlying model than merely whether atune cancannot fit the data and 3) the observations can be communicated to the model authorsin a more unambiguous way hopefully resulting in a speedier cycle of model improvements

We hope that the Monash 2013 tune parameters may serve as a useful starting point for phe-nomenology studies and for future PYTHIA 8 tuning efforts

Acknowledgments

We thank S Mrenna M Ritzmann and T Sjostrand for comments on the manuscript and L de Nooijfor pointing us to the ALICE Klowast and φ measurements [142] and to the ATLAS φ measurementsin [143] The work of J R is supported by an STFC Rutherford Fellowship STK0052271 Thiswork was supported in part by the Research Executive Agency (REA) of the European Commissionunder the Grant Agreements PITN-GA-2012-315877 (MCnet)

A Monash 2013 Tune Parameters

In tabs 3 ndash 7 we list the FSR fragmentation parameters for the Monash tune of PYTHIA Forreference we compare them to the current default parameters

40

FSR Parameters Monash 13 (Default) CommentTimeShoweralphaSvalue = 01365 = 01383 Effective alphaS(mZ) valueTimeShoweralphaSorder = 1 = 1 Running orderTimeShoweralphaSuseCMW = off = off Translation from MS to CMWTimeShowerpTmin = 050 = 040 Cutoff for QCD radiationTimeShowerpTminChgQ = 050 = 040 Cutoff for QED radiationTimeShowerphiPolAsym = on = on Asymmetric azimuth distributions

Table 3 Final-state radiation (FSR) parameters

HAD Parameters Monash 13 (Default) Comment String breaks pT and z distributionsStringPTsigma = 0335 = 0304 Soft pT in string breaks (in GeV)StringPTenhancedFraction = 001 = 001 Fraction of breakups with enhanced pTStringPTenhancedWidth = 20 = 20 Enhancement factorStringZaLund = 068 = 03 Lund FF a (hard fragmentation supp)StringZbLund = 098 = 08 Lund FF b (soft fragmentation supp)StringZaExtraSquark = 00 = 00 Extra a when picking up an s quarkStringZaExtraDiquark = 097 = 050 Extra a when picking up a diquarkStringZrFactC = 132 = 100 Lund-Bowler c-quark parameterStringZrFactB = 0855 = 067 Lund-Bowler b-quark parameter Flavour composition mesonsStringFlavProbStoUD = 0217 = 019 Strangeness-to-UD ratioStringFlavmesonUDvector = 05 = 062 Light-flavour vector suppressionStringFlavmesonSvector = 055 = 0725 Strange vector suppressionStringFlavmesonCvector = 088 = 106 Charm vector suppressionStringFlavmesonBvector = 22 = 30 Bottom vector suppressionStringFlavetaSup = 060 = 063 Suppression of eta mesonsStringFlavetaPrimeSup = 012 = 012 Suppression of etarsquo mesons Flavour composition baryonsStringFlavprobQQtoQ = 0081 = 009 Diquark rate (for baryon production)StringFlavprobSQtoQQ = 0915 = 1000 Strange-diquark suppressionStringFlavprobQQ1toQQ0 = 00275 = 0027 Vector diquark suppressionStringFlavdecupletSup = 10 = 10 Spin-32 baryon suppressionStringFlavsuppressLeadingB = off = off Optional leading-baryon suppressionStringFlavpopcornSpair = 09 = 05 StringFlavpopcornSmeson = 05 = 05

Table 4 String-breaking parameters

PDF and ME Parameters Monash 13 (Default) CommentPDFpSet = 13 = 8 PDF set for the protonSigmaProcessalphaSvalue = 0130 0135 alphaS(MZ) for matrix elementsMultiPartonInteractionsalphaSvalue = 0130 0135 alphaS(MZ) for MPI

Table 5 Parton-distribution (PDF) and Matrix-Element (ME) parameters

41

ISR Parameters Monash 13 (Default) CommentSpaceShoweralphaSvalue = 01365 = 0137 Effective alphaS(mZ) valueSpaceShoweralphaSorder = 1 = 1 Running orderSpaceShoweralphaSuseCMW = off = off Translation from MS to CMWSpaceShowersamePTasMPI = off = off ISR cutoff typeSpaceShowerpT0Ref = 20 = 20 ISR pT0 cutoffSpaceShowerecmRef = 70000 = 18000 ISR pT0 reference ECM scaleSpaceShowerecmPow = 00 = 00 ISR pT0 scaling powerSpaceShowerrapidityOrder = on = on Approx coherence via y-orderingSpaceShowerphiPolAsym = on = on Azimuth asymmetries from gluon polSpaceShowerphiIntAsym = on = on Azimuth asymmetries from interferenceTimeShowerdampenBeamRecoil = on = on Recoil dampening in final-initial dipolesBeamRemnantsprimordialKTsoft = 09 = 05 Primordial kT for soft procsBeamRemnantsprimordialKThard = 18 = 20 Primordial kT for hard procsBeamRemnantshalfScaleForKT = 15 = 10 Primordial kT softhard boundaryBeamRemnantshalfMassForKT = 10 = 10 Primordial kT softhard mass boundary

Table 6 Initial-state radiation (ISR) and primordial-kT parameters

MPI Parameters Monash 13 (Default) CommentMultipartonInteractionspT0Ref = 228 = 2085 MPI pT0 IR regularization scaleMultipartonInteractionsecmRef = 70000 = 18000 MPI pT0 reference ECM scaleMultipartonInteractionsecmPow = 0215 = 019 MPI pT0 scaling powerMultipartonInteractionsbProfile = 3 = 3 Transverse matter overlap profileMultipartonInteractionsexpPow = 185 = 20 Shape parameterBeamRemnantsreconnectRange = 18 = 15 Colour ReconnectionsSigmaTotalzeroAXB = on = on Carried over from 4CSigmaDiffractivedampen = on = on Carried over from 4CSigmaDiffractivemaxXB = 650 = 650 Carried over from 4CSigmaDiffractivemaxAX = 650 = 650 Carried over from 4CSigmaDiffractivemaxXX = 650 = 650 Carried over from 4CDiffractionlargeMassSuppress = 40 = 20 High-mass diffraction suppression power

Table 7 Multi-Parton-Interaction (MPI) Colour-Reconnection (CR) and Diffractive parameters

42

B Additional Plots

B1 LEP Event-Shape Distributions

To keep the main body of the paper as uncluttered as possible we collect various plots of event-shapedistributions in figs 28 and 29 separated into light-flavour and b-tagged events on the left and rightrespectively

The experimental results come from the L3 experiment [26] However since the data points areonly available with 3-digit precision some of the least populated bins contain artifacts like uncertain-ties being reported as exactly zero etc Thus we have been forced to make the following modificationsto the data set

The statistical uncertainty was reported as zero for the last two bins of light-flavour Thrust as wellas for the last bin of the C D and BT parameters Uncertainties lt 10minus3 were derived using anapproximate statistical scaling based on the contents and uncertainties of the other bins Likewise thesystematical uncertainty for the last bin of Thrust was given as zero which we have replaced by theupper limit 5times 10minus4 The last bin of BT quoted a measured y value of zero removed in this study

For the heavy-flavour tagged event shapes more significant rounding issues were present Thusseveral of the first and last bins of each distribution either quoted zero (statistical andor systematic)uncertainties or ones with only a single digit of precision (such as 0001 for which the rounding errorcould be up to sim 50) We have interpreted all such values conservatively inserting by hand a fourthdigit on the uncertainties as large as could be consistent with rounding

B2 Additional Particle Spectra

In addition to the K and Λ spectra shown in the main body of the paper (sections 22 and 35) wehere include for reference the x spectra of φ mesons protons and Ξ baryons at LEP in figs 30 and 31the pT spectrum of Klowast mesons and the rapidity and pT spectra of φ mesons at LHC in fig 32 (withabsolute normalizations to the number of inelastic events) and the rapidity spectrum of Ξ baryons atLHC in fig 33

The transverse-momentum spectra of Klowast and φ mesons in fig 32 exhibit the same qualitativebehaviour as that of the KS mesons (fig 23) namely an excess at very soft momenta below sim 500MeV and a depletion at slightly higher momenta between 1 and 2 GeV As discussed in section 35we did not find a way to remove these undesirable features in the Monash 2013 tune suggesting thatthis is an issue that further theoretical modeling will be needed to resolve

The rapidity spectrum of Ξ baryons fig 33 shows that although the Monash tune does producemore Ξ baryons overall (as expected also from the relative increase of Ξ production at LEP cf fig 5)there is still a significant deficit of Ξ baryons at the LHC almost a factor 2 compared with the dataThis is qualitatively similar to the situation for Λ baryons (fig 24) discussed in section 35 Sincenew physics mechanisms may be required to ldquoexplainrdquo the missing baryons we conclude that furthermeasurements and better precision on both the Λ and Ξ sectors (in addition to any other baryonsthat may be accessible) would be highly interesting More explicit recommendations can be found insections 35 and 5

43

0 01 02 03 04

d(1

-T)

σ d

σ1

-310

-210

-110

1

10

2101-Thrust (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn03

01plusmn04

02plusmn05

V I

N C

I A

R O

O T

1-T (udsc)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

d(1

-T)

σ dσ

1

-310

-210

-110

1

10

2101-T (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn13

02plusmn12

02plusmn14

V I

N C

I A

R O

O T

1-T (b)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210

310C Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn03

00plusmn04

01plusmn04

V I

N C

I A

R O

O T

C0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210 C parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn17

01plusmn24

01plusmn27

V I

N C

I A

R O

O T

C (b)0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn06

01plusmn06

V I

N C

I A

R O

O T

D0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn24

02plusmn21

02plusmn26

V I

N C

I A

R O

O T

D (b)0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

Figure 28 Hadronic Z decays atradics = 912 GeV The T C and D event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

44

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn02

01plusmn03

01plusmn04

V I

N C

I A

R O

O T

WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn05

01plusmn12

01plusmn17

V I

N C

I A

R O

O T

(b)WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn02

00plusmn02

01plusmn03

V I

N C

I A

R O

O T

TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

04plusmn24

08plusmn49

08plusmn55

V I

N C

I A

R O

O T

(b)TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

Figure 29 Hadronic Z decays atradics = 912 GeV The BW and BT event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

45

0 02 04 06 08 1

dx

φgt

dn

φ1

ltn

-210

-110

1

10 )φx(

Pythia 8183Data from ALEPH_1996_S3486095d40-x01-y01

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn37

02plusmn53

03plusmn62

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

0608

112141618

Figure 30 Hadronic Z decays atradics = 912 GeV φ meson x spectrum

-5 -4 -3 -2 -1 0

dx

pgt

dn

p1

ltn

-410

-310

-210

-110

1

10

210) (Combined)px(p+

Pythia 8183Data from Zeit Phys C66 (1995) 355 PhysRev D59 (1998) 052001

ALEPH+SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn08

00plusmn09

00plusmn08

V I

N C

I A

R O

O T

px-5 -4 -3 -2 -1 0

The

ory

Dat

a

06

08

1

12

14

0 02 04

dx

Ξgt

dn

Ξ1

ltn

-110

1

10

)plusmnΞx(

Pythia 8183Data from Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn11

02plusmn13

02plusmn14

V I

N C

I A

R O

O T

Ex0 02 04

The

ory

Dat

a

06

08

1

12

14

Figure 31 Hadronic Z decays atradics = 912 GeV pplusmn and Ξplusmn x spectra

46

0 2 4 6

Td

pK

d

nIN

EL

1N

-510

-410

-310

-210

-110

(INEL |y|lt05)T

p0K

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn35

01plusmn26

01plusmn29

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 2 4 6

Td

pφ

dn

INE

L1

N-510

-410

-310

-210

-110

gt04)T

(INEL |y|lt05 pT

pφ

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn88

03plusmn84

04plusmn173

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

)dy

[mb]

-K

+K

rarrφ(σd

0

05

1

15

2 Rapidity (INEL ATLAS cuts)φ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn14

01plusmn19

01plusmn34

V I

N C

I A

R O

O T

pp 7000 GeV

|y|0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

06 08 1 12

[mb

GeV

]φ

T)

dp-

K+

Krarrφ(

σd

0

05

1

15

2

25 (INEL ATLAS cuts)

T pφ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn21

01plusmn30

02plusmn53

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p06 08 1 12

The

ory

Dat

a

06

08

1

12

14

Figure 32 pp collisions at 7 TeV Top row Klowast and φ pperp spectra compared with ALICE data [142]Bottom row φ rapidity and pperp spectrum compared with ATLAS data [143] The ATLAS cuts areφrarr K+Kminus pperpφ isin [05 12] GeV |y(φ)| lt 08 pperpK gt 023 GeV |pK | lt 08 GeV

47

0 05 1 15 2

dygt

Ξ lt

dnN

SD

1N

0

001

002

003

004)d|y|gt (NSD)Ξltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn89

01plusmn129

01plusmn192

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

0

05

1

15

2

Figure 33 pp collisions at 7 TeV Ξminus rapidity spectrum compared with CMS data [99]

48

B3 Energy Scaling of σ2rarr2(pTmin) vs σinel from 200 GeV to 100 TeV

In fig 34 we show the LO QCD 2rarr 2 cross section integrated above pTmin as a function of pTminin pp collisions at 4 different CM energies complementing and expanding on the 8-TeV CM energyshown in the main body of the paper We compare two different αs and PDF choices correspondingto those made in tunes Monash 13 (blue filled dots) and 4C (red open squares) respectively As areference for the total inelastic cross section at each energy we base ourselves on the best-fit curvein the TOTEM cross-section measurement paper [72] which in turn represents a fit produced by theCOMPETE collaboration [144] Uncertainties are rough conservative estimates based on the plot inthe TOTEM paper but they are in any case too small to significantly affect conclusions about the scaleat which the partonic cross section saturates the hadronic one

We observe that the pTmin value for which the LO QCD 2 rarr 2 partonic cross section formallybecomes equal to the total inelastic cross section (strongly suggesting that every event has at leastone such mini-jet pair) rises from values around 1 ndash 2 GeV at energies

radics lt 1 TeV to 5 GeV atradic

s = 13 TeV and finally 10 GeV atradics = 100 TeV

49

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

-8 -6 -4 -2 0

(x)

101

n dn

dLo

g

-510

-410

-310

-210

-110

1

10(x) including MPI

10Log

Pythia 8185

PY8 (Monash 13)PY8 (4C)PY8 (2C)

V I

N C

I A

R O

O T

pp 7000 GeV

(x)10

Log-8 -6 -4 -2 0

Rat

io

06

08

1

12

14

-8 -6 -4 -2 0

Rat

io0

05

1

15Gluon Fraction including MPI

Pythia 8185

PY8 (Monash 13)PY8 (4C)PY8 (2C)

V I

N C

I A

R O

O T

pp 7000 GeV

(x)10

Log-8 -6 -4 -2 0

Rat

io

06

08

1

12

14

-8 -6 -4 -2 0

Rat

io

-310

-210

-110

1

10

210u including MPIu

Pythia 8185

PY8 (Monash 13)PY8 (4C)PY8 (2C)

V I

N C

I A

R O

O T

pp 7000 GeV

(x)10

Log-8 -6 -4 -2 0

Rat

io

06

08

1

12

14

0 02 04 06 08 1

1n

dnd

X

-510

-410

-310

-210

-110

1

10

210MPIxΣBeam Remnant X = 1 -

Pythia 8185

PY8 (Monash 13)PY8 (4C)PY8 (2C)

V I

N C

I A

R O

O T

pp 7000 GeV

RemnantX0 02 04 06 08 1

Rat

io

06

08

1

12

14

Figure 17 PDF sampling by MPIs in inelastic non-diffractive pp collisions at 7 TeV Top Left thex distribution of all MPI initiators (including the hardest scattering) Top Right the fraction of MPIinitiators which are gluons as a function of x Bottom Left the uu ratio Bottom Right thedistribution of the amount of x left in the beam remnant after MPI (note linear scale in x)

26

PDFs themselves Indeed the NNPDF23 gluon is harder than the CTEQ6L one for x gt 02 and forx lt 10minus5

The relative dominance of the gluon PDF is illustrated by the bottom right-hand pane of fig 17showing the gluon fraction (relative to all MPI initiators) as a function of log10(x) Below x sim 01the NNPPDF sampling is 80 gluon-dominated and the gluon fraction is higher than in CTEQ6L1for both very small x lt 10minus5 as well as for very large x gt 02

A further consistency check is provided by the uu ratio shown in the bottom left-hand pane offig 17 This is consistent with unity (as expected for sea quarks) in the entire small-x region x lt 10minus2The valence bump appears to be slightly more pronounced in the NNPDF tune (relative to the sea)since the uu ratio drops off more quickly above 10minus2 This trend persists until the very highest binat x sim 1 where the experimental uncertainties are extremely large The CTEQ6L1 parametrizationthere forces the u PDF to zero while the NNPDF parametrization allows for a small amount of u toremain even at the largest x values though we note that they are still outnumbered by u quarks at alevel of hundred-to-one

The last pane of fig 17 shows the amount of x remaining in the beam remnant after all MPI(including both the hardest interaction and additional MPI) have been considered ie

Xrem = 1minussumiisinMPI

xi (10)

Note the linear scale in x on this plot and the highly logaritmic axis In the vast majority of casesthe beam remnant thus still retains over 90 of the initial hadron energy But there is a class ofevents at the level of 10minus4 or 10minus5 of the total cross section (depending on the tune) in whichthe beam remnant retains less than 10 of the incoming hadron energy Experiments studying theamount and distribution of forward scattered energy in particular may be able to tell us about whetherthis class of events which we term ldquoCatastrophic Energy Lossrdquo events really exists and at whatlevel Note that these events are typically not caused by a single hard partonic scattering processdue to the high penalty associated with accessing PDFs in the region x gt 05 Rather they arean intrinsic consequence of MPI A straightforward extrapolation requiring a catastrophic energyloss on both sides of the event mdash more than 90 of the energy scattered out of both beams whichwe term ldquoTotal Inelastic Scatteringrdquo mdash may occur at a level of 10minus10 minus 10minus8 of the cross sectionor between 10 - 1000 pb (though we of course only have PYTHIArsquos word for it) This would bean extremely interesting part of hadron-hadron collision physics to study very far from the single-interaction dominated limit and hence potentially very sensitive to the existence of possible collectiveeffects Designing efficient triggers for this class of events would be a great accomplishment

Turning now to physics distributions in min-bias events the broader MPI distribution in theMonash tune translates to a broader charged-multiplicity spectrum though the effect is modulatedby the colour-reconnection model The resulting multiplicity and pperp spectra are shown in fig 18for ldquostandardrdquo fiducial cuts (top row pperp ge 500 MeV |η| lt 25 nCh ge 1) and ldquosoftrdquo fiducial cuts(bottom row pperp ge 100 MeV |η| lt 25 nCh ge 2) with the latter representing the most inclusivephase-space region accessible with the ATLAS detector For both of the nCh distributions we notethat a significant ldquodouble-crested waverdquo pattern is still present in the ratio panes though it has beendampened slightly The pperp spectra in the right-hand panes are a bit below the data for the standardfiducial cuts and above it for the soft cuts hence we regard the Monash tune as a reasonable compro-mise

Pseudorapidity distributions are shown in fig 19 However due to the complicated interplaybetween diffractive contributions at low multiplicity and high-multiplicity multi-parton interactions(with associated questions of transverse matter density profile and colour reconnections) the average

27

0 50 100

)C

hP

rob(

n

-710

-610

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn27

00plusmn27

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

Chn0 50 100

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20

Td

pC

h d

nT

)p

π(

2C

h1

n

-810

-710

-610

-510

-410

-310

-210

-110

1

10|lt25)ηgt05 |

T 1 pge

Ch (n

Tp

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLAS PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn15

00plusmn08

01plusmn58

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 5 10 15 20

The

ory

Dat

a

06

08

1

12

14

0 50 100 150 200

)C

hP

rob(

n

-610

-510

-410

-310

-210

-110

1|lt25)ηgt01 |

T 2 pge

ChSoft Chg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn45

00plusmn49

01plusmn197

V I

N C

I A

R O

O T

pp 7000 GeV

Chn0 50 100 150 200

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20

Td

pC

h d

nT

)p

π(

2C

h1

n

-910

-710

-510

-310

-110

10|lt25)ηgt01 |

T 2 pge

Ch (n

Tp

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn43

01plusmn73

02plusmn155

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 5 10 15 20

The

ory

Dat

a

06

08

1

12

14

Figure 18 Min-bias pp collisions at 7 TeV Charged-multiplicity and pperp distributions with standard(top row) and soft (bottom row) fiducial cuts compared to ATLAS data [91]

28

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from PhysRevLett 105 (2010) 022002

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn00

00plusmn03

00plusmn71

V I

N C

I A

R O

O T

pp 7000 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

55 6 65

gtηd

Ch

ltdn

Tot

em1

n

0

1

2

3

4

5

6|lt65)ηgt004 53lt|

T1 pge

chgt (nηd

Chltdn

Pythia 8185Data from EurophysLett 98 (2012) 31002

TOTEMPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn01

00plusmn27

00plusmn62

V I

N C

I A

R O

O T

pp 7000 GeV

η55 6 65

The

ory

Dat

a

06

08

1

12

14

3 35 4 45 5

gtηlt

dEd

0

100

200

300

400

500|lt465)η1 in both 323lt|ge

chMB Fwd E Flow (n

Pythia 8185Data from JHEP 11 (2011) 148

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn01

00plusmn04

00plusmn22

V I

N C

I A

R O

O T

pp 7000 GeV

η3 35 4 45 5

The

ory

Dat

a

06

08

1

12

14

Figure 19 Charged-particle pseudorapidity distributions and forward energy flow in min-bias ppcollisions at 7 TeV compared to CMS [92 93] and TOTEM [94] data

29

0 50 100

0

05

1

15

2

25|lt25)ηgt05 |

T) (p

Chgt(n

Tltp

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn05

01plusmn01

05plusmn07

V I

N C

I A

R O

O T

pp 7000 GeV

0 50 100

The

ory

Dat

a

06

08

1

12

14

0 50 100 150 200

0

05

1

15|lt25)ηgt01 |

T 2 pge

Ch) (n

Chgt(n

TSoft ltp

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn06

00plusmn08

03plusmn40

V I

N C

I A

R O

O T

pp 7000 GeV

0 50 100 150 200

The

ory

Dat

a06

08

1

12

14

Figure 20 Average-pperp vs charged-multiplicity distributions in min-bias pp collisions at 7 TeV withstandard (left) and soft (right) fiducial cuts compared to ATLAS data [91]

multiplicity by itself is a very difficult quantity to extract reliable conclusions from Note also that theCMS measurement [92] shown in the top pane of fig 19 was corrected to an unphysical ldquonon-singlediffractiverdquo event definition which essentially amounts to switching off single-diffractive contributionsin the MC generator (We note that later CMS measurements instead use a physical observable relatedto the diffractive mass to define NSD) For the comparisons to CMS NSD data shown here the single-diffractive contributions were switched off in the generator With these caveats in mind we note thatboth the 4C and Monash 2013 tunes are in good agreement with the CMS measurement with theMonash one giving a slightly lower central charged-track density (by about 5) This is closer to thevalues observed in data though as already noted in section 11 we do not regard differences at the 5level as significant

In the bottom two panes of fig 19 we focus on the forward region (with physical event selections)In particular we see that the NNPDF set [20] generates a broader rapidity spectrum so that while theactivity in the central region (top pane) is reduced slightly the activity in the very forward regionactually increases and comes into agreement with the TOTEM measurement [94] covering the range53 lt |η| lt 64 The bottom right-hand pane shows the forward energy flow measured by CMS [93]in the intermediate region 323 lt |η| lt 465 The dependence on η is a bit steeper in the Monashtune than in the previous one and more similar to that seen in the data

A complementary observable which is highly sensitive to interconnection effects between theMPI (and hence eg to the effects of ldquocolour reconnectionsrdquo [95]) is the average charged-particlepperp as a function of the number of charged particles In a strict leading-colour picture each MPIwould cause one or two new strings to be stretched between the remnants but each such string wouldbe independent (modulo endpoint effects) therefore (modulo jets) the pperp spectrum of the hadronsproduced by each of these strings would be independent of the number of strings The result would bea flat 〈pperp〉 (nCh) spectrum Jets and colour reconnections both produce a rising spectrum The spectraobserved by ATLAS [91] are compared to the Monash 2C and 4C tunes in fig 20 for standard

30

0 1 2 3

gtφ|dη

d|

Ch

n2

ltd

0

02

04

06

08

1gt01)

T|lt25 pηgt1 (|

Tlead| wrt pφ∆|

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn16

00plusmn19

00plusmn56

V I

N C

I A

R O

O T

pp 7000 GeV

| [rad]φ∆|0 1 2 3

The

ory

Dat

a

06

08

1

12

14

0 1 2 3

gtφ|dη

d|

Ch

n2

ltd

0

05

1

15

2

gt05)T

|lt25 pηgt5 (|Tlead

| wrt pφ∆|

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn05

00plusmn05

00plusmn70

V I

N C

I A

R O

O T

pp 7000 GeV

| [rad]φ∆|0 1 2 3

The

ory

Dat

a06

08

1

12

14

Figure 21 pp collisions at 7 TeV ∆φ of charged particles with respect to the hardest track for twodifferent hardest-track triggers compared with ATLAS data [98]

(left) and soft (right) fiducial cuts Both of the Monash and 4C tunes reproduce the data quite wellwith χ2

5 lt 1 while the older tune 2C had a higher CR strength optimized to describe Tevatrondata [96] We certainly consider the energy scaling of the effective CR strength among the mostuncertain parameters of the current min-biasunderlying-event modelling (a similar conclusion wasreached for the CR modelling in PYTHIA 6 in [97]) and intend to study the physics aspects of thisissue more closely in a forthcoming paper

For a more differential look at the event structure we consider the charged-track ∆φ distributionswith respect to the azimuthal angle of the leading track in fig 21 compared with ATLAS data [98]The plot in the left-hand pane corresponds to a requirement of pperplead ge 1 GeV while the one in theright-hand pane is for a harder trigger pperplead ge 5 GeV The former can roughly be taken as charac-teristic of min-bias events while the latter is related to the differential distribution of the underlyingevent In both cases the activity in the wide-angle region near π2 is significantly better described bythe 4C and Monash 2013 tunes (which agrees with their improved description of the overall activity)while there is a too strong peaking at low ∆φ especially for the lowest pperplead cut (left) possibly indi-cating that the structure of the min-bias events is still slightly too ldquolumpyrdquo (ie jetty) For the higherpperplead cut (right) the overcounting at very low ∆φ is already significantly milder and we observe agood agreement with the data

Turning now to the underlying event (UE) what matters most for high-pperp jet studies is that theMC models describe the UE contamination per ∆R jet area The most important UE observable fromthis perspective is thus the pperp sum density in the UE and its fluctuations For charged particles atLHC typically a pperp cut of 500 MeV is relevant since softer tracks will form helices and hence notcontribute to calorimetric jet energies Neutral particles are of course relevant across all pperp scalesIn fig 22 we show the charged pperp sum density (left with the lowest possible pperp cut of 100 MeV)and the charged-track density (right with a pperp cut of 500 MeV) in the so-called ldquoTransverse Regionrdquo(defined by 60 lt ∆φ lt 120 with respect to the leading track) inside the ATLAS acceptance of

31

0 5 10 15 20

)φ∆η

∆gt

(T

psum

lt

0

05

1

15

2

25gt01)

T|lt25 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn03

01plusmn09

02plusmn112

V I

N C

I A

R O

O T

pp 7000 GeV

(hardest track) [GeV]T1

p0 5 10 15 20

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20

)φ∆η

∆gt

(C

hlt

n

0

05

1

15

2

25gt05)

T|lt25 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn02

00plusmn04

02plusmn104

V I

N C

I A

R O

O T

pp 7000 GeV

(hardest track) [GeV]T1

p0 5 10 15 20

The

ory

Dat

a06

08

1

12

14

Figure 22 pp collisions at 7 TeV UE (ldquoTransverse regionrdquo) transverse-momentum sum density (left)and charged-track density (right) compared with ATLAS data [98]

|η| lt 25 [98] As is now well known the Tevatron extrapolations (represented here by Tune 2C)predicted a UE level which was 10 ndash 20 below the LHC data Both the current default tune 4C(which included LHC data) and the Monash 2013 tune exhibit significantly better agreement with theLHC measurements with the Monash one giving a slight additional improvement in the χ2

5 valuesWe conclude that the Monash 2013 tune parameters are appropriate for both min-bias and UE studies

35 Identified Particles at LHC

While the description of inclusive charged particles discussed in the previous section is acceptablelarger discrepancies emerge when we consider the spectra of identified particles We here focus onstrange particles in particular K0

S mesons and Λ0 hyperons in figs 23 and 24 respectively Theexperimental measurements come from CMS [99] Additional comparisons to strange-particle spectra(Klowast φ and Ξ) are collected in appendix B2

In the K0S rapidity distribution shown in the left-hand pane of fig 23 we observe that tune 4C

exhibits a mild underproduction of about 10 Though it might be tempting to speculate whether thiscould indicate some small reduction of strangeness suppression in pp collisions however we alreadynoted in section 21 that the strangeness production in ee collisions also needed to be increased byabout 10 After this adjustment we see that the overall K0

S yield in the Monash 2013 tune is fullyconsistent with the CMS measurement Nonetheless we note that the momentum distribution is stillnot satisfactorily described as shown in the right-hand pane of fig 23 Our current best guess istherefore that the overall rate of strange quarks is consistent at least in the average min-bias collision(dedicated comparisons in high-multiplicity samples would still be interesting) but that the phase-space distribution of strange hadrons needs more work Similarly to the case in ee collisions cf fig 6the model predicts too many very soft kaons though we do not currently know whether there is adynamic link between the ee and pp observations

For strange baryons we note that the increase in the Λ0 fraction in ee collisions (cf fig 5) does

32

0 05 1 15 2

dygt

K lt

dnN

SD

1n

0

02

04

06

08)d|y|gt Rapidity (NSD)

S

0ltdn(K

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn01

00plusmn09

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8 10

Td

pK

dn

NS

D1

N

-510

-410

-310

-210

-110

1

10 (|y|lt20 NSD)

T pS

0K

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn78

01plusmn34

02plusmn22

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6 8 10

The

ory

Dat

a06

08

1

12

14

Figure 23 pp collisions at 7 TeV K0S rapidity and pperp spectrum compared with CMS data [99]

0 05 1 15 2

dygt

Λ lt

dnN

SD

1N

0

01

02

03

04)d|y|gt (NSD)0Λltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn64

00plusmn78

01plusmn147

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8 10

Td

pΛ

dn

Λ1

n

-510

-410

-310

-210

-110

1

10 (|y|lt20 NSD)

T p0Λ

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn59

03plusmn66

05plusmn105

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6 8 10

The

ory

Dat

a

06

08

1

12

14

Figure 24 pp collisions at 7 TeV Λ0 rapidity and pperp spectrum compared with CMS data [99]

not result in an equivalent improvement of the Λ0 rate in pp collisions shown in fig 24 The Monash2013 tune still produces only about 23 of the observed Λ0 rate (and just over half of the observedΞminus rate cf appendix B2) We therefore believe it to be likely that an additional source of net baryonproduction is needed (at least within the limited context of the current PYTHIA modelling) in orderto describe the LHC data The momentum spectrum is likewise quite discrepant exhibiting an excessat very low momenta (stronger than that for kaons) a dip between 1ndash4 GeV and then an excess of veryhard Λ0 production The latter hard tail is somewhat milder in the Monash 2013 tune than previously

33

and it may be consistent with the trend also seen in the Λ0 spectrum at LEP cf fig 6 We concludethat baryon production still requires further modelling and tuning efforts

4 Energy Scaling

Though energy scaling these days mostly refers to the scaling of pp collisions (see eg [97]) animportant first step is to consider the scaling of observables in ee rarr γlowastZ rarr hadrons This scalingcontains information on the relative contributions of perturbative and non-perturbative fragmentationThus at low ee energies the non-perturbative components of the fragmentation model dominatewhile perturbative bremsstrahlung increases in importance towards higher ee energies In fig 25we consider the scaling of the average charged-particle multiplicity and that of charged Kaons andLambda baryons from CM energies of 14 GeV to 200 GeV obtained from measurements availableat HEPDATA Below the Z pole the measurements we include mostly come from TASSO [100]though a few points on 〈nCh〉 come from HRS (at 29 GeV [101]) and TOPAZ (at 578 GeV [102]) Atthe Z pole the data come from the four LEP experiments [38 51ndash53] with the latter extending alsoto energies above MZ [103ndash108] For completeness and as reference for future ee collider studiesmodel extrapolations for CM energies up to 1000 GeV are also shown (though still only including theeerarr γlowastZ rarr hadrons component as usual with photon ISR switched off)

From the plots in fig 25 it is clear that there are no significant differences between the energyscaling of the three ee tunes considered here (mainly reflecting that they have been tuned to samereference point at 912 GeV and that their scaling is dictated by the same underlying physics model)and that their energy dependence closely matches that observed in data However the increasedamount of non-perturbative strangeness production in the Monash tune leads to a better agreementwith the overall normalization of the Kplusmn and Λ rates at all energies

Moving to pp collisions the plots in fig 26 show the scaling of the average charged multiplicity(left column) and multiplicity distributions (right column) in min-bias collisions from 7000 GeV (toprow) to 900 GeV (middle row) and 200 GeV (bottom row) compared with data from CMS [92 109]ATLAS [91] and UA5 [110 111] We regret the omission of additional relevant min-bias measure-ments from the Tevatron and RHIC experiments here but have chosen to focus in this paper mainlyon the LHC The comparisons at 7 TeV were already discussed in the main section on pp collisionssection 3 At 900 GeV the Monash 2013 tune again gives a roughly 5 lower average central chargedmultiplicity than the 4C one with a better description of the tail towards high multiplicities At 200GeV the UA5 measurement we include here extends over the full rapidity and pperp range hence the in-terplay between diffraction and low-multiplicity non-diffractive processes is presumably (much) moreimportant We believe imperfections in this modelling to be the likely cause of the significant discrep-ancies observed at high η and for nCh le 20 at these energies Since a dedicated study of this interplayis beyond the scope of this study we limit ourselves merely to stating this observation as a point forfuture studies to help clarify

Finally in fig 27 we compare to the underlying event measured in the highly useful energyscan that was performed at the Tevatron in the last days before its shutdown [22 23] during whichextremely high min-bias statistics were collected at 300 and 900 GeV CM energy over a period of afew days As was already noted in section 3 the UE at 7 TeV is slightly larger in the Monash 2013tune than in tune 4C As can be seen from the plots here the two tunes give comparable results for allthe Tevatron energies Interestingly the UE plateau region at 900 and 1960 GeV is reached sooner inthese models than in the data translating to a roughly 10 - 20 too low UE level for leading-trackpperp values in the neighbourhood of the transition from the rise to the plateau (roughly for leading-

34

14 22 29 35 44 58 91 91 91 91 133 161 183 189 200 250 350 500 1000

gtC

hlt

n

0

20

40

60

Average Charged Multiplicity vs ECM

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN25

χ00plusmn03 00plusmn02 00plusmn02

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 22 29 35 44 58 91 91 91 91 133 161 183 189 200 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

14 22 35 44 91 91 133 161 183 189 250 350 500 1000

gtK

ltn

0

2

4

6 Multiplicity vs ECM+-Average K

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN25

χ00plusmn06 00plusmn20

00plusmn18

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 22 35 44 91 91 133 161 183 189 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

14 35 91 91 91 91 133 200 250 350 500 1000

gtΛ

ltn

0

02

04

06

08

1

12 Multiplicity vs ECM0ΛAverage

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn06

01plusmn22

01plusmn18

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 35 91 91 91 91 133 200 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

Figure 25 e+eminus rarr hadrons Energy scaling of 〈nCh〉 〈nKplusmn〉 and 〈nΛ〉 in e+eminus rarr qq eventsincluding comparisons to measurements from HEPDATA for CM energies from 14 GeV to 200 GeVAlso shown are model extrapolations up to 1000 GeV

35

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from PhysRevLett 105 (2010) 022002

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn00

00plusmn03

00plusmn71

V I

N C

I A

R O

O T

pp 7000 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

0 50 100

)C

hP

rob(

n

-710

-610

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn27

00plusmn27

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

Chn0 50 100

The

ory

Dat

a

06

08

1

12

14

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from JHEP 1002 (2010) 041

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn03

00plusmn05

00plusmn29

V I

N C

I A

R O

O T

pp 900 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

0 10 20 30 40

)C

hP

rob(

n

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn17

01plusmn25

02plusmn127

V I

N C

I A

R O

O T

pp 900 GeV

Chn0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

0 1 2 3 4 5

gtηd

ch lt

dnN

SD

1n

0

1

2

3

4

5gt (NSD)ηd

chltdn

Pythia 8185Data from ZPhys C33 (1986) 1-6

UA5PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn36

00plusmn24

00plusmn16

V I

N C

I A

R O

O T

ppbar 200 GeV

η0 1 2 3 4 5

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)C

hP

rob(

n

-410

-310

-210

-110

1

)T

|lt05 all pηChg Mult (NSD |

Pythia 8185Data from ZPhys C43 (1989) 357

UA5PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn24

00plusmn24

00plusmn08

V I

N C

I A

R O

O T

ppbar 200 GeV

Chn0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 26 Min-bias pp events from 200 to 7000 GeV Energy scaling of 〈dnChdη〉 (left) andP (nCh) (right)

36

0 10 20 30

)φ∆η

∆gt

(T

psum

lt

0

05

1

15gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn24

26plusmn33

12plusmn143

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 10 20 30

)φ∆η

∆gt

(C

hlt

n

0

05

1

15gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

04plusmn05

13plusmn08

14plusmn100

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn58

06plusmn53

08plusmn193

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn16

15plusmn20

06plusmn114

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

gt05)T

|lt10 pη (|T1

)gt vs pT

TRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn10

02plusmn07

05plusmn22

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

gt05)T

|lt10 pη (|T1

gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn20

02plusmn11

03plusmn08

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 27 The Tevatron energy scan The underlying event (left average summed-pperp density andright average track density in the transverse region as function of leading-track pperp) for pp collisionsat 300 (bottom row) 900 GeV (middle row) and 1960 GeV (top row)

37

track pperp values 2 lt pT1 lt 10 GeV) This indicates that the energy scaling of the UE modeling and inparticular the details of its transition between central and peripheral collisions is still not satisfactorilyunderstood

5 Conclusions and Exhortation

We have presented a reanalysis of the constraints on fragmentation in ee collisions and applied theresults to update the final-state fragmentation parameters in PYTHIA 8 We combine these parameterswith a tune to hadron-collider data using a new NNPDF 23 LO QCD+QED PDF set which has beenencoded so it is available as an internal PDF set in PYTHIA 8 independently of LHAPDF [112]

In this PDF set as well as in our tune the value of the strong coupling for hard-scattering matrixelements is fixed to be αs(MZ) = 013 consistent with other LO determinations of it For initial-and final-state radiation our tune uses the effective value αs(MZ) = 01365 The difference isconsistent with an effective translation between the MS and CMW schemes We note that alternative(LO NLO and NNLO) NNPDF 23 QCD+QED sets with αs(MZ) = 0119 are also available inthe code for people who want to check the impact of using a different αs(MZ) value andor higher-order PDF sets on hard-scattering events For the purpose of such studies we point out that it ispossible in PYTHIA 8 to preserve most of the features of the shower- and underlying-event tuningby changing only the PDF for the hard-scattering matrix elements leaving the PDF choice for theshower evolution and MPI framework unaltered (see the PYTHIA 8 HTML manualrsquos PDF sectionunder PDFuseHard)

The updated parameters are available as an option starting from PYTHIA 8185 by setting

Tuneee = 7 and Tunepp = 14

By no means do we claim that this should be regarded as the final word in tuning the PYTHIA 8Monte Carlo model First of all the model continues to evolve For instance developments foreseenfor the near future include updates of colour reconnections diffraction and the treatment of g rarr qqsplittings Any of these should in principle be accompanied by a reevaluation of the model constraints

Moreover despite the comprehensive view of collider data we have attempted to take in thisstudy there still remains several issues that were not addressed including initial-final interferenceand coherence effects [113 114] (probably more a modelling issue than a tuning one) reliable esti-mates of theoretical uncertainties [8 17 24 29 97 115] diffraction14 [74 116 117] and other colour-singlet phenomena such as onium production long-distance (eg forward-backward forward-centraland ldquoridgerdquo-type) correlations [88 118ndash123] B-hadron decays [124] and tuning in the presence ofmatrix-element matching at LO and NLO (see [21 29 115 125 126] for recent phenomenologi-cal studies) Especially in the latter context of matrix-element matching we expect that in manycases PYTHIA 8 will be used together with codes such as ALPGEN [127] MADGRAPH [128]aMCatNLO [129] or POWHEG [130] either using the matching algorithms of those programs them-selves or via any of PYTHIArsquos several internal (LHEF-based [131]) implementations of matchingschemes (POWHEG [85] CKKW-L [132ndash134] MLM [135 136] UMEPS [137] NL3 [138] UN-LOPS [139]) The impact of such corrections on MC tuning depends on the details of the matchingscheme (especially its treatment of unitarity) and there is in general a non-negligible possibility ofldquomis-tuningrdquo when combining a stand-alone tune with ME corrections A simple example illustrating

14In particular the constraints on fragmentation mainly come from SLD and LEP where the non-perturbative parametersare clearly defined at the shower cutoff scaleQhad whereas diffraction is dominated by soft physics for which the definitionof the effective hadronization scale is less clear The amount of MPI in hard diffractive events also requires tuning

38

this is the effective value of αs(MZ) which for a leading-order tune is typically of order 013 whilea consistent NLO correction scheme should be compatible with values closer to 012 [29] There isalso the question of the running order of αs The propagation of such changes from the level of hardmatrix elements through the shower and hadronization tuning process are still not fully explored andhence we advise users to perform simple cross-checks such as checking the distributions presented inthis paper before and after applying matrix-element corrections Parameters that appear on both sidesof the matching such as αs should also be checked for consistency [21]

We noted several issues concerning the ee data used to constrain the fragmentation modelling thatit would be good to resolve In particular we find some tensions between the identified-particle ratesextracted from 1) HEDPATA 2) Sec 46 of the PDG and 3) the Z boson summary table in the PDGas discussed in more detail in section 2 and concerning which we made some (subjective) decisionsto arrive at a set of hopefully self-consistent constraints for this work We also note that the overallprecision of the fragmentation constraints could likely be significantly improved by an FCC-ee typemachine such as Tera-Z a possibility we hope to see more fully explored in the context of future eeQCD phenomenology studies

We conclude that the new parameter set does improve significantly on the previous default valuesin several respects including better agreement with data on

1 the net strangeness fraction (has been increased by 10 reflected not only in improved kaonand hyperon yields but also in the Ds and Bs fractions)

2 the ultra-hard fragmentation tail (has been softened especially for leading baryons and for Dand B hadrons)

3 the pTZ spectrum (softened at low pTZ)

4 the minimum-bias charged multiplicity in the forward region (has increased by 10)

5 the underlying event at 7 TeV (is very slightly higher than before)

Some questions that remain open include the following We see a roughly 20 excess of verysoft kaons in both ee and pp environments cf figs 6 and 23 despite the overall kaon yields beingwell described and the overall baryon yields at LHC appear to be underestimated by at least 30despite good agreement at LEP The momentum spectra of heavier strange particles are also poorlyreproduced in particular at LHC It is interesting and exciting that some of the LHC spectra appearto be better described by allowing collective flow in a fraction of events (cf the EPOS model [140])though we believe the jury is still out on whether this accurately reflects the underlying physics Forinstance it has been argued that colour reconnections can mimick flow effects [90] and they may alsobe able to modify the yield of baryons if the creationdestruction of string junctions is allowed [141]We look forward to future discussions on these issues

We round off with an exhortation for follow-ups on this study to provide

bull Not only central tunes experiments and other user-end colleagues need more than central de-scriptions of data there is an increasing need for serious uncertainty estimates In the contextof tune variations it is important to keep in mind that the modelling uncertainties are often in-trinsically non-universal Therefore the constraints obtained by considering data uncertaintiesonly (eg in the spirit of PROFESSORrsquos eigentunes [17]) can at most constitute a lower boundon the theoretical uncertainty (similarly to the case for PDFs) A serious uncertainty estimateincludes some systematic modelling variation irrespectively of and in addition to what data

39

allows (eg in the spirit of the Perugia set of tunes for PYTHIA 6 [8]) We therefore hope thefuture will see more elaborate combinations of data- and theory-driven approaches to systematictune uncertainties

bull Not only global tunes the power of MC models lies in their ability to simultaneously describea large variety of data hence we do not mean to imply that one should give up on universalityand tune to increasingly specific corners of phase space disregarding (or de-emphasizing withlower weights) all others However as proposed in [97] one can obtain useful explicit tests ofthe universality of the underlying physics model by performing independent tunes on separateldquophysics windowsrdquo say in the forward vs central regions for different event-selection crite-ria at different collider energies or even for different collider types In this connection justmaking one global ldquobest-fitrdquo tune may obscure tensions between the descriptions of differentcomplementary data sets By performing independent tunes to each data set separately andchecking the degree of universality of the resulting parameters one obtains a powerful crosscheck on the underlying physics model If all sets produce the same or similar parameters thenuniversality is OK hence a global tune makes very good sense and the remaining uncertain-ties can presumably be reliably estimated from data alone If instead some data sets resultin significantly different tune parameters one has a powerful indication that the universality ofthe underlying modeling is breaking down which can lead to several productive actions 1) itcan be taken into account in the context of uncertainty variations 2) the nature of the data setsfor which non-universal tune parameters are obtained can implicitly indicate the nature of theproblem leading to more robust conclusions about the underlying model than merely whether atune cancannot fit the data and 3) the observations can be communicated to the model authorsin a more unambiguous way hopefully resulting in a speedier cycle of model improvements

We hope that the Monash 2013 tune parameters may serve as a useful starting point for phe-nomenology studies and for future PYTHIA 8 tuning efforts

Acknowledgments

We thank S Mrenna M Ritzmann and T Sjostrand for comments on the manuscript and L de Nooijfor pointing us to the ALICE Klowast and φ measurements [142] and to the ATLAS φ measurementsin [143] The work of J R is supported by an STFC Rutherford Fellowship STK0052271 Thiswork was supported in part by the Research Executive Agency (REA) of the European Commissionunder the Grant Agreements PITN-GA-2012-315877 (MCnet)

A Monash 2013 Tune Parameters

In tabs 3 ndash 7 we list the FSR fragmentation parameters for the Monash tune of PYTHIA Forreference we compare them to the current default parameters

40

FSR Parameters Monash 13 (Default) CommentTimeShoweralphaSvalue = 01365 = 01383 Effective alphaS(mZ) valueTimeShoweralphaSorder = 1 = 1 Running orderTimeShoweralphaSuseCMW = off = off Translation from MS to CMWTimeShowerpTmin = 050 = 040 Cutoff for QCD radiationTimeShowerpTminChgQ = 050 = 040 Cutoff for QED radiationTimeShowerphiPolAsym = on = on Asymmetric azimuth distributions

Table 3 Final-state radiation (FSR) parameters

HAD Parameters Monash 13 (Default) Comment String breaks pT and z distributionsStringPTsigma = 0335 = 0304 Soft pT in string breaks (in GeV)StringPTenhancedFraction = 001 = 001 Fraction of breakups with enhanced pTStringPTenhancedWidth = 20 = 20 Enhancement factorStringZaLund = 068 = 03 Lund FF a (hard fragmentation supp)StringZbLund = 098 = 08 Lund FF b (soft fragmentation supp)StringZaExtraSquark = 00 = 00 Extra a when picking up an s quarkStringZaExtraDiquark = 097 = 050 Extra a when picking up a diquarkStringZrFactC = 132 = 100 Lund-Bowler c-quark parameterStringZrFactB = 0855 = 067 Lund-Bowler b-quark parameter Flavour composition mesonsStringFlavProbStoUD = 0217 = 019 Strangeness-to-UD ratioStringFlavmesonUDvector = 05 = 062 Light-flavour vector suppressionStringFlavmesonSvector = 055 = 0725 Strange vector suppressionStringFlavmesonCvector = 088 = 106 Charm vector suppressionStringFlavmesonBvector = 22 = 30 Bottom vector suppressionStringFlavetaSup = 060 = 063 Suppression of eta mesonsStringFlavetaPrimeSup = 012 = 012 Suppression of etarsquo mesons Flavour composition baryonsStringFlavprobQQtoQ = 0081 = 009 Diquark rate (for baryon production)StringFlavprobSQtoQQ = 0915 = 1000 Strange-diquark suppressionStringFlavprobQQ1toQQ0 = 00275 = 0027 Vector diquark suppressionStringFlavdecupletSup = 10 = 10 Spin-32 baryon suppressionStringFlavsuppressLeadingB = off = off Optional leading-baryon suppressionStringFlavpopcornSpair = 09 = 05 StringFlavpopcornSmeson = 05 = 05

Table 4 String-breaking parameters

PDF and ME Parameters Monash 13 (Default) CommentPDFpSet = 13 = 8 PDF set for the protonSigmaProcessalphaSvalue = 0130 0135 alphaS(MZ) for matrix elementsMultiPartonInteractionsalphaSvalue = 0130 0135 alphaS(MZ) for MPI

Table 5 Parton-distribution (PDF) and Matrix-Element (ME) parameters

41

ISR Parameters Monash 13 (Default) CommentSpaceShoweralphaSvalue = 01365 = 0137 Effective alphaS(mZ) valueSpaceShoweralphaSorder = 1 = 1 Running orderSpaceShoweralphaSuseCMW = off = off Translation from MS to CMWSpaceShowersamePTasMPI = off = off ISR cutoff typeSpaceShowerpT0Ref = 20 = 20 ISR pT0 cutoffSpaceShowerecmRef = 70000 = 18000 ISR pT0 reference ECM scaleSpaceShowerecmPow = 00 = 00 ISR pT0 scaling powerSpaceShowerrapidityOrder = on = on Approx coherence via y-orderingSpaceShowerphiPolAsym = on = on Azimuth asymmetries from gluon polSpaceShowerphiIntAsym = on = on Azimuth asymmetries from interferenceTimeShowerdampenBeamRecoil = on = on Recoil dampening in final-initial dipolesBeamRemnantsprimordialKTsoft = 09 = 05 Primordial kT for soft procsBeamRemnantsprimordialKThard = 18 = 20 Primordial kT for hard procsBeamRemnantshalfScaleForKT = 15 = 10 Primordial kT softhard boundaryBeamRemnantshalfMassForKT = 10 = 10 Primordial kT softhard mass boundary

Table 6 Initial-state radiation (ISR) and primordial-kT parameters

MPI Parameters Monash 13 (Default) CommentMultipartonInteractionspT0Ref = 228 = 2085 MPI pT0 IR regularization scaleMultipartonInteractionsecmRef = 70000 = 18000 MPI pT0 reference ECM scaleMultipartonInteractionsecmPow = 0215 = 019 MPI pT0 scaling powerMultipartonInteractionsbProfile = 3 = 3 Transverse matter overlap profileMultipartonInteractionsexpPow = 185 = 20 Shape parameterBeamRemnantsreconnectRange = 18 = 15 Colour ReconnectionsSigmaTotalzeroAXB = on = on Carried over from 4CSigmaDiffractivedampen = on = on Carried over from 4CSigmaDiffractivemaxXB = 650 = 650 Carried over from 4CSigmaDiffractivemaxAX = 650 = 650 Carried over from 4CSigmaDiffractivemaxXX = 650 = 650 Carried over from 4CDiffractionlargeMassSuppress = 40 = 20 High-mass diffraction suppression power

Table 7 Multi-Parton-Interaction (MPI) Colour-Reconnection (CR) and Diffractive parameters

42

B Additional Plots

B1 LEP Event-Shape Distributions

To keep the main body of the paper as uncluttered as possible we collect various plots of event-shapedistributions in figs 28 and 29 separated into light-flavour and b-tagged events on the left and rightrespectively

The experimental results come from the L3 experiment [26] However since the data points areonly available with 3-digit precision some of the least populated bins contain artifacts like uncertain-ties being reported as exactly zero etc Thus we have been forced to make the following modificationsto the data set

The statistical uncertainty was reported as zero for the last two bins of light-flavour Thrust as wellas for the last bin of the C D and BT parameters Uncertainties lt 10minus3 were derived using anapproximate statistical scaling based on the contents and uncertainties of the other bins Likewise thesystematical uncertainty for the last bin of Thrust was given as zero which we have replaced by theupper limit 5times 10minus4 The last bin of BT quoted a measured y value of zero removed in this study

For the heavy-flavour tagged event shapes more significant rounding issues were present Thusseveral of the first and last bins of each distribution either quoted zero (statistical andor systematic)uncertainties or ones with only a single digit of precision (such as 0001 for which the rounding errorcould be up to sim 50) We have interpreted all such values conservatively inserting by hand a fourthdigit on the uncertainties as large as could be consistent with rounding

B2 Additional Particle Spectra

In addition to the K and Λ spectra shown in the main body of the paper (sections 22 and 35) wehere include for reference the x spectra of φ mesons protons and Ξ baryons at LEP in figs 30 and 31the pT spectrum of Klowast mesons and the rapidity and pT spectra of φ mesons at LHC in fig 32 (withabsolute normalizations to the number of inelastic events) and the rapidity spectrum of Ξ baryons atLHC in fig 33

The transverse-momentum spectra of Klowast and φ mesons in fig 32 exhibit the same qualitativebehaviour as that of the KS mesons (fig 23) namely an excess at very soft momenta below sim 500MeV and a depletion at slightly higher momenta between 1 and 2 GeV As discussed in section 35we did not find a way to remove these undesirable features in the Monash 2013 tune suggesting thatthis is an issue that further theoretical modeling will be needed to resolve

The rapidity spectrum of Ξ baryons fig 33 shows that although the Monash tune does producemore Ξ baryons overall (as expected also from the relative increase of Ξ production at LEP cf fig 5)there is still a significant deficit of Ξ baryons at the LHC almost a factor 2 compared with the dataThis is qualitatively similar to the situation for Λ baryons (fig 24) discussed in section 35 Sincenew physics mechanisms may be required to ldquoexplainrdquo the missing baryons we conclude that furthermeasurements and better precision on both the Λ and Ξ sectors (in addition to any other baryonsthat may be accessible) would be highly interesting More explicit recommendations can be found insections 35 and 5

43

0 01 02 03 04

d(1

-T)

σ d

σ1

-310

-210

-110

1

10

2101-Thrust (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn03

01plusmn04

02plusmn05

V I

N C

I A

R O

O T

1-T (udsc)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

d(1

-T)

σ dσ

1

-310

-210

-110

1

10

2101-T (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn13

02plusmn12

02plusmn14

V I

N C

I A

R O

O T

1-T (b)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210

310C Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn03

00plusmn04

01plusmn04

V I

N C

I A

R O

O T

C0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210 C parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn17

01plusmn24

01plusmn27

V I

N C

I A

R O

O T

C (b)0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn06

01plusmn06

V I

N C

I A

R O

O T

D0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn24

02plusmn21

02plusmn26

V I

N C

I A

R O

O T

D (b)0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

Figure 28 Hadronic Z decays atradics = 912 GeV The T C and D event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

44

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn02

01plusmn03

01plusmn04

V I

N C

I A

R O

O T

WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn05

01plusmn12

01plusmn17

V I

N C

I A

R O

O T

(b)WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn02

00plusmn02

01plusmn03

V I

N C

I A

R O

O T

TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

04plusmn24

08plusmn49

08plusmn55

V I

N C

I A

R O

O T

(b)TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

Figure 29 Hadronic Z decays atradics = 912 GeV The BW and BT event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

45

0 02 04 06 08 1

dx

φgt

dn

φ1

ltn

-210

-110

1

10 )φx(

Pythia 8183Data from ALEPH_1996_S3486095d40-x01-y01

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn37

02plusmn53

03plusmn62

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

0608

112141618

Figure 30 Hadronic Z decays atradics = 912 GeV φ meson x spectrum

-5 -4 -3 -2 -1 0

dx

pgt

dn

p1

ltn

-410

-310

-210

-110

1

10

210) (Combined)px(p+

Pythia 8183Data from Zeit Phys C66 (1995) 355 PhysRev D59 (1998) 052001

ALEPH+SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn08

00plusmn09

00plusmn08

V I

N C

I A

R O

O T

px-5 -4 -3 -2 -1 0

The

ory

Dat

a

06

08

1

12

14

0 02 04

dx

Ξgt

dn

Ξ1

ltn

-110

1

10

)plusmnΞx(

Pythia 8183Data from Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn11

02plusmn13

02plusmn14

V I

N C

I A

R O

O T

Ex0 02 04

The

ory

Dat

a

06

08

1

12

14

Figure 31 Hadronic Z decays atradics = 912 GeV pplusmn and Ξplusmn x spectra

46

0 2 4 6

Td

pK

d

nIN

EL

1N

-510

-410

-310

-210

-110

(INEL |y|lt05)T

p0K

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn35

01plusmn26

01plusmn29

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 2 4 6

Td

pφ

dn

INE

L1

N-510

-410

-310

-210

-110

gt04)T

(INEL |y|lt05 pT

pφ

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn88

03plusmn84

04plusmn173

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

)dy

[mb]

-K

+K

rarrφ(σd

0

05

1

15

2 Rapidity (INEL ATLAS cuts)φ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn14

01plusmn19

01plusmn34

V I

N C

I A

R O

O T

pp 7000 GeV

|y|0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

06 08 1 12

[mb

GeV

]φ

T)

dp-

K+

Krarrφ(

σd

0

05

1

15

2

25 (INEL ATLAS cuts)

T pφ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn21

01plusmn30

02plusmn53

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p06 08 1 12

The

ory

Dat

a

06

08

1

12

14

Figure 32 pp collisions at 7 TeV Top row Klowast and φ pperp spectra compared with ALICE data [142]Bottom row φ rapidity and pperp spectrum compared with ATLAS data [143] The ATLAS cuts areφrarr K+Kminus pperpφ isin [05 12] GeV |y(φ)| lt 08 pperpK gt 023 GeV |pK | lt 08 GeV

47

0 05 1 15 2

dygt

Ξ lt

dnN

SD

1N

0

001

002

003

004)d|y|gt (NSD)Ξltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn89

01plusmn129

01plusmn192

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

0

05

1

15

2

Figure 33 pp collisions at 7 TeV Ξminus rapidity spectrum compared with CMS data [99]

48

B3 Energy Scaling of σ2rarr2(pTmin) vs σinel from 200 GeV to 100 TeV

In fig 34 we show the LO QCD 2rarr 2 cross section integrated above pTmin as a function of pTminin pp collisions at 4 different CM energies complementing and expanding on the 8-TeV CM energyshown in the main body of the paper We compare two different αs and PDF choices correspondingto those made in tunes Monash 13 (blue filled dots) and 4C (red open squares) respectively As areference for the total inelastic cross section at each energy we base ourselves on the best-fit curvein the TOTEM cross-section measurement paper [72] which in turn represents a fit produced by theCOMPETE collaboration [144] Uncertainties are rough conservative estimates based on the plot inthe TOTEM paper but they are in any case too small to significantly affect conclusions about the scaleat which the partonic cross section saturates the hadronic one

We observe that the pTmin value for which the LO QCD 2 rarr 2 partonic cross section formallybecomes equal to the total inelastic cross section (strongly suggesting that every event has at leastone such mini-jet pair) rises from values around 1 ndash 2 GeV at energies

radics lt 1 TeV to 5 GeV atradic

s = 13 TeV and finally 10 GeV atradics = 100 TeV

49

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

PDFs themselves Indeed the NNPDF23 gluon is harder than the CTEQ6L one for x gt 02 and forx lt 10minus5

The relative dominance of the gluon PDF is illustrated by the bottom right-hand pane of fig 17showing the gluon fraction (relative to all MPI initiators) as a function of log10(x) Below x sim 01the NNPPDF sampling is 80 gluon-dominated and the gluon fraction is higher than in CTEQ6L1for both very small x lt 10minus5 as well as for very large x gt 02

A further consistency check is provided by the uu ratio shown in the bottom left-hand pane offig 17 This is consistent with unity (as expected for sea quarks) in the entire small-x region x lt 10minus2The valence bump appears to be slightly more pronounced in the NNPDF tune (relative to the sea)since the uu ratio drops off more quickly above 10minus2 This trend persists until the very highest binat x sim 1 where the experimental uncertainties are extremely large The CTEQ6L1 parametrizationthere forces the u PDF to zero while the NNPDF parametrization allows for a small amount of u toremain even at the largest x values though we note that they are still outnumbered by u quarks at alevel of hundred-to-one

The last pane of fig 17 shows the amount of x remaining in the beam remnant after all MPI(including both the hardest interaction and additional MPI) have been considered ie

Xrem = 1minussumiisinMPI

xi (10)

Note the linear scale in x on this plot and the highly logaritmic axis In the vast majority of casesthe beam remnant thus still retains over 90 of the initial hadron energy But there is a class ofevents at the level of 10minus4 or 10minus5 of the total cross section (depending on the tune) in whichthe beam remnant retains less than 10 of the incoming hadron energy Experiments studying theamount and distribution of forward scattered energy in particular may be able to tell us about whetherthis class of events which we term ldquoCatastrophic Energy Lossrdquo events really exists and at whatlevel Note that these events are typically not caused by a single hard partonic scattering processdue to the high penalty associated with accessing PDFs in the region x gt 05 Rather they arean intrinsic consequence of MPI A straightforward extrapolation requiring a catastrophic energyloss on both sides of the event mdash more than 90 of the energy scattered out of both beams whichwe term ldquoTotal Inelastic Scatteringrdquo mdash may occur at a level of 10minus10 minus 10minus8 of the cross sectionor between 10 - 1000 pb (though we of course only have PYTHIArsquos word for it) This would bean extremely interesting part of hadron-hadron collision physics to study very far from the single-interaction dominated limit and hence potentially very sensitive to the existence of possible collectiveeffects Designing efficient triggers for this class of events would be a great accomplishment

Turning now to physics distributions in min-bias events the broader MPI distribution in theMonash tune translates to a broader charged-multiplicity spectrum though the effect is modulatedby the colour-reconnection model The resulting multiplicity and pperp spectra are shown in fig 18for ldquostandardrdquo fiducial cuts (top row pperp ge 500 MeV |η| lt 25 nCh ge 1) and ldquosoftrdquo fiducial cuts(bottom row pperp ge 100 MeV |η| lt 25 nCh ge 2) with the latter representing the most inclusivephase-space region accessible with the ATLAS detector For both of the nCh distributions we notethat a significant ldquodouble-crested waverdquo pattern is still present in the ratio panes though it has beendampened slightly The pperp spectra in the right-hand panes are a bit below the data for the standardfiducial cuts and above it for the soft cuts hence we regard the Monash tune as a reasonable compro-mise

Pseudorapidity distributions are shown in fig 19 However due to the complicated interplaybetween diffractive contributions at low multiplicity and high-multiplicity multi-parton interactions(with associated questions of transverse matter density profile and colour reconnections) the average

27

0 50 100

)C

hP

rob(

n

-710

-610

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn27

00plusmn27

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

Chn0 50 100

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20

Td

pC

h d

nT

)p

π(

2C

h1

n

-810

-710

-610

-510

-410

-310

-210

-110

1

10|lt25)ηgt05 |

T 1 pge

Ch (n

Tp

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLAS PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn15

00plusmn08

01plusmn58

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 5 10 15 20

The

ory

Dat

a

06

08

1

12

14

0 50 100 150 200

)C

hP

rob(

n

-610

-510

-410

-310

-210

-110

1|lt25)ηgt01 |

T 2 pge

ChSoft Chg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn45

00plusmn49

01plusmn197

V I

N C

I A

R O

O T

pp 7000 GeV

Chn0 50 100 150 200

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20

Td

pC

h d

nT

)p

π(

2C

h1

n

-910

-710

-510

-310

-110

10|lt25)ηgt01 |

T 2 pge

Ch (n

Tp

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn43

01plusmn73

02plusmn155

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 5 10 15 20

The

ory

Dat

a

06

08

1

12

14

Figure 18 Min-bias pp collisions at 7 TeV Charged-multiplicity and pperp distributions with standard(top row) and soft (bottom row) fiducial cuts compared to ATLAS data [91]

28

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from PhysRevLett 105 (2010) 022002

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn00

00plusmn03

00plusmn71

V I

N C

I A

R O

O T

pp 7000 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

55 6 65

gtηd

Ch

ltdn

Tot

em1

n

0

1

2

3

4

5

6|lt65)ηgt004 53lt|

T1 pge

chgt (nηd

Chltdn

Pythia 8185Data from EurophysLett 98 (2012) 31002

TOTEMPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn01

00plusmn27

00plusmn62

V I

N C

I A

R O

O T

pp 7000 GeV

η55 6 65

The

ory

Dat

a

06

08

1

12

14

3 35 4 45 5

gtηlt

dEd

0

100

200

300

400

500|lt465)η1 in both 323lt|ge

chMB Fwd E Flow (n

Pythia 8185Data from JHEP 11 (2011) 148

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn01

00plusmn04

00plusmn22

V I

N C

I A

R O

O T

pp 7000 GeV

η3 35 4 45 5

The

ory

Dat

a

06

08

1

12

14

Figure 19 Charged-particle pseudorapidity distributions and forward energy flow in min-bias ppcollisions at 7 TeV compared to CMS [92 93] and TOTEM [94] data

29

0 50 100

0

05

1

15

2

25|lt25)ηgt05 |

T) (p

Chgt(n

Tltp

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn05

01plusmn01

05plusmn07

V I

N C

I A

R O

O T

pp 7000 GeV

0 50 100

The

ory

Dat

a

06

08

1

12

14

0 50 100 150 200

0

05

1

15|lt25)ηgt01 |

T 2 pge

Ch) (n

Chgt(n

TSoft ltp

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn06

00plusmn08

03plusmn40

V I

N C

I A

R O

O T

pp 7000 GeV

0 50 100 150 200

The

ory

Dat

a06

08

1

12

14

Figure 20 Average-pperp vs charged-multiplicity distributions in min-bias pp collisions at 7 TeV withstandard (left) and soft (right) fiducial cuts compared to ATLAS data [91]

multiplicity by itself is a very difficult quantity to extract reliable conclusions from Note also that theCMS measurement [92] shown in the top pane of fig 19 was corrected to an unphysical ldquonon-singlediffractiverdquo event definition which essentially amounts to switching off single-diffractive contributionsin the MC generator (We note that later CMS measurements instead use a physical observable relatedto the diffractive mass to define NSD) For the comparisons to CMS NSD data shown here the single-diffractive contributions were switched off in the generator With these caveats in mind we note thatboth the 4C and Monash 2013 tunes are in good agreement with the CMS measurement with theMonash one giving a slightly lower central charged-track density (by about 5) This is closer to thevalues observed in data though as already noted in section 11 we do not regard differences at the 5level as significant

In the bottom two panes of fig 19 we focus on the forward region (with physical event selections)In particular we see that the NNPDF set [20] generates a broader rapidity spectrum so that while theactivity in the central region (top pane) is reduced slightly the activity in the very forward regionactually increases and comes into agreement with the TOTEM measurement [94] covering the range53 lt |η| lt 64 The bottom right-hand pane shows the forward energy flow measured by CMS [93]in the intermediate region 323 lt |η| lt 465 The dependence on η is a bit steeper in the Monashtune than in the previous one and more similar to that seen in the data

A complementary observable which is highly sensitive to interconnection effects between theMPI (and hence eg to the effects of ldquocolour reconnectionsrdquo [95]) is the average charged-particlepperp as a function of the number of charged particles In a strict leading-colour picture each MPIwould cause one or two new strings to be stretched between the remnants but each such string wouldbe independent (modulo endpoint effects) therefore (modulo jets) the pperp spectrum of the hadronsproduced by each of these strings would be independent of the number of strings The result would bea flat 〈pperp〉 (nCh) spectrum Jets and colour reconnections both produce a rising spectrum The spectraobserved by ATLAS [91] are compared to the Monash 2C and 4C tunes in fig 20 for standard

30

0 1 2 3

gtφ|dη

d|

Ch

n2

ltd

0

02

04

06

08

1gt01)

T|lt25 pηgt1 (|

Tlead| wrt pφ∆|

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn16

00plusmn19

00plusmn56

V I

N C

I A

R O

O T

pp 7000 GeV

| [rad]φ∆|0 1 2 3

The

ory

Dat

a

06

08

1

12

14

0 1 2 3

gtφ|dη

d|

Ch

n2

ltd

0

05

1

15

2

gt05)T

|lt25 pηgt5 (|Tlead

| wrt pφ∆|

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn05

00plusmn05

00plusmn70

V I

N C

I A

R O

O T

pp 7000 GeV

| [rad]φ∆|0 1 2 3

The

ory

Dat

a06

08

1

12

14

Figure 21 pp collisions at 7 TeV ∆φ of charged particles with respect to the hardest track for twodifferent hardest-track triggers compared with ATLAS data [98]

(left) and soft (right) fiducial cuts Both of the Monash and 4C tunes reproduce the data quite wellwith χ2

5 lt 1 while the older tune 2C had a higher CR strength optimized to describe Tevatrondata [96] We certainly consider the energy scaling of the effective CR strength among the mostuncertain parameters of the current min-biasunderlying-event modelling (a similar conclusion wasreached for the CR modelling in PYTHIA 6 in [97]) and intend to study the physics aspects of thisissue more closely in a forthcoming paper

For a more differential look at the event structure we consider the charged-track ∆φ distributionswith respect to the azimuthal angle of the leading track in fig 21 compared with ATLAS data [98]The plot in the left-hand pane corresponds to a requirement of pperplead ge 1 GeV while the one in theright-hand pane is for a harder trigger pperplead ge 5 GeV The former can roughly be taken as charac-teristic of min-bias events while the latter is related to the differential distribution of the underlyingevent In both cases the activity in the wide-angle region near π2 is significantly better described bythe 4C and Monash 2013 tunes (which agrees with their improved description of the overall activity)while there is a too strong peaking at low ∆φ especially for the lowest pperplead cut (left) possibly indi-cating that the structure of the min-bias events is still slightly too ldquolumpyrdquo (ie jetty) For the higherpperplead cut (right) the overcounting at very low ∆φ is already significantly milder and we observe agood agreement with the data

Turning now to the underlying event (UE) what matters most for high-pperp jet studies is that theMC models describe the UE contamination per ∆R jet area The most important UE observable fromthis perspective is thus the pperp sum density in the UE and its fluctuations For charged particles atLHC typically a pperp cut of 500 MeV is relevant since softer tracks will form helices and hence notcontribute to calorimetric jet energies Neutral particles are of course relevant across all pperp scalesIn fig 22 we show the charged pperp sum density (left with the lowest possible pperp cut of 100 MeV)and the charged-track density (right with a pperp cut of 500 MeV) in the so-called ldquoTransverse Regionrdquo(defined by 60 lt ∆φ lt 120 with respect to the leading track) inside the ATLAS acceptance of

31

0 5 10 15 20

)φ∆η

∆gt

(T

psum

lt

0

05

1

15

2

25gt01)

T|lt25 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn03

01plusmn09

02plusmn112

V I

N C

I A

R O

O T

pp 7000 GeV

(hardest track) [GeV]T1

p0 5 10 15 20

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20

)φ∆η

∆gt

(C

hlt

n

0

05

1

15

2

25gt05)

T|lt25 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn02

00plusmn04

02plusmn104

V I

N C

I A

R O

O T

pp 7000 GeV

(hardest track) [GeV]T1

p0 5 10 15 20

The

ory

Dat

a06

08

1

12

14

Figure 22 pp collisions at 7 TeV UE (ldquoTransverse regionrdquo) transverse-momentum sum density (left)and charged-track density (right) compared with ATLAS data [98]

|η| lt 25 [98] As is now well known the Tevatron extrapolations (represented here by Tune 2C)predicted a UE level which was 10 ndash 20 below the LHC data Both the current default tune 4C(which included LHC data) and the Monash 2013 tune exhibit significantly better agreement with theLHC measurements with the Monash one giving a slight additional improvement in the χ2

5 valuesWe conclude that the Monash 2013 tune parameters are appropriate for both min-bias and UE studies

35 Identified Particles at LHC

While the description of inclusive charged particles discussed in the previous section is acceptablelarger discrepancies emerge when we consider the spectra of identified particles We here focus onstrange particles in particular K0

S mesons and Λ0 hyperons in figs 23 and 24 respectively Theexperimental measurements come from CMS [99] Additional comparisons to strange-particle spectra(Klowast φ and Ξ) are collected in appendix B2

In the K0S rapidity distribution shown in the left-hand pane of fig 23 we observe that tune 4C

exhibits a mild underproduction of about 10 Though it might be tempting to speculate whether thiscould indicate some small reduction of strangeness suppression in pp collisions however we alreadynoted in section 21 that the strangeness production in ee collisions also needed to be increased byabout 10 After this adjustment we see that the overall K0

S yield in the Monash 2013 tune is fullyconsistent with the CMS measurement Nonetheless we note that the momentum distribution is stillnot satisfactorily described as shown in the right-hand pane of fig 23 Our current best guess istherefore that the overall rate of strange quarks is consistent at least in the average min-bias collision(dedicated comparisons in high-multiplicity samples would still be interesting) but that the phase-space distribution of strange hadrons needs more work Similarly to the case in ee collisions cf fig 6the model predicts too many very soft kaons though we do not currently know whether there is adynamic link between the ee and pp observations

For strange baryons we note that the increase in the Λ0 fraction in ee collisions (cf fig 5) does

32

0 05 1 15 2

dygt

K lt

dnN

SD

1n

0

02

04

06

08)d|y|gt Rapidity (NSD)

S

0ltdn(K

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn01

00plusmn09

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8 10

Td

pK

dn

NS

D1

N

-510

-410

-310

-210

-110

1

10 (|y|lt20 NSD)

T pS

0K

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn78

01plusmn34

02plusmn22

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6 8 10

The

ory

Dat

a06

08

1

12

14

Figure 23 pp collisions at 7 TeV K0S rapidity and pperp spectrum compared with CMS data [99]

0 05 1 15 2

dygt

Λ lt

dnN

SD

1N

0

01

02

03

04)d|y|gt (NSD)0Λltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn64

00plusmn78

01plusmn147

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8 10

Td

pΛ

dn

Λ1

n

-510

-410

-310

-210

-110

1

10 (|y|lt20 NSD)

T p0Λ

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn59

03plusmn66

05plusmn105

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6 8 10

The

ory

Dat

a

06

08

1

12

14

Figure 24 pp collisions at 7 TeV Λ0 rapidity and pperp spectrum compared with CMS data [99]

not result in an equivalent improvement of the Λ0 rate in pp collisions shown in fig 24 The Monash2013 tune still produces only about 23 of the observed Λ0 rate (and just over half of the observedΞminus rate cf appendix B2) We therefore believe it to be likely that an additional source of net baryonproduction is needed (at least within the limited context of the current PYTHIA modelling) in orderto describe the LHC data The momentum spectrum is likewise quite discrepant exhibiting an excessat very low momenta (stronger than that for kaons) a dip between 1ndash4 GeV and then an excess of veryhard Λ0 production The latter hard tail is somewhat milder in the Monash 2013 tune than previously

33

and it may be consistent with the trend also seen in the Λ0 spectrum at LEP cf fig 6 We concludethat baryon production still requires further modelling and tuning efforts

4 Energy Scaling

Though energy scaling these days mostly refers to the scaling of pp collisions (see eg [97]) animportant first step is to consider the scaling of observables in ee rarr γlowastZ rarr hadrons This scalingcontains information on the relative contributions of perturbative and non-perturbative fragmentationThus at low ee energies the non-perturbative components of the fragmentation model dominatewhile perturbative bremsstrahlung increases in importance towards higher ee energies In fig 25we consider the scaling of the average charged-particle multiplicity and that of charged Kaons andLambda baryons from CM energies of 14 GeV to 200 GeV obtained from measurements availableat HEPDATA Below the Z pole the measurements we include mostly come from TASSO [100]though a few points on 〈nCh〉 come from HRS (at 29 GeV [101]) and TOPAZ (at 578 GeV [102]) Atthe Z pole the data come from the four LEP experiments [38 51ndash53] with the latter extending alsoto energies above MZ [103ndash108] For completeness and as reference for future ee collider studiesmodel extrapolations for CM energies up to 1000 GeV are also shown (though still only including theeerarr γlowastZ rarr hadrons component as usual with photon ISR switched off)

From the plots in fig 25 it is clear that there are no significant differences between the energyscaling of the three ee tunes considered here (mainly reflecting that they have been tuned to samereference point at 912 GeV and that their scaling is dictated by the same underlying physics model)and that their energy dependence closely matches that observed in data However the increasedamount of non-perturbative strangeness production in the Monash tune leads to a better agreementwith the overall normalization of the Kplusmn and Λ rates at all energies

Moving to pp collisions the plots in fig 26 show the scaling of the average charged multiplicity(left column) and multiplicity distributions (right column) in min-bias collisions from 7000 GeV (toprow) to 900 GeV (middle row) and 200 GeV (bottom row) compared with data from CMS [92 109]ATLAS [91] and UA5 [110 111] We regret the omission of additional relevant min-bias measure-ments from the Tevatron and RHIC experiments here but have chosen to focus in this paper mainlyon the LHC The comparisons at 7 TeV were already discussed in the main section on pp collisionssection 3 At 900 GeV the Monash 2013 tune again gives a roughly 5 lower average central chargedmultiplicity than the 4C one with a better description of the tail towards high multiplicities At 200GeV the UA5 measurement we include here extends over the full rapidity and pperp range hence the in-terplay between diffraction and low-multiplicity non-diffractive processes is presumably (much) moreimportant We believe imperfections in this modelling to be the likely cause of the significant discrep-ancies observed at high η and for nCh le 20 at these energies Since a dedicated study of this interplayis beyond the scope of this study we limit ourselves merely to stating this observation as a point forfuture studies to help clarify

Finally in fig 27 we compare to the underlying event measured in the highly useful energyscan that was performed at the Tevatron in the last days before its shutdown [22 23] during whichextremely high min-bias statistics were collected at 300 and 900 GeV CM energy over a period of afew days As was already noted in section 3 the UE at 7 TeV is slightly larger in the Monash 2013tune than in tune 4C As can be seen from the plots here the two tunes give comparable results for allthe Tevatron energies Interestingly the UE plateau region at 900 and 1960 GeV is reached sooner inthese models than in the data translating to a roughly 10 - 20 too low UE level for leading-trackpperp values in the neighbourhood of the transition from the rise to the plateau (roughly for leading-

34

14 22 29 35 44 58 91 91 91 91 133 161 183 189 200 250 350 500 1000

gtC

hlt

n

0

20

40

60

Average Charged Multiplicity vs ECM

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN25

χ00plusmn03 00plusmn02 00plusmn02

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 22 29 35 44 58 91 91 91 91 133 161 183 189 200 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

14 22 35 44 91 91 133 161 183 189 250 350 500 1000

gtK

ltn

0

2

4

6 Multiplicity vs ECM+-Average K

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN25

χ00plusmn06 00plusmn20

00plusmn18

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 22 35 44 91 91 133 161 183 189 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

14 35 91 91 91 91 133 200 250 350 500 1000

gtΛ

ltn

0

02

04

06

08

1

12 Multiplicity vs ECM0ΛAverage

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn06

01plusmn22

01plusmn18

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 35 91 91 91 91 133 200 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

Figure 25 e+eminus rarr hadrons Energy scaling of 〈nCh〉 〈nKplusmn〉 and 〈nΛ〉 in e+eminus rarr qq eventsincluding comparisons to measurements from HEPDATA for CM energies from 14 GeV to 200 GeVAlso shown are model extrapolations up to 1000 GeV

35

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from PhysRevLett 105 (2010) 022002

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn00

00plusmn03

00plusmn71

V I

N C

I A

R O

O T

pp 7000 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

0 50 100

)C

hP

rob(

n

-710

-610

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn27

00plusmn27

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

Chn0 50 100

The

ory

Dat

a

06

08

1

12

14

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from JHEP 1002 (2010) 041

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn03

00plusmn05

00plusmn29

V I

N C

I A

R O

O T

pp 900 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

0 10 20 30 40

)C

hP

rob(

n

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn17

01plusmn25

02plusmn127

V I

N C

I A

R O

O T

pp 900 GeV

Chn0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

0 1 2 3 4 5

gtηd

ch lt

dnN

SD

1n

0

1

2

3

4

5gt (NSD)ηd

chltdn

Pythia 8185Data from ZPhys C33 (1986) 1-6

UA5PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn36

00plusmn24

00plusmn16

V I

N C

I A

R O

O T

ppbar 200 GeV

η0 1 2 3 4 5

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)C

hP

rob(

n

-410

-310

-210

-110

1

)T

|lt05 all pηChg Mult (NSD |

Pythia 8185Data from ZPhys C43 (1989) 357

UA5PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn24

00plusmn24

00plusmn08

V I

N C

I A

R O

O T

ppbar 200 GeV

Chn0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 26 Min-bias pp events from 200 to 7000 GeV Energy scaling of 〈dnChdη〉 (left) andP (nCh) (right)

36

0 10 20 30

)φ∆η

∆gt

(T

psum

lt

0

05

1

15gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn24

26plusmn33

12plusmn143

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 10 20 30

)φ∆η

∆gt

(C

hlt

n

0

05

1

15gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

04plusmn05

13plusmn08

14plusmn100

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn58

06plusmn53

08plusmn193

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn16

15plusmn20

06plusmn114

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

gt05)T

|lt10 pη (|T1

)gt vs pT

TRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn10

02plusmn07

05plusmn22

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

gt05)T

|lt10 pη (|T1

gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn20

02plusmn11

03plusmn08

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 27 The Tevatron energy scan The underlying event (left average summed-pperp density andright average track density in the transverse region as function of leading-track pperp) for pp collisionsat 300 (bottom row) 900 GeV (middle row) and 1960 GeV (top row)

37

track pperp values 2 lt pT1 lt 10 GeV) This indicates that the energy scaling of the UE modeling and inparticular the details of its transition between central and peripheral collisions is still not satisfactorilyunderstood

5 Conclusions and Exhortation

We have presented a reanalysis of the constraints on fragmentation in ee collisions and applied theresults to update the final-state fragmentation parameters in PYTHIA 8 We combine these parameterswith a tune to hadron-collider data using a new NNPDF 23 LO QCD+QED PDF set which has beenencoded so it is available as an internal PDF set in PYTHIA 8 independently of LHAPDF [112]

In this PDF set as well as in our tune the value of the strong coupling for hard-scattering matrixelements is fixed to be αs(MZ) = 013 consistent with other LO determinations of it For initial-and final-state radiation our tune uses the effective value αs(MZ) = 01365 The difference isconsistent with an effective translation between the MS and CMW schemes We note that alternative(LO NLO and NNLO) NNPDF 23 QCD+QED sets with αs(MZ) = 0119 are also available inthe code for people who want to check the impact of using a different αs(MZ) value andor higher-order PDF sets on hard-scattering events For the purpose of such studies we point out that it ispossible in PYTHIA 8 to preserve most of the features of the shower- and underlying-event tuningby changing only the PDF for the hard-scattering matrix elements leaving the PDF choice for theshower evolution and MPI framework unaltered (see the PYTHIA 8 HTML manualrsquos PDF sectionunder PDFuseHard)

The updated parameters are available as an option starting from PYTHIA 8185 by setting

Tuneee = 7 and Tunepp = 14

By no means do we claim that this should be regarded as the final word in tuning the PYTHIA 8Monte Carlo model First of all the model continues to evolve For instance developments foreseenfor the near future include updates of colour reconnections diffraction and the treatment of g rarr qqsplittings Any of these should in principle be accompanied by a reevaluation of the model constraints

Moreover despite the comprehensive view of collider data we have attempted to take in thisstudy there still remains several issues that were not addressed including initial-final interferenceand coherence effects [113 114] (probably more a modelling issue than a tuning one) reliable esti-mates of theoretical uncertainties [8 17 24 29 97 115] diffraction14 [74 116 117] and other colour-singlet phenomena such as onium production long-distance (eg forward-backward forward-centraland ldquoridgerdquo-type) correlations [88 118ndash123] B-hadron decays [124] and tuning in the presence ofmatrix-element matching at LO and NLO (see [21 29 115 125 126] for recent phenomenologi-cal studies) Especially in the latter context of matrix-element matching we expect that in manycases PYTHIA 8 will be used together with codes such as ALPGEN [127] MADGRAPH [128]aMCatNLO [129] or POWHEG [130] either using the matching algorithms of those programs them-selves or via any of PYTHIArsquos several internal (LHEF-based [131]) implementations of matchingschemes (POWHEG [85] CKKW-L [132ndash134] MLM [135 136] UMEPS [137] NL3 [138] UN-LOPS [139]) The impact of such corrections on MC tuning depends on the details of the matchingscheme (especially its treatment of unitarity) and there is in general a non-negligible possibility ofldquomis-tuningrdquo when combining a stand-alone tune with ME corrections A simple example illustrating

14In particular the constraints on fragmentation mainly come from SLD and LEP where the non-perturbative parametersare clearly defined at the shower cutoff scaleQhad whereas diffraction is dominated by soft physics for which the definitionof the effective hadronization scale is less clear The amount of MPI in hard diffractive events also requires tuning

38

this is the effective value of αs(MZ) which for a leading-order tune is typically of order 013 whilea consistent NLO correction scheme should be compatible with values closer to 012 [29] There isalso the question of the running order of αs The propagation of such changes from the level of hardmatrix elements through the shower and hadronization tuning process are still not fully explored andhence we advise users to perform simple cross-checks such as checking the distributions presented inthis paper before and after applying matrix-element corrections Parameters that appear on both sidesof the matching such as αs should also be checked for consistency [21]

We noted several issues concerning the ee data used to constrain the fragmentation modelling thatit would be good to resolve In particular we find some tensions between the identified-particle ratesextracted from 1) HEDPATA 2) Sec 46 of the PDG and 3) the Z boson summary table in the PDGas discussed in more detail in section 2 and concerning which we made some (subjective) decisionsto arrive at a set of hopefully self-consistent constraints for this work We also note that the overallprecision of the fragmentation constraints could likely be significantly improved by an FCC-ee typemachine such as Tera-Z a possibility we hope to see more fully explored in the context of future eeQCD phenomenology studies

We conclude that the new parameter set does improve significantly on the previous default valuesin several respects including better agreement with data on

1 the net strangeness fraction (has been increased by 10 reflected not only in improved kaonand hyperon yields but also in the Ds and Bs fractions)

2 the ultra-hard fragmentation tail (has been softened especially for leading baryons and for Dand B hadrons)

3 the pTZ spectrum (softened at low pTZ)

4 the minimum-bias charged multiplicity in the forward region (has increased by 10)

5 the underlying event at 7 TeV (is very slightly higher than before)

Some questions that remain open include the following We see a roughly 20 excess of verysoft kaons in both ee and pp environments cf figs 6 and 23 despite the overall kaon yields beingwell described and the overall baryon yields at LHC appear to be underestimated by at least 30despite good agreement at LEP The momentum spectra of heavier strange particles are also poorlyreproduced in particular at LHC It is interesting and exciting that some of the LHC spectra appearto be better described by allowing collective flow in a fraction of events (cf the EPOS model [140])though we believe the jury is still out on whether this accurately reflects the underlying physics Forinstance it has been argued that colour reconnections can mimick flow effects [90] and they may alsobe able to modify the yield of baryons if the creationdestruction of string junctions is allowed [141]We look forward to future discussions on these issues

We round off with an exhortation for follow-ups on this study to provide

bull Not only central tunes experiments and other user-end colleagues need more than central de-scriptions of data there is an increasing need for serious uncertainty estimates In the contextof tune variations it is important to keep in mind that the modelling uncertainties are often in-trinsically non-universal Therefore the constraints obtained by considering data uncertaintiesonly (eg in the spirit of PROFESSORrsquos eigentunes [17]) can at most constitute a lower boundon the theoretical uncertainty (similarly to the case for PDFs) A serious uncertainty estimateincludes some systematic modelling variation irrespectively of and in addition to what data

39

allows (eg in the spirit of the Perugia set of tunes for PYTHIA 6 [8]) We therefore hope thefuture will see more elaborate combinations of data- and theory-driven approaches to systematictune uncertainties

bull Not only global tunes the power of MC models lies in their ability to simultaneously describea large variety of data hence we do not mean to imply that one should give up on universalityand tune to increasingly specific corners of phase space disregarding (or de-emphasizing withlower weights) all others However as proposed in [97] one can obtain useful explicit tests ofthe universality of the underlying physics model by performing independent tunes on separateldquophysics windowsrdquo say in the forward vs central regions for different event-selection crite-ria at different collider energies or even for different collider types In this connection justmaking one global ldquobest-fitrdquo tune may obscure tensions between the descriptions of differentcomplementary data sets By performing independent tunes to each data set separately andchecking the degree of universality of the resulting parameters one obtains a powerful crosscheck on the underlying physics model If all sets produce the same or similar parameters thenuniversality is OK hence a global tune makes very good sense and the remaining uncertain-ties can presumably be reliably estimated from data alone If instead some data sets resultin significantly different tune parameters one has a powerful indication that the universality ofthe underlying modeling is breaking down which can lead to several productive actions 1) itcan be taken into account in the context of uncertainty variations 2) the nature of the data setsfor which non-universal tune parameters are obtained can implicitly indicate the nature of theproblem leading to more robust conclusions about the underlying model than merely whether atune cancannot fit the data and 3) the observations can be communicated to the model authorsin a more unambiguous way hopefully resulting in a speedier cycle of model improvements

We hope that the Monash 2013 tune parameters may serve as a useful starting point for phe-nomenology studies and for future PYTHIA 8 tuning efforts

Acknowledgments

We thank S Mrenna M Ritzmann and T Sjostrand for comments on the manuscript and L de Nooijfor pointing us to the ALICE Klowast and φ measurements [142] and to the ATLAS φ measurementsin [143] The work of J R is supported by an STFC Rutherford Fellowship STK0052271 Thiswork was supported in part by the Research Executive Agency (REA) of the European Commissionunder the Grant Agreements PITN-GA-2012-315877 (MCnet)

A Monash 2013 Tune Parameters

In tabs 3 ndash 7 we list the FSR fragmentation parameters for the Monash tune of PYTHIA Forreference we compare them to the current default parameters

40

FSR Parameters Monash 13 (Default) CommentTimeShoweralphaSvalue = 01365 = 01383 Effective alphaS(mZ) valueTimeShoweralphaSorder = 1 = 1 Running orderTimeShoweralphaSuseCMW = off = off Translation from MS to CMWTimeShowerpTmin = 050 = 040 Cutoff for QCD radiationTimeShowerpTminChgQ = 050 = 040 Cutoff for QED radiationTimeShowerphiPolAsym = on = on Asymmetric azimuth distributions

Table 3 Final-state radiation (FSR) parameters

HAD Parameters Monash 13 (Default) Comment String breaks pT and z distributionsStringPTsigma = 0335 = 0304 Soft pT in string breaks (in GeV)StringPTenhancedFraction = 001 = 001 Fraction of breakups with enhanced pTStringPTenhancedWidth = 20 = 20 Enhancement factorStringZaLund = 068 = 03 Lund FF a (hard fragmentation supp)StringZbLund = 098 = 08 Lund FF b (soft fragmentation supp)StringZaExtraSquark = 00 = 00 Extra a when picking up an s quarkStringZaExtraDiquark = 097 = 050 Extra a when picking up a diquarkStringZrFactC = 132 = 100 Lund-Bowler c-quark parameterStringZrFactB = 0855 = 067 Lund-Bowler b-quark parameter Flavour composition mesonsStringFlavProbStoUD = 0217 = 019 Strangeness-to-UD ratioStringFlavmesonUDvector = 05 = 062 Light-flavour vector suppressionStringFlavmesonSvector = 055 = 0725 Strange vector suppressionStringFlavmesonCvector = 088 = 106 Charm vector suppressionStringFlavmesonBvector = 22 = 30 Bottom vector suppressionStringFlavetaSup = 060 = 063 Suppression of eta mesonsStringFlavetaPrimeSup = 012 = 012 Suppression of etarsquo mesons Flavour composition baryonsStringFlavprobQQtoQ = 0081 = 009 Diquark rate (for baryon production)StringFlavprobSQtoQQ = 0915 = 1000 Strange-diquark suppressionStringFlavprobQQ1toQQ0 = 00275 = 0027 Vector diquark suppressionStringFlavdecupletSup = 10 = 10 Spin-32 baryon suppressionStringFlavsuppressLeadingB = off = off Optional leading-baryon suppressionStringFlavpopcornSpair = 09 = 05 StringFlavpopcornSmeson = 05 = 05

Table 4 String-breaking parameters

PDF and ME Parameters Monash 13 (Default) CommentPDFpSet = 13 = 8 PDF set for the protonSigmaProcessalphaSvalue = 0130 0135 alphaS(MZ) for matrix elementsMultiPartonInteractionsalphaSvalue = 0130 0135 alphaS(MZ) for MPI

Table 5 Parton-distribution (PDF) and Matrix-Element (ME) parameters

41

ISR Parameters Monash 13 (Default) CommentSpaceShoweralphaSvalue = 01365 = 0137 Effective alphaS(mZ) valueSpaceShoweralphaSorder = 1 = 1 Running orderSpaceShoweralphaSuseCMW = off = off Translation from MS to CMWSpaceShowersamePTasMPI = off = off ISR cutoff typeSpaceShowerpT0Ref = 20 = 20 ISR pT0 cutoffSpaceShowerecmRef = 70000 = 18000 ISR pT0 reference ECM scaleSpaceShowerecmPow = 00 = 00 ISR pT0 scaling powerSpaceShowerrapidityOrder = on = on Approx coherence via y-orderingSpaceShowerphiPolAsym = on = on Azimuth asymmetries from gluon polSpaceShowerphiIntAsym = on = on Azimuth asymmetries from interferenceTimeShowerdampenBeamRecoil = on = on Recoil dampening in final-initial dipolesBeamRemnantsprimordialKTsoft = 09 = 05 Primordial kT for soft procsBeamRemnantsprimordialKThard = 18 = 20 Primordial kT for hard procsBeamRemnantshalfScaleForKT = 15 = 10 Primordial kT softhard boundaryBeamRemnantshalfMassForKT = 10 = 10 Primordial kT softhard mass boundary

Table 6 Initial-state radiation (ISR) and primordial-kT parameters

MPI Parameters Monash 13 (Default) CommentMultipartonInteractionspT0Ref = 228 = 2085 MPI pT0 IR regularization scaleMultipartonInteractionsecmRef = 70000 = 18000 MPI pT0 reference ECM scaleMultipartonInteractionsecmPow = 0215 = 019 MPI pT0 scaling powerMultipartonInteractionsbProfile = 3 = 3 Transverse matter overlap profileMultipartonInteractionsexpPow = 185 = 20 Shape parameterBeamRemnantsreconnectRange = 18 = 15 Colour ReconnectionsSigmaTotalzeroAXB = on = on Carried over from 4CSigmaDiffractivedampen = on = on Carried over from 4CSigmaDiffractivemaxXB = 650 = 650 Carried over from 4CSigmaDiffractivemaxAX = 650 = 650 Carried over from 4CSigmaDiffractivemaxXX = 650 = 650 Carried over from 4CDiffractionlargeMassSuppress = 40 = 20 High-mass diffraction suppression power

Table 7 Multi-Parton-Interaction (MPI) Colour-Reconnection (CR) and Diffractive parameters

42

B Additional Plots

B1 LEP Event-Shape Distributions

To keep the main body of the paper as uncluttered as possible we collect various plots of event-shapedistributions in figs 28 and 29 separated into light-flavour and b-tagged events on the left and rightrespectively

The experimental results come from the L3 experiment [26] However since the data points areonly available with 3-digit precision some of the least populated bins contain artifacts like uncertain-ties being reported as exactly zero etc Thus we have been forced to make the following modificationsto the data set

The statistical uncertainty was reported as zero for the last two bins of light-flavour Thrust as wellas for the last bin of the C D and BT parameters Uncertainties lt 10minus3 were derived using anapproximate statistical scaling based on the contents and uncertainties of the other bins Likewise thesystematical uncertainty for the last bin of Thrust was given as zero which we have replaced by theupper limit 5times 10minus4 The last bin of BT quoted a measured y value of zero removed in this study

For the heavy-flavour tagged event shapes more significant rounding issues were present Thusseveral of the first and last bins of each distribution either quoted zero (statistical andor systematic)uncertainties or ones with only a single digit of precision (such as 0001 for which the rounding errorcould be up to sim 50) We have interpreted all such values conservatively inserting by hand a fourthdigit on the uncertainties as large as could be consistent with rounding

B2 Additional Particle Spectra

In addition to the K and Λ spectra shown in the main body of the paper (sections 22 and 35) wehere include for reference the x spectra of φ mesons protons and Ξ baryons at LEP in figs 30 and 31the pT spectrum of Klowast mesons and the rapidity and pT spectra of φ mesons at LHC in fig 32 (withabsolute normalizations to the number of inelastic events) and the rapidity spectrum of Ξ baryons atLHC in fig 33

The transverse-momentum spectra of Klowast and φ mesons in fig 32 exhibit the same qualitativebehaviour as that of the KS mesons (fig 23) namely an excess at very soft momenta below sim 500MeV and a depletion at slightly higher momenta between 1 and 2 GeV As discussed in section 35we did not find a way to remove these undesirable features in the Monash 2013 tune suggesting thatthis is an issue that further theoretical modeling will be needed to resolve

The rapidity spectrum of Ξ baryons fig 33 shows that although the Monash tune does producemore Ξ baryons overall (as expected also from the relative increase of Ξ production at LEP cf fig 5)there is still a significant deficit of Ξ baryons at the LHC almost a factor 2 compared with the dataThis is qualitatively similar to the situation for Λ baryons (fig 24) discussed in section 35 Sincenew physics mechanisms may be required to ldquoexplainrdquo the missing baryons we conclude that furthermeasurements and better precision on both the Λ and Ξ sectors (in addition to any other baryonsthat may be accessible) would be highly interesting More explicit recommendations can be found insections 35 and 5

43

0 01 02 03 04

d(1

-T)

σ d

σ1

-310

-210

-110

1

10

2101-Thrust (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn03

01plusmn04

02plusmn05

V I

N C

I A

R O

O T

1-T (udsc)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

d(1

-T)

σ dσ

1

-310

-210

-110

1

10

2101-T (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn13

02plusmn12

02plusmn14

V I

N C

I A

R O

O T

1-T (b)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210

310C Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn03

00plusmn04

01plusmn04

V I

N C

I A

R O

O T

C0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210 C parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn17

01plusmn24

01plusmn27

V I

N C

I A

R O

O T

C (b)0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn06

01plusmn06

V I

N C

I A

R O

O T

D0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn24

02plusmn21

02plusmn26

V I

N C

I A

R O

O T

D (b)0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

Figure 28 Hadronic Z decays atradics = 912 GeV The T C and D event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

44

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn02

01plusmn03

01plusmn04

V I

N C

I A

R O

O T

WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn05

01plusmn12

01plusmn17

V I

N C

I A

R O

O T

(b)WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn02

00plusmn02

01plusmn03

V I

N C

I A

R O

O T

TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

04plusmn24

08plusmn49

08plusmn55

V I

N C

I A

R O

O T

(b)TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

Figure 29 Hadronic Z decays atradics = 912 GeV The BW and BT event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

45

0 02 04 06 08 1

dx

φgt

dn

φ1

ltn

-210

-110

1

10 )φx(

Pythia 8183Data from ALEPH_1996_S3486095d40-x01-y01

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn37

02plusmn53

03plusmn62

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

0608

112141618

Figure 30 Hadronic Z decays atradics = 912 GeV φ meson x spectrum

-5 -4 -3 -2 -1 0

dx

pgt

dn

p1

ltn

-410

-310

-210

-110

1

10

210) (Combined)px(p+

Pythia 8183Data from Zeit Phys C66 (1995) 355 PhysRev D59 (1998) 052001

ALEPH+SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn08

00plusmn09

00plusmn08

V I

N C

I A

R O

O T

px-5 -4 -3 -2 -1 0

The

ory

Dat

a

06

08

1

12

14

0 02 04

dx

Ξgt

dn

Ξ1

ltn

-110

1

10

)plusmnΞx(

Pythia 8183Data from Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn11

02plusmn13

02plusmn14

V I

N C

I A

R O

O T

Ex0 02 04

The

ory

Dat

a

06

08

1

12

14

Figure 31 Hadronic Z decays atradics = 912 GeV pplusmn and Ξplusmn x spectra

46

0 2 4 6

Td

pK

d

nIN

EL

1N

-510

-410

-310

-210

-110

(INEL |y|lt05)T

p0K

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn35

01plusmn26

01plusmn29

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 2 4 6

Td

pφ

dn

INE

L1

N-510

-410

-310

-210

-110

gt04)T

(INEL |y|lt05 pT

pφ

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn88

03plusmn84

04plusmn173

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

)dy

[mb]

-K

+K

rarrφ(σd

0

05

1

15

2 Rapidity (INEL ATLAS cuts)φ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn14

01plusmn19

01plusmn34

V I

N C

I A

R O

O T

pp 7000 GeV

|y|0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

06 08 1 12

[mb

GeV

]φ

T)

dp-

K+

Krarrφ(

σd

0

05

1

15

2

25 (INEL ATLAS cuts)

T pφ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn21

01plusmn30

02plusmn53

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p06 08 1 12

The

ory

Dat

a

06

08

1

12

14

Figure 32 pp collisions at 7 TeV Top row Klowast and φ pperp spectra compared with ALICE data [142]Bottom row φ rapidity and pperp spectrum compared with ATLAS data [143] The ATLAS cuts areφrarr K+Kminus pperpφ isin [05 12] GeV |y(φ)| lt 08 pperpK gt 023 GeV |pK | lt 08 GeV

47

0 05 1 15 2

dygt

Ξ lt

dnN

SD

1N

0

001

002

003

004)d|y|gt (NSD)Ξltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn89

01plusmn129

01plusmn192

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

0

05

1

15

2

Figure 33 pp collisions at 7 TeV Ξminus rapidity spectrum compared with CMS data [99]

48

B3 Energy Scaling of σ2rarr2(pTmin) vs σinel from 200 GeV to 100 TeV

In fig 34 we show the LO QCD 2rarr 2 cross section integrated above pTmin as a function of pTminin pp collisions at 4 different CM energies complementing and expanding on the 8-TeV CM energyshown in the main body of the paper We compare two different αs and PDF choices correspondingto those made in tunes Monash 13 (blue filled dots) and 4C (red open squares) respectively As areference for the total inelastic cross section at each energy we base ourselves on the best-fit curvein the TOTEM cross-section measurement paper [72] which in turn represents a fit produced by theCOMPETE collaboration [144] Uncertainties are rough conservative estimates based on the plot inthe TOTEM paper but they are in any case too small to significantly affect conclusions about the scaleat which the partonic cross section saturates the hadronic one

We observe that the pTmin value for which the LO QCD 2 rarr 2 partonic cross section formallybecomes equal to the total inelastic cross section (strongly suggesting that every event has at leastone such mini-jet pair) rises from values around 1 ndash 2 GeV at energies

radics lt 1 TeV to 5 GeV atradic

s = 13 TeV and finally 10 GeV atradics = 100 TeV

49

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

0 50 100

)C

hP

rob(

n

-710

-610

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn27

00plusmn27

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

Chn0 50 100

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20

Td

pC

h d

nT

)p

π(

2C

h1

n

-810

-710

-610

-510

-410

-310

-210

-110

1

10|lt25)ηgt05 |

T 1 pge

Ch (n

Tp

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLAS PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn15

00plusmn08

01plusmn58

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 5 10 15 20

The

ory

Dat

a

06

08

1

12

14

0 50 100 150 200

)C

hP

rob(

n

-610

-510

-410

-310

-210

-110

1|lt25)ηgt01 |

T 2 pge

ChSoft Chg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn45

00plusmn49

01plusmn197

V I

N C

I A

R O

O T

pp 7000 GeV

Chn0 50 100 150 200

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20

Td

pC

h d

nT

)p

π(

2C

h1

n

-910

-710

-510

-310

-110

10|lt25)ηgt01 |

T 2 pge

Ch (n

Tp

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn43

01plusmn73

02plusmn155

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 5 10 15 20

The

ory

Dat

a

06

08

1

12

14

Figure 18 Min-bias pp collisions at 7 TeV Charged-multiplicity and pperp distributions with standard(top row) and soft (bottom row) fiducial cuts compared to ATLAS data [91]

28

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from PhysRevLett 105 (2010) 022002

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn00

00plusmn03

00plusmn71

V I

N C

I A

R O

O T

pp 7000 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

55 6 65

gtηd

Ch

ltdn

Tot

em1

n

0

1

2

3

4

5

6|lt65)ηgt004 53lt|

T1 pge

chgt (nηd

Chltdn

Pythia 8185Data from EurophysLett 98 (2012) 31002

TOTEMPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn01

00plusmn27

00plusmn62

V I

N C

I A

R O

O T

pp 7000 GeV

η55 6 65

The

ory

Dat

a

06

08

1

12

14

3 35 4 45 5

gtηlt

dEd

0

100

200

300

400

500|lt465)η1 in both 323lt|ge

chMB Fwd E Flow (n

Pythia 8185Data from JHEP 11 (2011) 148

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn01

00plusmn04

00plusmn22

V I

N C

I A

R O

O T

pp 7000 GeV

η3 35 4 45 5

The

ory

Dat

a

06

08

1

12

14

Figure 19 Charged-particle pseudorapidity distributions and forward energy flow in min-bias ppcollisions at 7 TeV compared to CMS [92 93] and TOTEM [94] data

29

0 50 100

0

05

1

15

2

25|lt25)ηgt05 |

T) (p

Chgt(n

Tltp

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn05

01plusmn01

05plusmn07

V I

N C

I A

R O

O T

pp 7000 GeV

0 50 100

The

ory

Dat

a

06

08

1

12

14

0 50 100 150 200

0

05

1

15|lt25)ηgt01 |

T 2 pge

Ch) (n

Chgt(n

TSoft ltp

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn06

00plusmn08

03plusmn40

V I

N C

I A

R O

O T

pp 7000 GeV

0 50 100 150 200

The

ory

Dat

a06

08

1

12

14

Figure 20 Average-pperp vs charged-multiplicity distributions in min-bias pp collisions at 7 TeV withstandard (left) and soft (right) fiducial cuts compared to ATLAS data [91]

multiplicity by itself is a very difficult quantity to extract reliable conclusions from Note also that theCMS measurement [92] shown in the top pane of fig 19 was corrected to an unphysical ldquonon-singlediffractiverdquo event definition which essentially amounts to switching off single-diffractive contributionsin the MC generator (We note that later CMS measurements instead use a physical observable relatedto the diffractive mass to define NSD) For the comparisons to CMS NSD data shown here the single-diffractive contributions were switched off in the generator With these caveats in mind we note thatboth the 4C and Monash 2013 tunes are in good agreement with the CMS measurement with theMonash one giving a slightly lower central charged-track density (by about 5) This is closer to thevalues observed in data though as already noted in section 11 we do not regard differences at the 5level as significant

In the bottom two panes of fig 19 we focus on the forward region (with physical event selections)In particular we see that the NNPDF set [20] generates a broader rapidity spectrum so that while theactivity in the central region (top pane) is reduced slightly the activity in the very forward regionactually increases and comes into agreement with the TOTEM measurement [94] covering the range53 lt |η| lt 64 The bottom right-hand pane shows the forward energy flow measured by CMS [93]in the intermediate region 323 lt |η| lt 465 The dependence on η is a bit steeper in the Monashtune than in the previous one and more similar to that seen in the data

A complementary observable which is highly sensitive to interconnection effects between theMPI (and hence eg to the effects of ldquocolour reconnectionsrdquo [95]) is the average charged-particlepperp as a function of the number of charged particles In a strict leading-colour picture each MPIwould cause one or two new strings to be stretched between the remnants but each such string wouldbe independent (modulo endpoint effects) therefore (modulo jets) the pperp spectrum of the hadronsproduced by each of these strings would be independent of the number of strings The result would bea flat 〈pperp〉 (nCh) spectrum Jets and colour reconnections both produce a rising spectrum The spectraobserved by ATLAS [91] are compared to the Monash 2C and 4C tunes in fig 20 for standard

30

0 1 2 3

gtφ|dη

d|

Ch

n2

ltd

0

02

04

06

08

1gt01)

T|lt25 pηgt1 (|

Tlead| wrt pφ∆|

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn16

00plusmn19

00plusmn56

V I

N C

I A

R O

O T

pp 7000 GeV

| [rad]φ∆|0 1 2 3

The

ory

Dat

a

06

08

1

12

14

0 1 2 3

gtφ|dη

d|

Ch

n2

ltd

0

05

1

15

2

gt05)T

|lt25 pηgt5 (|Tlead

| wrt pφ∆|

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn05

00plusmn05

00plusmn70

V I

N C

I A

R O

O T

pp 7000 GeV

| [rad]φ∆|0 1 2 3

The

ory

Dat

a06

08

1

12

14

Figure 21 pp collisions at 7 TeV ∆φ of charged particles with respect to the hardest track for twodifferent hardest-track triggers compared with ATLAS data [98]

(left) and soft (right) fiducial cuts Both of the Monash and 4C tunes reproduce the data quite wellwith χ2

5 lt 1 while the older tune 2C had a higher CR strength optimized to describe Tevatrondata [96] We certainly consider the energy scaling of the effective CR strength among the mostuncertain parameters of the current min-biasunderlying-event modelling (a similar conclusion wasreached for the CR modelling in PYTHIA 6 in [97]) and intend to study the physics aspects of thisissue more closely in a forthcoming paper

For a more differential look at the event structure we consider the charged-track ∆φ distributionswith respect to the azimuthal angle of the leading track in fig 21 compared with ATLAS data [98]The plot in the left-hand pane corresponds to a requirement of pperplead ge 1 GeV while the one in theright-hand pane is for a harder trigger pperplead ge 5 GeV The former can roughly be taken as charac-teristic of min-bias events while the latter is related to the differential distribution of the underlyingevent In both cases the activity in the wide-angle region near π2 is significantly better described bythe 4C and Monash 2013 tunes (which agrees with their improved description of the overall activity)while there is a too strong peaking at low ∆φ especially for the lowest pperplead cut (left) possibly indi-cating that the structure of the min-bias events is still slightly too ldquolumpyrdquo (ie jetty) For the higherpperplead cut (right) the overcounting at very low ∆φ is already significantly milder and we observe agood agreement with the data

Turning now to the underlying event (UE) what matters most for high-pperp jet studies is that theMC models describe the UE contamination per ∆R jet area The most important UE observable fromthis perspective is thus the pperp sum density in the UE and its fluctuations For charged particles atLHC typically a pperp cut of 500 MeV is relevant since softer tracks will form helices and hence notcontribute to calorimetric jet energies Neutral particles are of course relevant across all pperp scalesIn fig 22 we show the charged pperp sum density (left with the lowest possible pperp cut of 100 MeV)and the charged-track density (right with a pperp cut of 500 MeV) in the so-called ldquoTransverse Regionrdquo(defined by 60 lt ∆φ lt 120 with respect to the leading track) inside the ATLAS acceptance of

31

0 5 10 15 20

)φ∆η

∆gt

(T

psum

lt

0

05

1

15

2

25gt01)

T|lt25 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn03

01plusmn09

02plusmn112

V I

N C

I A

R O

O T

pp 7000 GeV

(hardest track) [GeV]T1

p0 5 10 15 20

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20

)φ∆η

∆gt

(C

hlt

n

0

05

1

15

2

25gt05)

T|lt25 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn02

00plusmn04

02plusmn104

V I

N C

I A

R O

O T

pp 7000 GeV

(hardest track) [GeV]T1

p0 5 10 15 20

The

ory

Dat

a06

08

1

12

14

Figure 22 pp collisions at 7 TeV UE (ldquoTransverse regionrdquo) transverse-momentum sum density (left)and charged-track density (right) compared with ATLAS data [98]

|η| lt 25 [98] As is now well known the Tevatron extrapolations (represented here by Tune 2C)predicted a UE level which was 10 ndash 20 below the LHC data Both the current default tune 4C(which included LHC data) and the Monash 2013 tune exhibit significantly better agreement with theLHC measurements with the Monash one giving a slight additional improvement in the χ2

5 valuesWe conclude that the Monash 2013 tune parameters are appropriate for both min-bias and UE studies

35 Identified Particles at LHC

While the description of inclusive charged particles discussed in the previous section is acceptablelarger discrepancies emerge when we consider the spectra of identified particles We here focus onstrange particles in particular K0

S mesons and Λ0 hyperons in figs 23 and 24 respectively Theexperimental measurements come from CMS [99] Additional comparisons to strange-particle spectra(Klowast φ and Ξ) are collected in appendix B2

In the K0S rapidity distribution shown in the left-hand pane of fig 23 we observe that tune 4C

exhibits a mild underproduction of about 10 Though it might be tempting to speculate whether thiscould indicate some small reduction of strangeness suppression in pp collisions however we alreadynoted in section 21 that the strangeness production in ee collisions also needed to be increased byabout 10 After this adjustment we see that the overall K0

S yield in the Monash 2013 tune is fullyconsistent with the CMS measurement Nonetheless we note that the momentum distribution is stillnot satisfactorily described as shown in the right-hand pane of fig 23 Our current best guess istherefore that the overall rate of strange quarks is consistent at least in the average min-bias collision(dedicated comparisons in high-multiplicity samples would still be interesting) but that the phase-space distribution of strange hadrons needs more work Similarly to the case in ee collisions cf fig 6the model predicts too many very soft kaons though we do not currently know whether there is adynamic link between the ee and pp observations

For strange baryons we note that the increase in the Λ0 fraction in ee collisions (cf fig 5) does

32

0 05 1 15 2

dygt

K lt

dnN

SD

1n

0

02

04

06

08)d|y|gt Rapidity (NSD)

S

0ltdn(K

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn01

00plusmn09

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8 10

Td

pK

dn

NS

D1

N

-510

-410

-310

-210

-110

1

10 (|y|lt20 NSD)

T pS

0K

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn78

01plusmn34

02plusmn22

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6 8 10

The

ory

Dat

a06

08

1

12

14

Figure 23 pp collisions at 7 TeV K0S rapidity and pperp spectrum compared with CMS data [99]

0 05 1 15 2

dygt

Λ lt

dnN

SD

1N

0

01

02

03

04)d|y|gt (NSD)0Λltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn64

00plusmn78

01plusmn147

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8 10

Td

pΛ

dn

Λ1

n

-510

-410

-310

-210

-110

1

10 (|y|lt20 NSD)

T p0Λ

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn59

03plusmn66

05plusmn105

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6 8 10

The

ory

Dat

a

06

08

1

12

14

Figure 24 pp collisions at 7 TeV Λ0 rapidity and pperp spectrum compared with CMS data [99]

not result in an equivalent improvement of the Λ0 rate in pp collisions shown in fig 24 The Monash2013 tune still produces only about 23 of the observed Λ0 rate (and just over half of the observedΞminus rate cf appendix B2) We therefore believe it to be likely that an additional source of net baryonproduction is needed (at least within the limited context of the current PYTHIA modelling) in orderto describe the LHC data The momentum spectrum is likewise quite discrepant exhibiting an excessat very low momenta (stronger than that for kaons) a dip between 1ndash4 GeV and then an excess of veryhard Λ0 production The latter hard tail is somewhat milder in the Monash 2013 tune than previously

33

and it may be consistent with the trend also seen in the Λ0 spectrum at LEP cf fig 6 We concludethat baryon production still requires further modelling and tuning efforts

4 Energy Scaling

Though energy scaling these days mostly refers to the scaling of pp collisions (see eg [97]) animportant first step is to consider the scaling of observables in ee rarr γlowastZ rarr hadrons This scalingcontains information on the relative contributions of perturbative and non-perturbative fragmentationThus at low ee energies the non-perturbative components of the fragmentation model dominatewhile perturbative bremsstrahlung increases in importance towards higher ee energies In fig 25we consider the scaling of the average charged-particle multiplicity and that of charged Kaons andLambda baryons from CM energies of 14 GeV to 200 GeV obtained from measurements availableat HEPDATA Below the Z pole the measurements we include mostly come from TASSO [100]though a few points on 〈nCh〉 come from HRS (at 29 GeV [101]) and TOPAZ (at 578 GeV [102]) Atthe Z pole the data come from the four LEP experiments [38 51ndash53] with the latter extending alsoto energies above MZ [103ndash108] For completeness and as reference for future ee collider studiesmodel extrapolations for CM energies up to 1000 GeV are also shown (though still only including theeerarr γlowastZ rarr hadrons component as usual with photon ISR switched off)

From the plots in fig 25 it is clear that there are no significant differences between the energyscaling of the three ee tunes considered here (mainly reflecting that they have been tuned to samereference point at 912 GeV and that their scaling is dictated by the same underlying physics model)and that their energy dependence closely matches that observed in data However the increasedamount of non-perturbative strangeness production in the Monash tune leads to a better agreementwith the overall normalization of the Kplusmn and Λ rates at all energies

Moving to pp collisions the plots in fig 26 show the scaling of the average charged multiplicity(left column) and multiplicity distributions (right column) in min-bias collisions from 7000 GeV (toprow) to 900 GeV (middle row) and 200 GeV (bottom row) compared with data from CMS [92 109]ATLAS [91] and UA5 [110 111] We regret the omission of additional relevant min-bias measure-ments from the Tevatron and RHIC experiments here but have chosen to focus in this paper mainlyon the LHC The comparisons at 7 TeV were already discussed in the main section on pp collisionssection 3 At 900 GeV the Monash 2013 tune again gives a roughly 5 lower average central chargedmultiplicity than the 4C one with a better description of the tail towards high multiplicities At 200GeV the UA5 measurement we include here extends over the full rapidity and pperp range hence the in-terplay between diffraction and low-multiplicity non-diffractive processes is presumably (much) moreimportant We believe imperfections in this modelling to be the likely cause of the significant discrep-ancies observed at high η and for nCh le 20 at these energies Since a dedicated study of this interplayis beyond the scope of this study we limit ourselves merely to stating this observation as a point forfuture studies to help clarify

Finally in fig 27 we compare to the underlying event measured in the highly useful energyscan that was performed at the Tevatron in the last days before its shutdown [22 23] during whichextremely high min-bias statistics were collected at 300 and 900 GeV CM energy over a period of afew days As was already noted in section 3 the UE at 7 TeV is slightly larger in the Monash 2013tune than in tune 4C As can be seen from the plots here the two tunes give comparable results for allthe Tevatron energies Interestingly the UE plateau region at 900 and 1960 GeV is reached sooner inthese models than in the data translating to a roughly 10 - 20 too low UE level for leading-trackpperp values in the neighbourhood of the transition from the rise to the plateau (roughly for leading-

34

14 22 29 35 44 58 91 91 91 91 133 161 183 189 200 250 350 500 1000

gtC

hlt

n

0

20

40

60

Average Charged Multiplicity vs ECM

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN25

χ00plusmn03 00plusmn02 00plusmn02

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 22 29 35 44 58 91 91 91 91 133 161 183 189 200 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

14 22 35 44 91 91 133 161 183 189 250 350 500 1000

gtK

ltn

0

2

4

6 Multiplicity vs ECM+-Average K

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN25

χ00plusmn06 00plusmn20

00plusmn18

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 22 35 44 91 91 133 161 183 189 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

14 35 91 91 91 91 133 200 250 350 500 1000

gtΛ

ltn

0

02

04

06

08

1

12 Multiplicity vs ECM0ΛAverage

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn06

01plusmn22

01plusmn18

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 35 91 91 91 91 133 200 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

Figure 25 e+eminus rarr hadrons Energy scaling of 〈nCh〉 〈nKplusmn〉 and 〈nΛ〉 in e+eminus rarr qq eventsincluding comparisons to measurements from HEPDATA for CM energies from 14 GeV to 200 GeVAlso shown are model extrapolations up to 1000 GeV

35

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from PhysRevLett 105 (2010) 022002

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn00

00plusmn03

00plusmn71

V I

N C

I A

R O

O T

pp 7000 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

0 50 100

)C

hP

rob(

n

-710

-610

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn27

00plusmn27

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

Chn0 50 100

The

ory

Dat

a

06

08

1

12

14

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from JHEP 1002 (2010) 041

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn03

00plusmn05

00plusmn29

V I

N C

I A

R O

O T

pp 900 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

0 10 20 30 40

)C

hP

rob(

n

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn17

01plusmn25

02plusmn127

V I

N C

I A

R O

O T

pp 900 GeV

Chn0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

0 1 2 3 4 5

gtηd

ch lt

dnN

SD

1n

0

1

2

3

4

5gt (NSD)ηd

chltdn

Pythia 8185Data from ZPhys C33 (1986) 1-6

UA5PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn36

00plusmn24

00plusmn16

V I

N C

I A

R O

O T

ppbar 200 GeV

η0 1 2 3 4 5

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)C

hP

rob(

n

-410

-310

-210

-110

1

)T

|lt05 all pηChg Mult (NSD |

Pythia 8185Data from ZPhys C43 (1989) 357

UA5PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn24

00plusmn24

00plusmn08

V I

N C

I A

R O

O T

ppbar 200 GeV

Chn0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 26 Min-bias pp events from 200 to 7000 GeV Energy scaling of 〈dnChdη〉 (left) andP (nCh) (right)

36

0 10 20 30

)φ∆η

∆gt

(T

psum

lt

0

05

1

15gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn24

26plusmn33

12plusmn143

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 10 20 30

)φ∆η

∆gt

(C

hlt

n

0

05

1

15gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

04plusmn05

13plusmn08

14plusmn100

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn58

06plusmn53

08plusmn193

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn16

15plusmn20

06plusmn114

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

gt05)T

|lt10 pη (|T1

)gt vs pT

TRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn10

02plusmn07

05plusmn22

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

gt05)T

|lt10 pη (|T1

gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn20

02plusmn11

03plusmn08

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 27 The Tevatron energy scan The underlying event (left average summed-pperp density andright average track density in the transverse region as function of leading-track pperp) for pp collisionsat 300 (bottom row) 900 GeV (middle row) and 1960 GeV (top row)

37

track pperp values 2 lt pT1 lt 10 GeV) This indicates that the energy scaling of the UE modeling and inparticular the details of its transition between central and peripheral collisions is still not satisfactorilyunderstood

5 Conclusions and Exhortation

We have presented a reanalysis of the constraints on fragmentation in ee collisions and applied theresults to update the final-state fragmentation parameters in PYTHIA 8 We combine these parameterswith a tune to hadron-collider data using a new NNPDF 23 LO QCD+QED PDF set which has beenencoded so it is available as an internal PDF set in PYTHIA 8 independently of LHAPDF [112]

In this PDF set as well as in our tune the value of the strong coupling for hard-scattering matrixelements is fixed to be αs(MZ) = 013 consistent with other LO determinations of it For initial-and final-state radiation our tune uses the effective value αs(MZ) = 01365 The difference isconsistent with an effective translation between the MS and CMW schemes We note that alternative(LO NLO and NNLO) NNPDF 23 QCD+QED sets with αs(MZ) = 0119 are also available inthe code for people who want to check the impact of using a different αs(MZ) value andor higher-order PDF sets on hard-scattering events For the purpose of such studies we point out that it ispossible in PYTHIA 8 to preserve most of the features of the shower- and underlying-event tuningby changing only the PDF for the hard-scattering matrix elements leaving the PDF choice for theshower evolution and MPI framework unaltered (see the PYTHIA 8 HTML manualrsquos PDF sectionunder PDFuseHard)

The updated parameters are available as an option starting from PYTHIA 8185 by setting

Tuneee = 7 and Tunepp = 14

By no means do we claim that this should be regarded as the final word in tuning the PYTHIA 8Monte Carlo model First of all the model continues to evolve For instance developments foreseenfor the near future include updates of colour reconnections diffraction and the treatment of g rarr qqsplittings Any of these should in principle be accompanied by a reevaluation of the model constraints

Moreover despite the comprehensive view of collider data we have attempted to take in thisstudy there still remains several issues that were not addressed including initial-final interferenceand coherence effects [113 114] (probably more a modelling issue than a tuning one) reliable esti-mates of theoretical uncertainties [8 17 24 29 97 115] diffraction14 [74 116 117] and other colour-singlet phenomena such as onium production long-distance (eg forward-backward forward-centraland ldquoridgerdquo-type) correlations [88 118ndash123] B-hadron decays [124] and tuning in the presence ofmatrix-element matching at LO and NLO (see [21 29 115 125 126] for recent phenomenologi-cal studies) Especially in the latter context of matrix-element matching we expect that in manycases PYTHIA 8 will be used together with codes such as ALPGEN [127] MADGRAPH [128]aMCatNLO [129] or POWHEG [130] either using the matching algorithms of those programs them-selves or via any of PYTHIArsquos several internal (LHEF-based [131]) implementations of matchingschemes (POWHEG [85] CKKW-L [132ndash134] MLM [135 136] UMEPS [137] NL3 [138] UN-LOPS [139]) The impact of such corrections on MC tuning depends on the details of the matchingscheme (especially its treatment of unitarity) and there is in general a non-negligible possibility ofldquomis-tuningrdquo when combining a stand-alone tune with ME corrections A simple example illustrating

14In particular the constraints on fragmentation mainly come from SLD and LEP where the non-perturbative parametersare clearly defined at the shower cutoff scaleQhad whereas diffraction is dominated by soft physics for which the definitionof the effective hadronization scale is less clear The amount of MPI in hard diffractive events also requires tuning

38

this is the effective value of αs(MZ) which for a leading-order tune is typically of order 013 whilea consistent NLO correction scheme should be compatible with values closer to 012 [29] There isalso the question of the running order of αs The propagation of such changes from the level of hardmatrix elements through the shower and hadronization tuning process are still not fully explored andhence we advise users to perform simple cross-checks such as checking the distributions presented inthis paper before and after applying matrix-element corrections Parameters that appear on both sidesof the matching such as αs should also be checked for consistency [21]

We noted several issues concerning the ee data used to constrain the fragmentation modelling thatit would be good to resolve In particular we find some tensions between the identified-particle ratesextracted from 1) HEDPATA 2) Sec 46 of the PDG and 3) the Z boson summary table in the PDGas discussed in more detail in section 2 and concerning which we made some (subjective) decisionsto arrive at a set of hopefully self-consistent constraints for this work We also note that the overallprecision of the fragmentation constraints could likely be significantly improved by an FCC-ee typemachine such as Tera-Z a possibility we hope to see more fully explored in the context of future eeQCD phenomenology studies

We conclude that the new parameter set does improve significantly on the previous default valuesin several respects including better agreement with data on

1 the net strangeness fraction (has been increased by 10 reflected not only in improved kaonand hyperon yields but also in the Ds and Bs fractions)

2 the ultra-hard fragmentation tail (has been softened especially for leading baryons and for Dand B hadrons)

3 the pTZ spectrum (softened at low pTZ)

4 the minimum-bias charged multiplicity in the forward region (has increased by 10)

5 the underlying event at 7 TeV (is very slightly higher than before)

Some questions that remain open include the following We see a roughly 20 excess of verysoft kaons in both ee and pp environments cf figs 6 and 23 despite the overall kaon yields beingwell described and the overall baryon yields at LHC appear to be underestimated by at least 30despite good agreement at LEP The momentum spectra of heavier strange particles are also poorlyreproduced in particular at LHC It is interesting and exciting that some of the LHC spectra appearto be better described by allowing collective flow in a fraction of events (cf the EPOS model [140])though we believe the jury is still out on whether this accurately reflects the underlying physics Forinstance it has been argued that colour reconnections can mimick flow effects [90] and they may alsobe able to modify the yield of baryons if the creationdestruction of string junctions is allowed [141]We look forward to future discussions on these issues

We round off with an exhortation for follow-ups on this study to provide

bull Not only central tunes experiments and other user-end colleagues need more than central de-scriptions of data there is an increasing need for serious uncertainty estimates In the contextof tune variations it is important to keep in mind that the modelling uncertainties are often in-trinsically non-universal Therefore the constraints obtained by considering data uncertaintiesonly (eg in the spirit of PROFESSORrsquos eigentunes [17]) can at most constitute a lower boundon the theoretical uncertainty (similarly to the case for PDFs) A serious uncertainty estimateincludes some systematic modelling variation irrespectively of and in addition to what data

39

allows (eg in the spirit of the Perugia set of tunes for PYTHIA 6 [8]) We therefore hope thefuture will see more elaborate combinations of data- and theory-driven approaches to systematictune uncertainties

bull Not only global tunes the power of MC models lies in their ability to simultaneously describea large variety of data hence we do not mean to imply that one should give up on universalityand tune to increasingly specific corners of phase space disregarding (or de-emphasizing withlower weights) all others However as proposed in [97] one can obtain useful explicit tests ofthe universality of the underlying physics model by performing independent tunes on separateldquophysics windowsrdquo say in the forward vs central regions for different event-selection crite-ria at different collider energies or even for different collider types In this connection justmaking one global ldquobest-fitrdquo tune may obscure tensions between the descriptions of differentcomplementary data sets By performing independent tunes to each data set separately andchecking the degree of universality of the resulting parameters one obtains a powerful crosscheck on the underlying physics model If all sets produce the same or similar parameters thenuniversality is OK hence a global tune makes very good sense and the remaining uncertain-ties can presumably be reliably estimated from data alone If instead some data sets resultin significantly different tune parameters one has a powerful indication that the universality ofthe underlying modeling is breaking down which can lead to several productive actions 1) itcan be taken into account in the context of uncertainty variations 2) the nature of the data setsfor which non-universal tune parameters are obtained can implicitly indicate the nature of theproblem leading to more robust conclusions about the underlying model than merely whether atune cancannot fit the data and 3) the observations can be communicated to the model authorsin a more unambiguous way hopefully resulting in a speedier cycle of model improvements

We hope that the Monash 2013 tune parameters may serve as a useful starting point for phe-nomenology studies and for future PYTHIA 8 tuning efforts

Acknowledgments

We thank S Mrenna M Ritzmann and T Sjostrand for comments on the manuscript and L de Nooijfor pointing us to the ALICE Klowast and φ measurements [142] and to the ATLAS φ measurementsin [143] The work of J R is supported by an STFC Rutherford Fellowship STK0052271 Thiswork was supported in part by the Research Executive Agency (REA) of the European Commissionunder the Grant Agreements PITN-GA-2012-315877 (MCnet)

A Monash 2013 Tune Parameters

In tabs 3 ndash 7 we list the FSR fragmentation parameters for the Monash tune of PYTHIA Forreference we compare them to the current default parameters

40

FSR Parameters Monash 13 (Default) CommentTimeShoweralphaSvalue = 01365 = 01383 Effective alphaS(mZ) valueTimeShoweralphaSorder = 1 = 1 Running orderTimeShoweralphaSuseCMW = off = off Translation from MS to CMWTimeShowerpTmin = 050 = 040 Cutoff for QCD radiationTimeShowerpTminChgQ = 050 = 040 Cutoff for QED radiationTimeShowerphiPolAsym = on = on Asymmetric azimuth distributions

Table 3 Final-state radiation (FSR) parameters

HAD Parameters Monash 13 (Default) Comment String breaks pT and z distributionsStringPTsigma = 0335 = 0304 Soft pT in string breaks (in GeV)StringPTenhancedFraction = 001 = 001 Fraction of breakups with enhanced pTStringPTenhancedWidth = 20 = 20 Enhancement factorStringZaLund = 068 = 03 Lund FF a (hard fragmentation supp)StringZbLund = 098 = 08 Lund FF b (soft fragmentation supp)StringZaExtraSquark = 00 = 00 Extra a when picking up an s quarkStringZaExtraDiquark = 097 = 050 Extra a when picking up a diquarkStringZrFactC = 132 = 100 Lund-Bowler c-quark parameterStringZrFactB = 0855 = 067 Lund-Bowler b-quark parameter Flavour composition mesonsStringFlavProbStoUD = 0217 = 019 Strangeness-to-UD ratioStringFlavmesonUDvector = 05 = 062 Light-flavour vector suppressionStringFlavmesonSvector = 055 = 0725 Strange vector suppressionStringFlavmesonCvector = 088 = 106 Charm vector suppressionStringFlavmesonBvector = 22 = 30 Bottom vector suppressionStringFlavetaSup = 060 = 063 Suppression of eta mesonsStringFlavetaPrimeSup = 012 = 012 Suppression of etarsquo mesons Flavour composition baryonsStringFlavprobQQtoQ = 0081 = 009 Diquark rate (for baryon production)StringFlavprobSQtoQQ = 0915 = 1000 Strange-diquark suppressionStringFlavprobQQ1toQQ0 = 00275 = 0027 Vector diquark suppressionStringFlavdecupletSup = 10 = 10 Spin-32 baryon suppressionStringFlavsuppressLeadingB = off = off Optional leading-baryon suppressionStringFlavpopcornSpair = 09 = 05 StringFlavpopcornSmeson = 05 = 05

Table 4 String-breaking parameters

PDF and ME Parameters Monash 13 (Default) CommentPDFpSet = 13 = 8 PDF set for the protonSigmaProcessalphaSvalue = 0130 0135 alphaS(MZ) for matrix elementsMultiPartonInteractionsalphaSvalue = 0130 0135 alphaS(MZ) for MPI

Table 5 Parton-distribution (PDF) and Matrix-Element (ME) parameters

41

ISR Parameters Monash 13 (Default) CommentSpaceShoweralphaSvalue = 01365 = 0137 Effective alphaS(mZ) valueSpaceShoweralphaSorder = 1 = 1 Running orderSpaceShoweralphaSuseCMW = off = off Translation from MS to CMWSpaceShowersamePTasMPI = off = off ISR cutoff typeSpaceShowerpT0Ref = 20 = 20 ISR pT0 cutoffSpaceShowerecmRef = 70000 = 18000 ISR pT0 reference ECM scaleSpaceShowerecmPow = 00 = 00 ISR pT0 scaling powerSpaceShowerrapidityOrder = on = on Approx coherence via y-orderingSpaceShowerphiPolAsym = on = on Azimuth asymmetries from gluon polSpaceShowerphiIntAsym = on = on Azimuth asymmetries from interferenceTimeShowerdampenBeamRecoil = on = on Recoil dampening in final-initial dipolesBeamRemnantsprimordialKTsoft = 09 = 05 Primordial kT for soft procsBeamRemnantsprimordialKThard = 18 = 20 Primordial kT for hard procsBeamRemnantshalfScaleForKT = 15 = 10 Primordial kT softhard boundaryBeamRemnantshalfMassForKT = 10 = 10 Primordial kT softhard mass boundary

Table 6 Initial-state radiation (ISR) and primordial-kT parameters

MPI Parameters Monash 13 (Default) CommentMultipartonInteractionspT0Ref = 228 = 2085 MPI pT0 IR regularization scaleMultipartonInteractionsecmRef = 70000 = 18000 MPI pT0 reference ECM scaleMultipartonInteractionsecmPow = 0215 = 019 MPI pT0 scaling powerMultipartonInteractionsbProfile = 3 = 3 Transverse matter overlap profileMultipartonInteractionsexpPow = 185 = 20 Shape parameterBeamRemnantsreconnectRange = 18 = 15 Colour ReconnectionsSigmaTotalzeroAXB = on = on Carried over from 4CSigmaDiffractivedampen = on = on Carried over from 4CSigmaDiffractivemaxXB = 650 = 650 Carried over from 4CSigmaDiffractivemaxAX = 650 = 650 Carried over from 4CSigmaDiffractivemaxXX = 650 = 650 Carried over from 4CDiffractionlargeMassSuppress = 40 = 20 High-mass diffraction suppression power

Table 7 Multi-Parton-Interaction (MPI) Colour-Reconnection (CR) and Diffractive parameters

42

B Additional Plots

B1 LEP Event-Shape Distributions

To keep the main body of the paper as uncluttered as possible we collect various plots of event-shapedistributions in figs 28 and 29 separated into light-flavour and b-tagged events on the left and rightrespectively

The experimental results come from the L3 experiment [26] However since the data points areonly available with 3-digit precision some of the least populated bins contain artifacts like uncertain-ties being reported as exactly zero etc Thus we have been forced to make the following modificationsto the data set

The statistical uncertainty was reported as zero for the last two bins of light-flavour Thrust as wellas for the last bin of the C D and BT parameters Uncertainties lt 10minus3 were derived using anapproximate statistical scaling based on the contents and uncertainties of the other bins Likewise thesystematical uncertainty for the last bin of Thrust was given as zero which we have replaced by theupper limit 5times 10minus4 The last bin of BT quoted a measured y value of zero removed in this study

For the heavy-flavour tagged event shapes more significant rounding issues were present Thusseveral of the first and last bins of each distribution either quoted zero (statistical andor systematic)uncertainties or ones with only a single digit of precision (such as 0001 for which the rounding errorcould be up to sim 50) We have interpreted all such values conservatively inserting by hand a fourthdigit on the uncertainties as large as could be consistent with rounding

B2 Additional Particle Spectra

In addition to the K and Λ spectra shown in the main body of the paper (sections 22 and 35) wehere include for reference the x spectra of φ mesons protons and Ξ baryons at LEP in figs 30 and 31the pT spectrum of Klowast mesons and the rapidity and pT spectra of φ mesons at LHC in fig 32 (withabsolute normalizations to the number of inelastic events) and the rapidity spectrum of Ξ baryons atLHC in fig 33

The transverse-momentum spectra of Klowast and φ mesons in fig 32 exhibit the same qualitativebehaviour as that of the KS mesons (fig 23) namely an excess at very soft momenta below sim 500MeV and a depletion at slightly higher momenta between 1 and 2 GeV As discussed in section 35we did not find a way to remove these undesirable features in the Monash 2013 tune suggesting thatthis is an issue that further theoretical modeling will be needed to resolve

The rapidity spectrum of Ξ baryons fig 33 shows that although the Monash tune does producemore Ξ baryons overall (as expected also from the relative increase of Ξ production at LEP cf fig 5)there is still a significant deficit of Ξ baryons at the LHC almost a factor 2 compared with the dataThis is qualitatively similar to the situation for Λ baryons (fig 24) discussed in section 35 Sincenew physics mechanisms may be required to ldquoexplainrdquo the missing baryons we conclude that furthermeasurements and better precision on both the Λ and Ξ sectors (in addition to any other baryonsthat may be accessible) would be highly interesting More explicit recommendations can be found insections 35 and 5

43

0 01 02 03 04

d(1

-T)

σ d

σ1

-310

-210

-110

1

10

2101-Thrust (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn03

01plusmn04

02plusmn05

V I

N C

I A

R O

O T

1-T (udsc)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

d(1

-T)

σ dσ

1

-310

-210

-110

1

10

2101-T (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn13

02plusmn12

02plusmn14

V I

N C

I A

R O

O T

1-T (b)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210

310C Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn03

00plusmn04

01plusmn04

V I

N C

I A

R O

O T

C0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210 C parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn17

01plusmn24

01plusmn27

V I

N C

I A

R O

O T

C (b)0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn06

01plusmn06

V I

N C

I A

R O

O T

D0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn24

02plusmn21

02plusmn26

V I

N C

I A

R O

O T

D (b)0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

Figure 28 Hadronic Z decays atradics = 912 GeV The T C and D event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

44

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn02

01plusmn03

01plusmn04

V I

N C

I A

R O

O T

WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn05

01plusmn12

01plusmn17

V I

N C

I A

R O

O T

(b)WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn02

00plusmn02

01plusmn03

V I

N C

I A

R O

O T

TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

04plusmn24

08plusmn49

08plusmn55

V I

N C

I A

R O

O T

(b)TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

Figure 29 Hadronic Z decays atradics = 912 GeV The BW and BT event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

45

0 02 04 06 08 1

dx

φgt

dn

φ1

ltn

-210

-110

1

10 )φx(

Pythia 8183Data from ALEPH_1996_S3486095d40-x01-y01

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn37

02plusmn53

03plusmn62

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

0608

112141618

Figure 30 Hadronic Z decays atradics = 912 GeV φ meson x spectrum

-5 -4 -3 -2 -1 0

dx

pgt

dn

p1

ltn

-410

-310

-210

-110

1

10

210) (Combined)px(p+

Pythia 8183Data from Zeit Phys C66 (1995) 355 PhysRev D59 (1998) 052001

ALEPH+SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn08

00plusmn09

00plusmn08

V I

N C

I A

R O

O T

px-5 -4 -3 -2 -1 0

The

ory

Dat

a

06

08

1

12

14

0 02 04

dx

Ξgt

dn

Ξ1

ltn

-110

1

10

)plusmnΞx(

Pythia 8183Data from Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn11

02plusmn13

02plusmn14

V I

N C

I A

R O

O T

Ex0 02 04

The

ory

Dat

a

06

08

1

12

14

Figure 31 Hadronic Z decays atradics = 912 GeV pplusmn and Ξplusmn x spectra

46

0 2 4 6

Td

pK

d

nIN

EL

1N

-510

-410

-310

-210

-110

(INEL |y|lt05)T

p0K

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn35

01plusmn26

01plusmn29

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 2 4 6

Td

pφ

dn

INE

L1

N-510

-410

-310

-210

-110

gt04)T

(INEL |y|lt05 pT

pφ

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn88

03plusmn84

04plusmn173

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

)dy

[mb]

-K

+K

rarrφ(σd

0

05

1

15

2 Rapidity (INEL ATLAS cuts)φ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn14

01plusmn19

01plusmn34

V I

N C

I A

R O

O T

pp 7000 GeV

|y|0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

06 08 1 12

[mb

GeV

]φ

T)

dp-

K+

Krarrφ(

σd

0

05

1

15

2

25 (INEL ATLAS cuts)

T pφ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn21

01plusmn30

02plusmn53

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p06 08 1 12

The

ory

Dat

a

06

08

1

12

14

Figure 32 pp collisions at 7 TeV Top row Klowast and φ pperp spectra compared with ALICE data [142]Bottom row φ rapidity and pperp spectrum compared with ATLAS data [143] The ATLAS cuts areφrarr K+Kminus pperpφ isin [05 12] GeV |y(φ)| lt 08 pperpK gt 023 GeV |pK | lt 08 GeV

47

0 05 1 15 2

dygt

Ξ lt

dnN

SD

1N

0

001

002

003

004)d|y|gt (NSD)Ξltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn89

01plusmn129

01plusmn192

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

0

05

1

15

2

Figure 33 pp collisions at 7 TeV Ξminus rapidity spectrum compared with CMS data [99]

48

B3 Energy Scaling of σ2rarr2(pTmin) vs σinel from 200 GeV to 100 TeV

In fig 34 we show the LO QCD 2rarr 2 cross section integrated above pTmin as a function of pTminin pp collisions at 4 different CM energies complementing and expanding on the 8-TeV CM energyshown in the main body of the paper We compare two different αs and PDF choices correspondingto those made in tunes Monash 13 (blue filled dots) and 4C (red open squares) respectively As areference for the total inelastic cross section at each energy we base ourselves on the best-fit curvein the TOTEM cross-section measurement paper [72] which in turn represents a fit produced by theCOMPETE collaboration [144] Uncertainties are rough conservative estimates based on the plot inthe TOTEM paper but they are in any case too small to significantly affect conclusions about the scaleat which the partonic cross section saturates the hadronic one

We observe that the pTmin value for which the LO QCD 2 rarr 2 partonic cross section formallybecomes equal to the total inelastic cross section (strongly suggesting that every event has at leastone such mini-jet pair) rises from values around 1 ndash 2 GeV at energies

radics lt 1 TeV to 5 GeV atradic

s = 13 TeV and finally 10 GeV atradics = 100 TeV

49

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from PhysRevLett 105 (2010) 022002

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn00

00plusmn03

00plusmn71

V I

N C

I A

R O

O T

pp 7000 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

55 6 65

gtηd

Ch

ltdn

Tot

em1

n

0

1

2

3

4

5

6|lt65)ηgt004 53lt|

T1 pge

chgt (nηd

Chltdn

Pythia 8185Data from EurophysLett 98 (2012) 31002

TOTEMPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn01

00plusmn27

00plusmn62

V I

N C

I A

R O

O T

pp 7000 GeV

η55 6 65

The

ory

Dat

a

06

08

1

12

14

3 35 4 45 5

gtηlt

dEd

0

100

200

300

400

500|lt465)η1 in both 323lt|ge

chMB Fwd E Flow (n

Pythia 8185Data from JHEP 11 (2011) 148

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn01

00plusmn04

00plusmn22

V I

N C

I A

R O

O T

pp 7000 GeV

η3 35 4 45 5

The

ory

Dat

a

06

08

1

12

14

Figure 19 Charged-particle pseudorapidity distributions and forward energy flow in min-bias ppcollisions at 7 TeV compared to CMS [92 93] and TOTEM [94] data

29

0 50 100

0

05

1

15

2

25|lt25)ηgt05 |

T) (p

Chgt(n

Tltp

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn05

01plusmn01

05plusmn07

V I

N C

I A

R O

O T

pp 7000 GeV

0 50 100

The

ory

Dat

a

06

08

1

12

14

0 50 100 150 200

0

05

1

15|lt25)ηgt01 |

T 2 pge

Ch) (n

Chgt(n

TSoft ltp

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn06

00plusmn08

03plusmn40

V I

N C

I A

R O

O T

pp 7000 GeV

0 50 100 150 200

The

ory

Dat

a06

08

1

12

14

Figure 20 Average-pperp vs charged-multiplicity distributions in min-bias pp collisions at 7 TeV withstandard (left) and soft (right) fiducial cuts compared to ATLAS data [91]

multiplicity by itself is a very difficult quantity to extract reliable conclusions from Note also that theCMS measurement [92] shown in the top pane of fig 19 was corrected to an unphysical ldquonon-singlediffractiverdquo event definition which essentially amounts to switching off single-diffractive contributionsin the MC generator (We note that later CMS measurements instead use a physical observable relatedto the diffractive mass to define NSD) For the comparisons to CMS NSD data shown here the single-diffractive contributions were switched off in the generator With these caveats in mind we note thatboth the 4C and Monash 2013 tunes are in good agreement with the CMS measurement with theMonash one giving a slightly lower central charged-track density (by about 5) This is closer to thevalues observed in data though as already noted in section 11 we do not regard differences at the 5level as significant

In the bottom two panes of fig 19 we focus on the forward region (with physical event selections)In particular we see that the NNPDF set [20] generates a broader rapidity spectrum so that while theactivity in the central region (top pane) is reduced slightly the activity in the very forward regionactually increases and comes into agreement with the TOTEM measurement [94] covering the range53 lt |η| lt 64 The bottom right-hand pane shows the forward energy flow measured by CMS [93]in the intermediate region 323 lt |η| lt 465 The dependence on η is a bit steeper in the Monashtune than in the previous one and more similar to that seen in the data

A complementary observable which is highly sensitive to interconnection effects between theMPI (and hence eg to the effects of ldquocolour reconnectionsrdquo [95]) is the average charged-particlepperp as a function of the number of charged particles In a strict leading-colour picture each MPIwould cause one or two new strings to be stretched between the remnants but each such string wouldbe independent (modulo endpoint effects) therefore (modulo jets) the pperp spectrum of the hadronsproduced by each of these strings would be independent of the number of strings The result would bea flat 〈pperp〉 (nCh) spectrum Jets and colour reconnections both produce a rising spectrum The spectraobserved by ATLAS [91] are compared to the Monash 2C and 4C tunes in fig 20 for standard

30

0 1 2 3

gtφ|dη

d|

Ch

n2

ltd

0

02

04

06

08

1gt01)

T|lt25 pηgt1 (|

Tlead| wrt pφ∆|

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn16

00plusmn19

00plusmn56

V I

N C

I A

R O

O T

pp 7000 GeV

| [rad]φ∆|0 1 2 3

The

ory

Dat

a

06

08

1

12

14

0 1 2 3

gtφ|dη

d|

Ch

n2

ltd

0

05

1

15

2

gt05)T

|lt25 pηgt5 (|Tlead

| wrt pφ∆|

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn05

00plusmn05

00plusmn70

V I

N C

I A

R O

O T

pp 7000 GeV

| [rad]φ∆|0 1 2 3

The

ory

Dat

a06

08

1

12

14

Figure 21 pp collisions at 7 TeV ∆φ of charged particles with respect to the hardest track for twodifferent hardest-track triggers compared with ATLAS data [98]

(left) and soft (right) fiducial cuts Both of the Monash and 4C tunes reproduce the data quite wellwith χ2

5 lt 1 while the older tune 2C had a higher CR strength optimized to describe Tevatrondata [96] We certainly consider the energy scaling of the effective CR strength among the mostuncertain parameters of the current min-biasunderlying-event modelling (a similar conclusion wasreached for the CR modelling in PYTHIA 6 in [97]) and intend to study the physics aspects of thisissue more closely in a forthcoming paper

For a more differential look at the event structure we consider the charged-track ∆φ distributionswith respect to the azimuthal angle of the leading track in fig 21 compared with ATLAS data [98]The plot in the left-hand pane corresponds to a requirement of pperplead ge 1 GeV while the one in theright-hand pane is for a harder trigger pperplead ge 5 GeV The former can roughly be taken as charac-teristic of min-bias events while the latter is related to the differential distribution of the underlyingevent In both cases the activity in the wide-angle region near π2 is significantly better described bythe 4C and Monash 2013 tunes (which agrees with their improved description of the overall activity)while there is a too strong peaking at low ∆φ especially for the lowest pperplead cut (left) possibly indi-cating that the structure of the min-bias events is still slightly too ldquolumpyrdquo (ie jetty) For the higherpperplead cut (right) the overcounting at very low ∆φ is already significantly milder and we observe agood agreement with the data

Turning now to the underlying event (UE) what matters most for high-pperp jet studies is that theMC models describe the UE contamination per ∆R jet area The most important UE observable fromthis perspective is thus the pperp sum density in the UE and its fluctuations For charged particles atLHC typically a pperp cut of 500 MeV is relevant since softer tracks will form helices and hence notcontribute to calorimetric jet energies Neutral particles are of course relevant across all pperp scalesIn fig 22 we show the charged pperp sum density (left with the lowest possible pperp cut of 100 MeV)and the charged-track density (right with a pperp cut of 500 MeV) in the so-called ldquoTransverse Regionrdquo(defined by 60 lt ∆φ lt 120 with respect to the leading track) inside the ATLAS acceptance of

31

0 5 10 15 20

)φ∆η

∆gt

(T

psum

lt

0

05

1

15

2

25gt01)

T|lt25 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn03

01plusmn09

02plusmn112

V I

N C

I A

R O

O T

pp 7000 GeV

(hardest track) [GeV]T1

p0 5 10 15 20

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20

)φ∆η

∆gt

(C

hlt

n

0

05

1

15

2

25gt05)

T|lt25 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn02

00plusmn04

02plusmn104

V I

N C

I A

R O

O T

pp 7000 GeV

(hardest track) [GeV]T1

p0 5 10 15 20

The

ory

Dat

a06

08

1

12

14

Figure 22 pp collisions at 7 TeV UE (ldquoTransverse regionrdquo) transverse-momentum sum density (left)and charged-track density (right) compared with ATLAS data [98]

|η| lt 25 [98] As is now well known the Tevatron extrapolations (represented here by Tune 2C)predicted a UE level which was 10 ndash 20 below the LHC data Both the current default tune 4C(which included LHC data) and the Monash 2013 tune exhibit significantly better agreement with theLHC measurements with the Monash one giving a slight additional improvement in the χ2

5 valuesWe conclude that the Monash 2013 tune parameters are appropriate for both min-bias and UE studies

35 Identified Particles at LHC

While the description of inclusive charged particles discussed in the previous section is acceptablelarger discrepancies emerge when we consider the spectra of identified particles We here focus onstrange particles in particular K0

S mesons and Λ0 hyperons in figs 23 and 24 respectively Theexperimental measurements come from CMS [99] Additional comparisons to strange-particle spectra(Klowast φ and Ξ) are collected in appendix B2

In the K0S rapidity distribution shown in the left-hand pane of fig 23 we observe that tune 4C

exhibits a mild underproduction of about 10 Though it might be tempting to speculate whether thiscould indicate some small reduction of strangeness suppression in pp collisions however we alreadynoted in section 21 that the strangeness production in ee collisions also needed to be increased byabout 10 After this adjustment we see that the overall K0

S yield in the Monash 2013 tune is fullyconsistent with the CMS measurement Nonetheless we note that the momentum distribution is stillnot satisfactorily described as shown in the right-hand pane of fig 23 Our current best guess istherefore that the overall rate of strange quarks is consistent at least in the average min-bias collision(dedicated comparisons in high-multiplicity samples would still be interesting) but that the phase-space distribution of strange hadrons needs more work Similarly to the case in ee collisions cf fig 6the model predicts too many very soft kaons though we do not currently know whether there is adynamic link between the ee and pp observations

For strange baryons we note that the increase in the Λ0 fraction in ee collisions (cf fig 5) does

32

0 05 1 15 2

dygt

K lt

dnN

SD

1n

0

02

04

06

08)d|y|gt Rapidity (NSD)

S

0ltdn(K

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn01

00plusmn09

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8 10

Td

pK

dn

NS

D1

N

-510

-410

-310

-210

-110

1

10 (|y|lt20 NSD)

T pS

0K

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn78

01plusmn34

02plusmn22

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6 8 10

The

ory

Dat

a06

08

1

12

14

Figure 23 pp collisions at 7 TeV K0S rapidity and pperp spectrum compared with CMS data [99]

0 05 1 15 2

dygt

Λ lt

dnN

SD

1N

0

01

02

03

04)d|y|gt (NSD)0Λltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn64

00plusmn78

01plusmn147

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8 10

Td

pΛ

dn

Λ1

n

-510

-410

-310

-210

-110

1

10 (|y|lt20 NSD)

T p0Λ

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn59

03plusmn66

05plusmn105

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6 8 10

The

ory

Dat

a

06

08

1

12

14

Figure 24 pp collisions at 7 TeV Λ0 rapidity and pperp spectrum compared with CMS data [99]

not result in an equivalent improvement of the Λ0 rate in pp collisions shown in fig 24 The Monash2013 tune still produces only about 23 of the observed Λ0 rate (and just over half of the observedΞminus rate cf appendix B2) We therefore believe it to be likely that an additional source of net baryonproduction is needed (at least within the limited context of the current PYTHIA modelling) in orderto describe the LHC data The momentum spectrum is likewise quite discrepant exhibiting an excessat very low momenta (stronger than that for kaons) a dip between 1ndash4 GeV and then an excess of veryhard Λ0 production The latter hard tail is somewhat milder in the Monash 2013 tune than previously

33

and it may be consistent with the trend also seen in the Λ0 spectrum at LEP cf fig 6 We concludethat baryon production still requires further modelling and tuning efforts

4 Energy Scaling

Though energy scaling these days mostly refers to the scaling of pp collisions (see eg [97]) animportant first step is to consider the scaling of observables in ee rarr γlowastZ rarr hadrons This scalingcontains information on the relative contributions of perturbative and non-perturbative fragmentationThus at low ee energies the non-perturbative components of the fragmentation model dominatewhile perturbative bremsstrahlung increases in importance towards higher ee energies In fig 25we consider the scaling of the average charged-particle multiplicity and that of charged Kaons andLambda baryons from CM energies of 14 GeV to 200 GeV obtained from measurements availableat HEPDATA Below the Z pole the measurements we include mostly come from TASSO [100]though a few points on 〈nCh〉 come from HRS (at 29 GeV [101]) and TOPAZ (at 578 GeV [102]) Atthe Z pole the data come from the four LEP experiments [38 51ndash53] with the latter extending alsoto energies above MZ [103ndash108] For completeness and as reference for future ee collider studiesmodel extrapolations for CM energies up to 1000 GeV are also shown (though still only including theeerarr γlowastZ rarr hadrons component as usual with photon ISR switched off)

From the plots in fig 25 it is clear that there are no significant differences between the energyscaling of the three ee tunes considered here (mainly reflecting that they have been tuned to samereference point at 912 GeV and that their scaling is dictated by the same underlying physics model)and that their energy dependence closely matches that observed in data However the increasedamount of non-perturbative strangeness production in the Monash tune leads to a better agreementwith the overall normalization of the Kplusmn and Λ rates at all energies

Moving to pp collisions the plots in fig 26 show the scaling of the average charged multiplicity(left column) and multiplicity distributions (right column) in min-bias collisions from 7000 GeV (toprow) to 900 GeV (middle row) and 200 GeV (bottom row) compared with data from CMS [92 109]ATLAS [91] and UA5 [110 111] We regret the omission of additional relevant min-bias measure-ments from the Tevatron and RHIC experiments here but have chosen to focus in this paper mainlyon the LHC The comparisons at 7 TeV were already discussed in the main section on pp collisionssection 3 At 900 GeV the Monash 2013 tune again gives a roughly 5 lower average central chargedmultiplicity than the 4C one with a better description of the tail towards high multiplicities At 200GeV the UA5 measurement we include here extends over the full rapidity and pperp range hence the in-terplay between diffraction and low-multiplicity non-diffractive processes is presumably (much) moreimportant We believe imperfections in this modelling to be the likely cause of the significant discrep-ancies observed at high η and for nCh le 20 at these energies Since a dedicated study of this interplayis beyond the scope of this study we limit ourselves merely to stating this observation as a point forfuture studies to help clarify

Finally in fig 27 we compare to the underlying event measured in the highly useful energyscan that was performed at the Tevatron in the last days before its shutdown [22 23] during whichextremely high min-bias statistics were collected at 300 and 900 GeV CM energy over a period of afew days As was already noted in section 3 the UE at 7 TeV is slightly larger in the Monash 2013tune than in tune 4C As can be seen from the plots here the two tunes give comparable results for allthe Tevatron energies Interestingly the UE plateau region at 900 and 1960 GeV is reached sooner inthese models than in the data translating to a roughly 10 - 20 too low UE level for leading-trackpperp values in the neighbourhood of the transition from the rise to the plateau (roughly for leading-

34

14 22 29 35 44 58 91 91 91 91 133 161 183 189 200 250 350 500 1000

gtC

hlt

n

0

20

40

60

Average Charged Multiplicity vs ECM

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN25

χ00plusmn03 00plusmn02 00plusmn02

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 22 29 35 44 58 91 91 91 91 133 161 183 189 200 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

14 22 35 44 91 91 133 161 183 189 250 350 500 1000

gtK

ltn

0

2

4

6 Multiplicity vs ECM+-Average K

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN25

χ00plusmn06 00plusmn20

00plusmn18

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 22 35 44 91 91 133 161 183 189 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

14 35 91 91 91 91 133 200 250 350 500 1000

gtΛ

ltn

0

02

04

06

08

1

12 Multiplicity vs ECM0ΛAverage

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn06

01plusmn22

01plusmn18

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 35 91 91 91 91 133 200 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

Figure 25 e+eminus rarr hadrons Energy scaling of 〈nCh〉 〈nKplusmn〉 and 〈nΛ〉 in e+eminus rarr qq eventsincluding comparisons to measurements from HEPDATA for CM energies from 14 GeV to 200 GeVAlso shown are model extrapolations up to 1000 GeV

35

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from PhysRevLett 105 (2010) 022002

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn00

00plusmn03

00plusmn71

V I

N C

I A

R O

O T

pp 7000 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

0 50 100

)C

hP

rob(

n

-710

-610

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn27

00plusmn27

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

Chn0 50 100

The

ory

Dat

a

06

08

1

12

14

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from JHEP 1002 (2010) 041

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn03

00plusmn05

00plusmn29

V I

N C

I A

R O

O T

pp 900 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

0 10 20 30 40

)C

hP

rob(

n

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn17

01plusmn25

02plusmn127

V I

N C

I A

R O

O T

pp 900 GeV

Chn0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

0 1 2 3 4 5

gtηd

ch lt

dnN

SD

1n

0

1

2

3

4

5gt (NSD)ηd

chltdn

Pythia 8185Data from ZPhys C33 (1986) 1-6

UA5PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn36

00plusmn24

00plusmn16

V I

N C

I A

R O

O T

ppbar 200 GeV

η0 1 2 3 4 5

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)C

hP

rob(

n

-410

-310

-210

-110

1

)T

|lt05 all pηChg Mult (NSD |

Pythia 8185Data from ZPhys C43 (1989) 357

UA5PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn24

00plusmn24

00plusmn08

V I

N C

I A

R O

O T

ppbar 200 GeV

Chn0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 26 Min-bias pp events from 200 to 7000 GeV Energy scaling of 〈dnChdη〉 (left) andP (nCh) (right)

36

0 10 20 30

)φ∆η

∆gt

(T

psum

lt

0

05

1

15gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn24

26plusmn33

12plusmn143

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 10 20 30

)φ∆η

∆gt

(C

hlt

n

0

05

1

15gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

04plusmn05

13plusmn08

14plusmn100

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn58

06plusmn53

08plusmn193

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn16

15plusmn20

06plusmn114

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

gt05)T

|lt10 pη (|T1

)gt vs pT

TRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn10

02plusmn07

05plusmn22

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

gt05)T

|lt10 pη (|T1

gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn20

02plusmn11

03plusmn08

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 27 The Tevatron energy scan The underlying event (left average summed-pperp density andright average track density in the transverse region as function of leading-track pperp) for pp collisionsat 300 (bottom row) 900 GeV (middle row) and 1960 GeV (top row)

37

track pperp values 2 lt pT1 lt 10 GeV) This indicates that the energy scaling of the UE modeling and inparticular the details of its transition between central and peripheral collisions is still not satisfactorilyunderstood

5 Conclusions and Exhortation

We have presented a reanalysis of the constraints on fragmentation in ee collisions and applied theresults to update the final-state fragmentation parameters in PYTHIA 8 We combine these parameterswith a tune to hadron-collider data using a new NNPDF 23 LO QCD+QED PDF set which has beenencoded so it is available as an internal PDF set in PYTHIA 8 independently of LHAPDF [112]

In this PDF set as well as in our tune the value of the strong coupling for hard-scattering matrixelements is fixed to be αs(MZ) = 013 consistent with other LO determinations of it For initial-and final-state radiation our tune uses the effective value αs(MZ) = 01365 The difference isconsistent with an effective translation between the MS and CMW schemes We note that alternative(LO NLO and NNLO) NNPDF 23 QCD+QED sets with αs(MZ) = 0119 are also available inthe code for people who want to check the impact of using a different αs(MZ) value andor higher-order PDF sets on hard-scattering events For the purpose of such studies we point out that it ispossible in PYTHIA 8 to preserve most of the features of the shower- and underlying-event tuningby changing only the PDF for the hard-scattering matrix elements leaving the PDF choice for theshower evolution and MPI framework unaltered (see the PYTHIA 8 HTML manualrsquos PDF sectionunder PDFuseHard)

The updated parameters are available as an option starting from PYTHIA 8185 by setting

Tuneee = 7 and Tunepp = 14

By no means do we claim that this should be regarded as the final word in tuning the PYTHIA 8Monte Carlo model First of all the model continues to evolve For instance developments foreseenfor the near future include updates of colour reconnections diffraction and the treatment of g rarr qqsplittings Any of these should in principle be accompanied by a reevaluation of the model constraints

Moreover despite the comprehensive view of collider data we have attempted to take in thisstudy there still remains several issues that were not addressed including initial-final interferenceand coherence effects [113 114] (probably more a modelling issue than a tuning one) reliable esti-mates of theoretical uncertainties [8 17 24 29 97 115] diffraction14 [74 116 117] and other colour-singlet phenomena such as onium production long-distance (eg forward-backward forward-centraland ldquoridgerdquo-type) correlations [88 118ndash123] B-hadron decays [124] and tuning in the presence ofmatrix-element matching at LO and NLO (see [21 29 115 125 126] for recent phenomenologi-cal studies) Especially in the latter context of matrix-element matching we expect that in manycases PYTHIA 8 will be used together with codes such as ALPGEN [127] MADGRAPH [128]aMCatNLO [129] or POWHEG [130] either using the matching algorithms of those programs them-selves or via any of PYTHIArsquos several internal (LHEF-based [131]) implementations of matchingschemes (POWHEG [85] CKKW-L [132ndash134] MLM [135 136] UMEPS [137] NL3 [138] UN-LOPS [139]) The impact of such corrections on MC tuning depends on the details of the matchingscheme (especially its treatment of unitarity) and there is in general a non-negligible possibility ofldquomis-tuningrdquo when combining a stand-alone tune with ME corrections A simple example illustrating

14In particular the constraints on fragmentation mainly come from SLD and LEP where the non-perturbative parametersare clearly defined at the shower cutoff scaleQhad whereas diffraction is dominated by soft physics for which the definitionof the effective hadronization scale is less clear The amount of MPI in hard diffractive events also requires tuning

38

this is the effective value of αs(MZ) which for a leading-order tune is typically of order 013 whilea consistent NLO correction scheme should be compatible with values closer to 012 [29] There isalso the question of the running order of αs The propagation of such changes from the level of hardmatrix elements through the shower and hadronization tuning process are still not fully explored andhence we advise users to perform simple cross-checks such as checking the distributions presented inthis paper before and after applying matrix-element corrections Parameters that appear on both sidesof the matching such as αs should also be checked for consistency [21]

We noted several issues concerning the ee data used to constrain the fragmentation modelling thatit would be good to resolve In particular we find some tensions between the identified-particle ratesextracted from 1) HEDPATA 2) Sec 46 of the PDG and 3) the Z boson summary table in the PDGas discussed in more detail in section 2 and concerning which we made some (subjective) decisionsto arrive at a set of hopefully self-consistent constraints for this work We also note that the overallprecision of the fragmentation constraints could likely be significantly improved by an FCC-ee typemachine such as Tera-Z a possibility we hope to see more fully explored in the context of future eeQCD phenomenology studies

We conclude that the new parameter set does improve significantly on the previous default valuesin several respects including better agreement with data on

1 the net strangeness fraction (has been increased by 10 reflected not only in improved kaonand hyperon yields but also in the Ds and Bs fractions)

2 the ultra-hard fragmentation tail (has been softened especially for leading baryons and for Dand B hadrons)

3 the pTZ spectrum (softened at low pTZ)

4 the minimum-bias charged multiplicity in the forward region (has increased by 10)

5 the underlying event at 7 TeV (is very slightly higher than before)

Some questions that remain open include the following We see a roughly 20 excess of verysoft kaons in both ee and pp environments cf figs 6 and 23 despite the overall kaon yields beingwell described and the overall baryon yields at LHC appear to be underestimated by at least 30despite good agreement at LEP The momentum spectra of heavier strange particles are also poorlyreproduced in particular at LHC It is interesting and exciting that some of the LHC spectra appearto be better described by allowing collective flow in a fraction of events (cf the EPOS model [140])though we believe the jury is still out on whether this accurately reflects the underlying physics Forinstance it has been argued that colour reconnections can mimick flow effects [90] and they may alsobe able to modify the yield of baryons if the creationdestruction of string junctions is allowed [141]We look forward to future discussions on these issues

We round off with an exhortation for follow-ups on this study to provide

bull Not only central tunes experiments and other user-end colleagues need more than central de-scriptions of data there is an increasing need for serious uncertainty estimates In the contextof tune variations it is important to keep in mind that the modelling uncertainties are often in-trinsically non-universal Therefore the constraints obtained by considering data uncertaintiesonly (eg in the spirit of PROFESSORrsquos eigentunes [17]) can at most constitute a lower boundon the theoretical uncertainty (similarly to the case for PDFs) A serious uncertainty estimateincludes some systematic modelling variation irrespectively of and in addition to what data

39

allows (eg in the spirit of the Perugia set of tunes for PYTHIA 6 [8]) We therefore hope thefuture will see more elaborate combinations of data- and theory-driven approaches to systematictune uncertainties

bull Not only global tunes the power of MC models lies in their ability to simultaneously describea large variety of data hence we do not mean to imply that one should give up on universalityand tune to increasingly specific corners of phase space disregarding (or de-emphasizing withlower weights) all others However as proposed in [97] one can obtain useful explicit tests ofthe universality of the underlying physics model by performing independent tunes on separateldquophysics windowsrdquo say in the forward vs central regions for different event-selection crite-ria at different collider energies or even for different collider types In this connection justmaking one global ldquobest-fitrdquo tune may obscure tensions between the descriptions of differentcomplementary data sets By performing independent tunes to each data set separately andchecking the degree of universality of the resulting parameters one obtains a powerful crosscheck on the underlying physics model If all sets produce the same or similar parameters thenuniversality is OK hence a global tune makes very good sense and the remaining uncertain-ties can presumably be reliably estimated from data alone If instead some data sets resultin significantly different tune parameters one has a powerful indication that the universality ofthe underlying modeling is breaking down which can lead to several productive actions 1) itcan be taken into account in the context of uncertainty variations 2) the nature of the data setsfor which non-universal tune parameters are obtained can implicitly indicate the nature of theproblem leading to more robust conclusions about the underlying model than merely whether atune cancannot fit the data and 3) the observations can be communicated to the model authorsin a more unambiguous way hopefully resulting in a speedier cycle of model improvements

We hope that the Monash 2013 tune parameters may serve as a useful starting point for phe-nomenology studies and for future PYTHIA 8 tuning efforts

Acknowledgments

We thank S Mrenna M Ritzmann and T Sjostrand for comments on the manuscript and L de Nooijfor pointing us to the ALICE Klowast and φ measurements [142] and to the ATLAS φ measurementsin [143] The work of J R is supported by an STFC Rutherford Fellowship STK0052271 Thiswork was supported in part by the Research Executive Agency (REA) of the European Commissionunder the Grant Agreements PITN-GA-2012-315877 (MCnet)

A Monash 2013 Tune Parameters

In tabs 3 ndash 7 we list the FSR fragmentation parameters for the Monash tune of PYTHIA Forreference we compare them to the current default parameters

40

FSR Parameters Monash 13 (Default) CommentTimeShoweralphaSvalue = 01365 = 01383 Effective alphaS(mZ) valueTimeShoweralphaSorder = 1 = 1 Running orderTimeShoweralphaSuseCMW = off = off Translation from MS to CMWTimeShowerpTmin = 050 = 040 Cutoff for QCD radiationTimeShowerpTminChgQ = 050 = 040 Cutoff for QED radiationTimeShowerphiPolAsym = on = on Asymmetric azimuth distributions

Table 3 Final-state radiation (FSR) parameters

HAD Parameters Monash 13 (Default) Comment String breaks pT and z distributionsStringPTsigma = 0335 = 0304 Soft pT in string breaks (in GeV)StringPTenhancedFraction = 001 = 001 Fraction of breakups with enhanced pTStringPTenhancedWidth = 20 = 20 Enhancement factorStringZaLund = 068 = 03 Lund FF a (hard fragmentation supp)StringZbLund = 098 = 08 Lund FF b (soft fragmentation supp)StringZaExtraSquark = 00 = 00 Extra a when picking up an s quarkStringZaExtraDiquark = 097 = 050 Extra a when picking up a diquarkStringZrFactC = 132 = 100 Lund-Bowler c-quark parameterStringZrFactB = 0855 = 067 Lund-Bowler b-quark parameter Flavour composition mesonsStringFlavProbStoUD = 0217 = 019 Strangeness-to-UD ratioStringFlavmesonUDvector = 05 = 062 Light-flavour vector suppressionStringFlavmesonSvector = 055 = 0725 Strange vector suppressionStringFlavmesonCvector = 088 = 106 Charm vector suppressionStringFlavmesonBvector = 22 = 30 Bottom vector suppressionStringFlavetaSup = 060 = 063 Suppression of eta mesonsStringFlavetaPrimeSup = 012 = 012 Suppression of etarsquo mesons Flavour composition baryonsStringFlavprobQQtoQ = 0081 = 009 Diquark rate (for baryon production)StringFlavprobSQtoQQ = 0915 = 1000 Strange-diquark suppressionStringFlavprobQQ1toQQ0 = 00275 = 0027 Vector diquark suppressionStringFlavdecupletSup = 10 = 10 Spin-32 baryon suppressionStringFlavsuppressLeadingB = off = off Optional leading-baryon suppressionStringFlavpopcornSpair = 09 = 05 StringFlavpopcornSmeson = 05 = 05

Table 4 String-breaking parameters

PDF and ME Parameters Monash 13 (Default) CommentPDFpSet = 13 = 8 PDF set for the protonSigmaProcessalphaSvalue = 0130 0135 alphaS(MZ) for matrix elementsMultiPartonInteractionsalphaSvalue = 0130 0135 alphaS(MZ) for MPI

Table 5 Parton-distribution (PDF) and Matrix-Element (ME) parameters

41

ISR Parameters Monash 13 (Default) CommentSpaceShoweralphaSvalue = 01365 = 0137 Effective alphaS(mZ) valueSpaceShoweralphaSorder = 1 = 1 Running orderSpaceShoweralphaSuseCMW = off = off Translation from MS to CMWSpaceShowersamePTasMPI = off = off ISR cutoff typeSpaceShowerpT0Ref = 20 = 20 ISR pT0 cutoffSpaceShowerecmRef = 70000 = 18000 ISR pT0 reference ECM scaleSpaceShowerecmPow = 00 = 00 ISR pT0 scaling powerSpaceShowerrapidityOrder = on = on Approx coherence via y-orderingSpaceShowerphiPolAsym = on = on Azimuth asymmetries from gluon polSpaceShowerphiIntAsym = on = on Azimuth asymmetries from interferenceTimeShowerdampenBeamRecoil = on = on Recoil dampening in final-initial dipolesBeamRemnantsprimordialKTsoft = 09 = 05 Primordial kT for soft procsBeamRemnantsprimordialKThard = 18 = 20 Primordial kT for hard procsBeamRemnantshalfScaleForKT = 15 = 10 Primordial kT softhard boundaryBeamRemnantshalfMassForKT = 10 = 10 Primordial kT softhard mass boundary

Table 6 Initial-state radiation (ISR) and primordial-kT parameters

MPI Parameters Monash 13 (Default) CommentMultipartonInteractionspT0Ref = 228 = 2085 MPI pT0 IR regularization scaleMultipartonInteractionsecmRef = 70000 = 18000 MPI pT0 reference ECM scaleMultipartonInteractionsecmPow = 0215 = 019 MPI pT0 scaling powerMultipartonInteractionsbProfile = 3 = 3 Transverse matter overlap profileMultipartonInteractionsexpPow = 185 = 20 Shape parameterBeamRemnantsreconnectRange = 18 = 15 Colour ReconnectionsSigmaTotalzeroAXB = on = on Carried over from 4CSigmaDiffractivedampen = on = on Carried over from 4CSigmaDiffractivemaxXB = 650 = 650 Carried over from 4CSigmaDiffractivemaxAX = 650 = 650 Carried over from 4CSigmaDiffractivemaxXX = 650 = 650 Carried over from 4CDiffractionlargeMassSuppress = 40 = 20 High-mass diffraction suppression power

Table 7 Multi-Parton-Interaction (MPI) Colour-Reconnection (CR) and Diffractive parameters

42

B Additional Plots

B1 LEP Event-Shape Distributions

To keep the main body of the paper as uncluttered as possible we collect various plots of event-shapedistributions in figs 28 and 29 separated into light-flavour and b-tagged events on the left and rightrespectively

The experimental results come from the L3 experiment [26] However since the data points areonly available with 3-digit precision some of the least populated bins contain artifacts like uncertain-ties being reported as exactly zero etc Thus we have been forced to make the following modificationsto the data set

The statistical uncertainty was reported as zero for the last two bins of light-flavour Thrust as wellas for the last bin of the C D and BT parameters Uncertainties lt 10minus3 were derived using anapproximate statistical scaling based on the contents and uncertainties of the other bins Likewise thesystematical uncertainty for the last bin of Thrust was given as zero which we have replaced by theupper limit 5times 10minus4 The last bin of BT quoted a measured y value of zero removed in this study

For the heavy-flavour tagged event shapes more significant rounding issues were present Thusseveral of the first and last bins of each distribution either quoted zero (statistical andor systematic)uncertainties or ones with only a single digit of precision (such as 0001 for which the rounding errorcould be up to sim 50) We have interpreted all such values conservatively inserting by hand a fourthdigit on the uncertainties as large as could be consistent with rounding

B2 Additional Particle Spectra

In addition to the K and Λ spectra shown in the main body of the paper (sections 22 and 35) wehere include for reference the x spectra of φ mesons protons and Ξ baryons at LEP in figs 30 and 31the pT spectrum of Klowast mesons and the rapidity and pT spectra of φ mesons at LHC in fig 32 (withabsolute normalizations to the number of inelastic events) and the rapidity spectrum of Ξ baryons atLHC in fig 33

The transverse-momentum spectra of Klowast and φ mesons in fig 32 exhibit the same qualitativebehaviour as that of the KS mesons (fig 23) namely an excess at very soft momenta below sim 500MeV and a depletion at slightly higher momenta between 1 and 2 GeV As discussed in section 35we did not find a way to remove these undesirable features in the Monash 2013 tune suggesting thatthis is an issue that further theoretical modeling will be needed to resolve

The rapidity spectrum of Ξ baryons fig 33 shows that although the Monash tune does producemore Ξ baryons overall (as expected also from the relative increase of Ξ production at LEP cf fig 5)there is still a significant deficit of Ξ baryons at the LHC almost a factor 2 compared with the dataThis is qualitatively similar to the situation for Λ baryons (fig 24) discussed in section 35 Sincenew physics mechanisms may be required to ldquoexplainrdquo the missing baryons we conclude that furthermeasurements and better precision on both the Λ and Ξ sectors (in addition to any other baryonsthat may be accessible) would be highly interesting More explicit recommendations can be found insections 35 and 5

43

0 01 02 03 04

d(1

-T)

σ d

σ1

-310

-210

-110

1

10

2101-Thrust (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn03

01plusmn04

02plusmn05

V I

N C

I A

R O

O T

1-T (udsc)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

d(1

-T)

σ dσ

1

-310

-210

-110

1

10

2101-T (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn13

02plusmn12

02plusmn14

V I

N C

I A

R O

O T

1-T (b)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210

310C Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn03

00plusmn04

01plusmn04

V I

N C

I A

R O

O T

C0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210 C parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn17

01plusmn24

01plusmn27

V I

N C

I A

R O

O T

C (b)0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn06

01plusmn06

V I

N C

I A

R O

O T

D0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn24

02plusmn21

02plusmn26

V I

N C

I A

R O

O T

D (b)0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

Figure 28 Hadronic Z decays atradics = 912 GeV The T C and D event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

44

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn02

01plusmn03

01plusmn04

V I

N C

I A

R O

O T

WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn05

01plusmn12

01plusmn17

V I

N C

I A

R O

O T

(b)WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn02

00plusmn02

01plusmn03

V I

N C

I A

R O

O T

TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

04plusmn24

08plusmn49

08plusmn55

V I

N C

I A

R O

O T

(b)TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

Figure 29 Hadronic Z decays atradics = 912 GeV The BW and BT event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

45

0 02 04 06 08 1

dx

φgt

dn

φ1

ltn

-210

-110

1

10 )φx(

Pythia 8183Data from ALEPH_1996_S3486095d40-x01-y01

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn37

02plusmn53

03plusmn62

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

0608

112141618

Figure 30 Hadronic Z decays atradics = 912 GeV φ meson x spectrum

-5 -4 -3 -2 -1 0

dx

pgt

dn

p1

ltn

-410

-310

-210

-110

1

10

210) (Combined)px(p+

Pythia 8183Data from Zeit Phys C66 (1995) 355 PhysRev D59 (1998) 052001

ALEPH+SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn08

00plusmn09

00plusmn08

V I

N C

I A

R O

O T

px-5 -4 -3 -2 -1 0

The

ory

Dat

a

06

08

1

12

14

0 02 04

dx

Ξgt

dn

Ξ1

ltn

-110

1

10

)plusmnΞx(

Pythia 8183Data from Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn11

02plusmn13

02plusmn14

V I

N C

I A

R O

O T

Ex0 02 04

The

ory

Dat

a

06

08

1

12

14

Figure 31 Hadronic Z decays atradics = 912 GeV pplusmn and Ξplusmn x spectra

46

0 2 4 6

Td

pK

d

nIN

EL

1N

-510

-410

-310

-210

-110

(INEL |y|lt05)T

p0K

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn35

01plusmn26

01plusmn29

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 2 4 6

Td

pφ

dn

INE

L1

N-510

-410

-310

-210

-110

gt04)T

(INEL |y|lt05 pT

pφ

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn88

03plusmn84

04plusmn173

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

)dy

[mb]

-K

+K

rarrφ(σd

0

05

1

15

2 Rapidity (INEL ATLAS cuts)φ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn14

01plusmn19

01plusmn34

V I

N C

I A

R O

O T

pp 7000 GeV

|y|0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

06 08 1 12

[mb

GeV

]φ

T)

dp-

K+

Krarrφ(

σd

0

05

1

15

2

25 (INEL ATLAS cuts)

T pφ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn21

01plusmn30

02plusmn53

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p06 08 1 12

The

ory

Dat

a

06

08

1

12

14

Figure 32 pp collisions at 7 TeV Top row Klowast and φ pperp spectra compared with ALICE data [142]Bottom row φ rapidity and pperp spectrum compared with ATLAS data [143] The ATLAS cuts areφrarr K+Kminus pperpφ isin [05 12] GeV |y(φ)| lt 08 pperpK gt 023 GeV |pK | lt 08 GeV

47

0 05 1 15 2

dygt

Ξ lt

dnN

SD

1N

0

001

002

003

004)d|y|gt (NSD)Ξltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn89

01plusmn129

01plusmn192

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

0

05

1

15

2

Figure 33 pp collisions at 7 TeV Ξminus rapidity spectrum compared with CMS data [99]

48

B3 Energy Scaling of σ2rarr2(pTmin) vs σinel from 200 GeV to 100 TeV

In fig 34 we show the LO QCD 2rarr 2 cross section integrated above pTmin as a function of pTminin pp collisions at 4 different CM energies complementing and expanding on the 8-TeV CM energyshown in the main body of the paper We compare two different αs and PDF choices correspondingto those made in tunes Monash 13 (blue filled dots) and 4C (red open squares) respectively As areference for the total inelastic cross section at each energy we base ourselves on the best-fit curvein the TOTEM cross-section measurement paper [72] which in turn represents a fit produced by theCOMPETE collaboration [144] Uncertainties are rough conservative estimates based on the plot inthe TOTEM paper but they are in any case too small to significantly affect conclusions about the scaleat which the partonic cross section saturates the hadronic one

We observe that the pTmin value for which the LO QCD 2 rarr 2 partonic cross section formallybecomes equal to the total inelastic cross section (strongly suggesting that every event has at leastone such mini-jet pair) rises from values around 1 ndash 2 GeV at energies

radics lt 1 TeV to 5 GeV atradic

s = 13 TeV and finally 10 GeV atradics = 100 TeV

49

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

0 50 100

0

05

1

15

2

25|lt25)ηgt05 |

T) (p

Chgt(n

Tltp

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn05

01plusmn01

05plusmn07

V I

N C

I A

R O

O T

pp 7000 GeV

0 50 100

The

ory

Dat

a

06

08

1

12

14

0 50 100 150 200

0

05

1

15|lt25)ηgt01 |

T 2 pge

Ch) (n

Chgt(n

TSoft ltp

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn06

00plusmn08

03plusmn40

V I

N C

I A

R O

O T

pp 7000 GeV

0 50 100 150 200

The

ory

Dat

a06

08

1

12

14

Figure 20 Average-pperp vs charged-multiplicity distributions in min-bias pp collisions at 7 TeV withstandard (left) and soft (right) fiducial cuts compared to ATLAS data [91]

multiplicity by itself is a very difficult quantity to extract reliable conclusions from Note also that theCMS measurement [92] shown in the top pane of fig 19 was corrected to an unphysical ldquonon-singlediffractiverdquo event definition which essentially amounts to switching off single-diffractive contributionsin the MC generator (We note that later CMS measurements instead use a physical observable relatedto the diffractive mass to define NSD) For the comparisons to CMS NSD data shown here the single-diffractive contributions were switched off in the generator With these caveats in mind we note thatboth the 4C and Monash 2013 tunes are in good agreement with the CMS measurement with theMonash one giving a slightly lower central charged-track density (by about 5) This is closer to thevalues observed in data though as already noted in section 11 we do not regard differences at the 5level as significant

In the bottom two panes of fig 19 we focus on the forward region (with physical event selections)In particular we see that the NNPDF set [20] generates a broader rapidity spectrum so that while theactivity in the central region (top pane) is reduced slightly the activity in the very forward regionactually increases and comes into agreement with the TOTEM measurement [94] covering the range53 lt |η| lt 64 The bottom right-hand pane shows the forward energy flow measured by CMS [93]in the intermediate region 323 lt |η| lt 465 The dependence on η is a bit steeper in the Monashtune than in the previous one and more similar to that seen in the data

A complementary observable which is highly sensitive to interconnection effects between theMPI (and hence eg to the effects of ldquocolour reconnectionsrdquo [95]) is the average charged-particlepperp as a function of the number of charged particles In a strict leading-colour picture each MPIwould cause one or two new strings to be stretched between the remnants but each such string wouldbe independent (modulo endpoint effects) therefore (modulo jets) the pperp spectrum of the hadronsproduced by each of these strings would be independent of the number of strings The result would bea flat 〈pperp〉 (nCh) spectrum Jets and colour reconnections both produce a rising spectrum The spectraobserved by ATLAS [91] are compared to the Monash 2C and 4C tunes in fig 20 for standard

30

0 1 2 3

gtφ|dη

d|

Ch

n2

ltd

0

02

04

06

08

1gt01)

T|lt25 pηgt1 (|

Tlead| wrt pφ∆|

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn16

00plusmn19

00plusmn56

V I

N C

I A

R O

O T

pp 7000 GeV

| [rad]φ∆|0 1 2 3

The

ory

Dat

a

06

08

1

12

14

0 1 2 3

gtφ|dη

d|

Ch

n2

ltd

0

05

1

15

2

gt05)T

|lt25 pηgt5 (|Tlead

| wrt pφ∆|

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn05

00plusmn05

00plusmn70

V I

N C

I A

R O

O T

pp 7000 GeV

| [rad]φ∆|0 1 2 3

The

ory

Dat

a06

08

1

12

14

Figure 21 pp collisions at 7 TeV ∆φ of charged particles with respect to the hardest track for twodifferent hardest-track triggers compared with ATLAS data [98]

(left) and soft (right) fiducial cuts Both of the Monash and 4C tunes reproduce the data quite wellwith χ2

5 lt 1 while the older tune 2C had a higher CR strength optimized to describe Tevatrondata [96] We certainly consider the energy scaling of the effective CR strength among the mostuncertain parameters of the current min-biasunderlying-event modelling (a similar conclusion wasreached for the CR modelling in PYTHIA 6 in [97]) and intend to study the physics aspects of thisissue more closely in a forthcoming paper

For a more differential look at the event structure we consider the charged-track ∆φ distributionswith respect to the azimuthal angle of the leading track in fig 21 compared with ATLAS data [98]The plot in the left-hand pane corresponds to a requirement of pperplead ge 1 GeV while the one in theright-hand pane is for a harder trigger pperplead ge 5 GeV The former can roughly be taken as charac-teristic of min-bias events while the latter is related to the differential distribution of the underlyingevent In both cases the activity in the wide-angle region near π2 is significantly better described bythe 4C and Monash 2013 tunes (which agrees with their improved description of the overall activity)while there is a too strong peaking at low ∆φ especially for the lowest pperplead cut (left) possibly indi-cating that the structure of the min-bias events is still slightly too ldquolumpyrdquo (ie jetty) For the higherpperplead cut (right) the overcounting at very low ∆φ is already significantly milder and we observe agood agreement with the data

Turning now to the underlying event (UE) what matters most for high-pperp jet studies is that theMC models describe the UE contamination per ∆R jet area The most important UE observable fromthis perspective is thus the pperp sum density in the UE and its fluctuations For charged particles atLHC typically a pperp cut of 500 MeV is relevant since softer tracks will form helices and hence notcontribute to calorimetric jet energies Neutral particles are of course relevant across all pperp scalesIn fig 22 we show the charged pperp sum density (left with the lowest possible pperp cut of 100 MeV)and the charged-track density (right with a pperp cut of 500 MeV) in the so-called ldquoTransverse Regionrdquo(defined by 60 lt ∆φ lt 120 with respect to the leading track) inside the ATLAS acceptance of

31

0 5 10 15 20

)φ∆η

∆gt

(T

psum

lt

0

05

1

15

2

25gt01)

T|lt25 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn03

01plusmn09

02plusmn112

V I

N C

I A

R O

O T

pp 7000 GeV

(hardest track) [GeV]T1

p0 5 10 15 20

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20

)φ∆η

∆gt

(C

hlt

n

0

05

1

15

2

25gt05)

T|lt25 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn02

00plusmn04

02plusmn104

V I

N C

I A

R O

O T

pp 7000 GeV

(hardest track) [GeV]T1

p0 5 10 15 20

The

ory

Dat

a06

08

1

12

14

Figure 22 pp collisions at 7 TeV UE (ldquoTransverse regionrdquo) transverse-momentum sum density (left)and charged-track density (right) compared with ATLAS data [98]

|η| lt 25 [98] As is now well known the Tevatron extrapolations (represented here by Tune 2C)predicted a UE level which was 10 ndash 20 below the LHC data Both the current default tune 4C(which included LHC data) and the Monash 2013 tune exhibit significantly better agreement with theLHC measurements with the Monash one giving a slight additional improvement in the χ2

5 valuesWe conclude that the Monash 2013 tune parameters are appropriate for both min-bias and UE studies

35 Identified Particles at LHC

While the description of inclusive charged particles discussed in the previous section is acceptablelarger discrepancies emerge when we consider the spectra of identified particles We here focus onstrange particles in particular K0

S mesons and Λ0 hyperons in figs 23 and 24 respectively Theexperimental measurements come from CMS [99] Additional comparisons to strange-particle spectra(Klowast φ and Ξ) are collected in appendix B2

In the K0S rapidity distribution shown in the left-hand pane of fig 23 we observe that tune 4C

exhibits a mild underproduction of about 10 Though it might be tempting to speculate whether thiscould indicate some small reduction of strangeness suppression in pp collisions however we alreadynoted in section 21 that the strangeness production in ee collisions also needed to be increased byabout 10 After this adjustment we see that the overall K0

S yield in the Monash 2013 tune is fullyconsistent with the CMS measurement Nonetheless we note that the momentum distribution is stillnot satisfactorily described as shown in the right-hand pane of fig 23 Our current best guess istherefore that the overall rate of strange quarks is consistent at least in the average min-bias collision(dedicated comparisons in high-multiplicity samples would still be interesting) but that the phase-space distribution of strange hadrons needs more work Similarly to the case in ee collisions cf fig 6the model predicts too many very soft kaons though we do not currently know whether there is adynamic link between the ee and pp observations

For strange baryons we note that the increase in the Λ0 fraction in ee collisions (cf fig 5) does

32

0 05 1 15 2

dygt

K lt

dnN

SD

1n

0

02

04

06

08)d|y|gt Rapidity (NSD)

S

0ltdn(K

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn01

00plusmn09

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8 10

Td

pK

dn

NS

D1

N

-510

-410

-310

-210

-110

1

10 (|y|lt20 NSD)

T pS

0K

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn78

01plusmn34

02plusmn22

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6 8 10

The

ory

Dat

a06

08

1

12

14

Figure 23 pp collisions at 7 TeV K0S rapidity and pperp spectrum compared with CMS data [99]

0 05 1 15 2

dygt

Λ lt

dnN

SD

1N

0

01

02

03

04)d|y|gt (NSD)0Λltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn64

00plusmn78

01plusmn147

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8 10

Td

pΛ

dn

Λ1

n

-510

-410

-310

-210

-110

1

10 (|y|lt20 NSD)

T p0Λ

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn59

03plusmn66

05plusmn105

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6 8 10

The

ory

Dat

a

06

08

1

12

14

Figure 24 pp collisions at 7 TeV Λ0 rapidity and pperp spectrum compared with CMS data [99]

not result in an equivalent improvement of the Λ0 rate in pp collisions shown in fig 24 The Monash2013 tune still produces only about 23 of the observed Λ0 rate (and just over half of the observedΞminus rate cf appendix B2) We therefore believe it to be likely that an additional source of net baryonproduction is needed (at least within the limited context of the current PYTHIA modelling) in orderto describe the LHC data The momentum spectrum is likewise quite discrepant exhibiting an excessat very low momenta (stronger than that for kaons) a dip between 1ndash4 GeV and then an excess of veryhard Λ0 production The latter hard tail is somewhat milder in the Monash 2013 tune than previously

33

and it may be consistent with the trend also seen in the Λ0 spectrum at LEP cf fig 6 We concludethat baryon production still requires further modelling and tuning efforts

4 Energy Scaling

Though energy scaling these days mostly refers to the scaling of pp collisions (see eg [97]) animportant first step is to consider the scaling of observables in ee rarr γlowastZ rarr hadrons This scalingcontains information on the relative contributions of perturbative and non-perturbative fragmentationThus at low ee energies the non-perturbative components of the fragmentation model dominatewhile perturbative bremsstrahlung increases in importance towards higher ee energies In fig 25we consider the scaling of the average charged-particle multiplicity and that of charged Kaons andLambda baryons from CM energies of 14 GeV to 200 GeV obtained from measurements availableat HEPDATA Below the Z pole the measurements we include mostly come from TASSO [100]though a few points on 〈nCh〉 come from HRS (at 29 GeV [101]) and TOPAZ (at 578 GeV [102]) Atthe Z pole the data come from the four LEP experiments [38 51ndash53] with the latter extending alsoto energies above MZ [103ndash108] For completeness and as reference for future ee collider studiesmodel extrapolations for CM energies up to 1000 GeV are also shown (though still only including theeerarr γlowastZ rarr hadrons component as usual with photon ISR switched off)

From the plots in fig 25 it is clear that there are no significant differences between the energyscaling of the three ee tunes considered here (mainly reflecting that they have been tuned to samereference point at 912 GeV and that their scaling is dictated by the same underlying physics model)and that their energy dependence closely matches that observed in data However the increasedamount of non-perturbative strangeness production in the Monash tune leads to a better agreementwith the overall normalization of the Kplusmn and Λ rates at all energies

Moving to pp collisions the plots in fig 26 show the scaling of the average charged multiplicity(left column) and multiplicity distributions (right column) in min-bias collisions from 7000 GeV (toprow) to 900 GeV (middle row) and 200 GeV (bottom row) compared with data from CMS [92 109]ATLAS [91] and UA5 [110 111] We regret the omission of additional relevant min-bias measure-ments from the Tevatron and RHIC experiments here but have chosen to focus in this paper mainlyon the LHC The comparisons at 7 TeV were already discussed in the main section on pp collisionssection 3 At 900 GeV the Monash 2013 tune again gives a roughly 5 lower average central chargedmultiplicity than the 4C one with a better description of the tail towards high multiplicities At 200GeV the UA5 measurement we include here extends over the full rapidity and pperp range hence the in-terplay between diffraction and low-multiplicity non-diffractive processes is presumably (much) moreimportant We believe imperfections in this modelling to be the likely cause of the significant discrep-ancies observed at high η and for nCh le 20 at these energies Since a dedicated study of this interplayis beyond the scope of this study we limit ourselves merely to stating this observation as a point forfuture studies to help clarify

Finally in fig 27 we compare to the underlying event measured in the highly useful energyscan that was performed at the Tevatron in the last days before its shutdown [22 23] during whichextremely high min-bias statistics were collected at 300 and 900 GeV CM energy over a period of afew days As was already noted in section 3 the UE at 7 TeV is slightly larger in the Monash 2013tune than in tune 4C As can be seen from the plots here the two tunes give comparable results for allthe Tevatron energies Interestingly the UE plateau region at 900 and 1960 GeV is reached sooner inthese models than in the data translating to a roughly 10 - 20 too low UE level for leading-trackpperp values in the neighbourhood of the transition from the rise to the plateau (roughly for leading-

34

14 22 29 35 44 58 91 91 91 91 133 161 183 189 200 250 350 500 1000

gtC

hlt

n

0

20

40

60

Average Charged Multiplicity vs ECM

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN25

χ00plusmn03 00plusmn02 00plusmn02

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 22 29 35 44 58 91 91 91 91 133 161 183 189 200 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

14 22 35 44 91 91 133 161 183 189 250 350 500 1000

gtK

ltn

0

2

4

6 Multiplicity vs ECM+-Average K

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN25

χ00plusmn06 00plusmn20

00plusmn18

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 22 35 44 91 91 133 161 183 189 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

14 35 91 91 91 91 133 200 250 350 500 1000

gtΛ

ltn

0

02

04

06

08

1

12 Multiplicity vs ECM0ΛAverage

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn06

01plusmn22

01plusmn18

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 35 91 91 91 91 133 200 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

Figure 25 e+eminus rarr hadrons Energy scaling of 〈nCh〉 〈nKplusmn〉 and 〈nΛ〉 in e+eminus rarr qq eventsincluding comparisons to measurements from HEPDATA for CM energies from 14 GeV to 200 GeVAlso shown are model extrapolations up to 1000 GeV

35

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from PhysRevLett 105 (2010) 022002

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn00

00plusmn03

00plusmn71

V I

N C

I A

R O

O T

pp 7000 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

0 50 100

)C

hP

rob(

n

-710

-610

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn27

00plusmn27

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

Chn0 50 100

The

ory

Dat

a

06

08

1

12

14

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from JHEP 1002 (2010) 041

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn03

00plusmn05

00plusmn29

V I

N C

I A

R O

O T

pp 900 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

0 10 20 30 40

)C

hP

rob(

n

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn17

01plusmn25

02plusmn127

V I

N C

I A

R O

O T

pp 900 GeV

Chn0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

0 1 2 3 4 5

gtηd

ch lt

dnN

SD

1n

0

1

2

3

4

5gt (NSD)ηd

chltdn

Pythia 8185Data from ZPhys C33 (1986) 1-6

UA5PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn36

00plusmn24

00plusmn16

V I

N C

I A

R O

O T

ppbar 200 GeV

η0 1 2 3 4 5

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)C

hP

rob(

n

-410

-310

-210

-110

1

)T

|lt05 all pηChg Mult (NSD |

Pythia 8185Data from ZPhys C43 (1989) 357

UA5PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn24

00plusmn24

00plusmn08

V I

N C

I A

R O

O T

ppbar 200 GeV

Chn0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 26 Min-bias pp events from 200 to 7000 GeV Energy scaling of 〈dnChdη〉 (left) andP (nCh) (right)

36

0 10 20 30

)φ∆η

∆gt

(T

psum

lt

0

05

1

15gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn24

26plusmn33

12plusmn143

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 10 20 30

)φ∆η

∆gt

(C

hlt

n

0

05

1

15gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

04plusmn05

13plusmn08

14plusmn100

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn58

06plusmn53

08plusmn193

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn16

15plusmn20

06plusmn114

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

gt05)T

|lt10 pη (|T1

)gt vs pT

TRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn10

02plusmn07

05plusmn22

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

gt05)T

|lt10 pη (|T1

gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn20

02plusmn11

03plusmn08

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 27 The Tevatron energy scan The underlying event (left average summed-pperp density andright average track density in the transverse region as function of leading-track pperp) for pp collisionsat 300 (bottom row) 900 GeV (middle row) and 1960 GeV (top row)

37

track pperp values 2 lt pT1 lt 10 GeV) This indicates that the energy scaling of the UE modeling and inparticular the details of its transition between central and peripheral collisions is still not satisfactorilyunderstood

5 Conclusions and Exhortation

We have presented a reanalysis of the constraints on fragmentation in ee collisions and applied theresults to update the final-state fragmentation parameters in PYTHIA 8 We combine these parameterswith a tune to hadron-collider data using a new NNPDF 23 LO QCD+QED PDF set which has beenencoded so it is available as an internal PDF set in PYTHIA 8 independently of LHAPDF [112]

In this PDF set as well as in our tune the value of the strong coupling for hard-scattering matrixelements is fixed to be αs(MZ) = 013 consistent with other LO determinations of it For initial-and final-state radiation our tune uses the effective value αs(MZ) = 01365 The difference isconsistent with an effective translation between the MS and CMW schemes We note that alternative(LO NLO and NNLO) NNPDF 23 QCD+QED sets with αs(MZ) = 0119 are also available inthe code for people who want to check the impact of using a different αs(MZ) value andor higher-order PDF sets on hard-scattering events For the purpose of such studies we point out that it ispossible in PYTHIA 8 to preserve most of the features of the shower- and underlying-event tuningby changing only the PDF for the hard-scattering matrix elements leaving the PDF choice for theshower evolution and MPI framework unaltered (see the PYTHIA 8 HTML manualrsquos PDF sectionunder PDFuseHard)

The updated parameters are available as an option starting from PYTHIA 8185 by setting

Tuneee = 7 and Tunepp = 14

By no means do we claim that this should be regarded as the final word in tuning the PYTHIA 8Monte Carlo model First of all the model continues to evolve For instance developments foreseenfor the near future include updates of colour reconnections diffraction and the treatment of g rarr qqsplittings Any of these should in principle be accompanied by a reevaluation of the model constraints

Moreover despite the comprehensive view of collider data we have attempted to take in thisstudy there still remains several issues that were not addressed including initial-final interferenceand coherence effects [113 114] (probably more a modelling issue than a tuning one) reliable esti-mates of theoretical uncertainties [8 17 24 29 97 115] diffraction14 [74 116 117] and other colour-singlet phenomena such as onium production long-distance (eg forward-backward forward-centraland ldquoridgerdquo-type) correlations [88 118ndash123] B-hadron decays [124] and tuning in the presence ofmatrix-element matching at LO and NLO (see [21 29 115 125 126] for recent phenomenologi-cal studies) Especially in the latter context of matrix-element matching we expect that in manycases PYTHIA 8 will be used together with codes such as ALPGEN [127] MADGRAPH [128]aMCatNLO [129] or POWHEG [130] either using the matching algorithms of those programs them-selves or via any of PYTHIArsquos several internal (LHEF-based [131]) implementations of matchingschemes (POWHEG [85] CKKW-L [132ndash134] MLM [135 136] UMEPS [137] NL3 [138] UN-LOPS [139]) The impact of such corrections on MC tuning depends on the details of the matchingscheme (especially its treatment of unitarity) and there is in general a non-negligible possibility ofldquomis-tuningrdquo when combining a stand-alone tune with ME corrections A simple example illustrating

14In particular the constraints on fragmentation mainly come from SLD and LEP where the non-perturbative parametersare clearly defined at the shower cutoff scaleQhad whereas diffraction is dominated by soft physics for which the definitionof the effective hadronization scale is less clear The amount of MPI in hard diffractive events also requires tuning

38

this is the effective value of αs(MZ) which for a leading-order tune is typically of order 013 whilea consistent NLO correction scheme should be compatible with values closer to 012 [29] There isalso the question of the running order of αs The propagation of such changes from the level of hardmatrix elements through the shower and hadronization tuning process are still not fully explored andhence we advise users to perform simple cross-checks such as checking the distributions presented inthis paper before and after applying matrix-element corrections Parameters that appear on both sidesof the matching such as αs should also be checked for consistency [21]

We noted several issues concerning the ee data used to constrain the fragmentation modelling thatit would be good to resolve In particular we find some tensions between the identified-particle ratesextracted from 1) HEDPATA 2) Sec 46 of the PDG and 3) the Z boson summary table in the PDGas discussed in more detail in section 2 and concerning which we made some (subjective) decisionsto arrive at a set of hopefully self-consistent constraints for this work We also note that the overallprecision of the fragmentation constraints could likely be significantly improved by an FCC-ee typemachine such as Tera-Z a possibility we hope to see more fully explored in the context of future eeQCD phenomenology studies

We conclude that the new parameter set does improve significantly on the previous default valuesin several respects including better agreement with data on

1 the net strangeness fraction (has been increased by 10 reflected not only in improved kaonand hyperon yields but also in the Ds and Bs fractions)

2 the ultra-hard fragmentation tail (has been softened especially for leading baryons and for Dand B hadrons)

3 the pTZ spectrum (softened at low pTZ)

4 the minimum-bias charged multiplicity in the forward region (has increased by 10)

5 the underlying event at 7 TeV (is very slightly higher than before)

Some questions that remain open include the following We see a roughly 20 excess of verysoft kaons in both ee and pp environments cf figs 6 and 23 despite the overall kaon yields beingwell described and the overall baryon yields at LHC appear to be underestimated by at least 30despite good agreement at LEP The momentum spectra of heavier strange particles are also poorlyreproduced in particular at LHC It is interesting and exciting that some of the LHC spectra appearto be better described by allowing collective flow in a fraction of events (cf the EPOS model [140])though we believe the jury is still out on whether this accurately reflects the underlying physics Forinstance it has been argued that colour reconnections can mimick flow effects [90] and they may alsobe able to modify the yield of baryons if the creationdestruction of string junctions is allowed [141]We look forward to future discussions on these issues

We round off with an exhortation for follow-ups on this study to provide

bull Not only central tunes experiments and other user-end colleagues need more than central de-scriptions of data there is an increasing need for serious uncertainty estimates In the contextof tune variations it is important to keep in mind that the modelling uncertainties are often in-trinsically non-universal Therefore the constraints obtained by considering data uncertaintiesonly (eg in the spirit of PROFESSORrsquos eigentunes [17]) can at most constitute a lower boundon the theoretical uncertainty (similarly to the case for PDFs) A serious uncertainty estimateincludes some systematic modelling variation irrespectively of and in addition to what data

39

allows (eg in the spirit of the Perugia set of tunes for PYTHIA 6 [8]) We therefore hope thefuture will see more elaborate combinations of data- and theory-driven approaches to systematictune uncertainties

bull Not only global tunes the power of MC models lies in their ability to simultaneously describea large variety of data hence we do not mean to imply that one should give up on universalityand tune to increasingly specific corners of phase space disregarding (or de-emphasizing withlower weights) all others However as proposed in [97] one can obtain useful explicit tests ofthe universality of the underlying physics model by performing independent tunes on separateldquophysics windowsrdquo say in the forward vs central regions for different event-selection crite-ria at different collider energies or even for different collider types In this connection justmaking one global ldquobest-fitrdquo tune may obscure tensions between the descriptions of differentcomplementary data sets By performing independent tunes to each data set separately andchecking the degree of universality of the resulting parameters one obtains a powerful crosscheck on the underlying physics model If all sets produce the same or similar parameters thenuniversality is OK hence a global tune makes very good sense and the remaining uncertain-ties can presumably be reliably estimated from data alone If instead some data sets resultin significantly different tune parameters one has a powerful indication that the universality ofthe underlying modeling is breaking down which can lead to several productive actions 1) itcan be taken into account in the context of uncertainty variations 2) the nature of the data setsfor which non-universal tune parameters are obtained can implicitly indicate the nature of theproblem leading to more robust conclusions about the underlying model than merely whether atune cancannot fit the data and 3) the observations can be communicated to the model authorsin a more unambiguous way hopefully resulting in a speedier cycle of model improvements

We hope that the Monash 2013 tune parameters may serve as a useful starting point for phe-nomenology studies and for future PYTHIA 8 tuning efforts

Acknowledgments

We thank S Mrenna M Ritzmann and T Sjostrand for comments on the manuscript and L de Nooijfor pointing us to the ALICE Klowast and φ measurements [142] and to the ATLAS φ measurementsin [143] The work of J R is supported by an STFC Rutherford Fellowship STK0052271 Thiswork was supported in part by the Research Executive Agency (REA) of the European Commissionunder the Grant Agreements PITN-GA-2012-315877 (MCnet)

A Monash 2013 Tune Parameters

In tabs 3 ndash 7 we list the FSR fragmentation parameters for the Monash tune of PYTHIA Forreference we compare them to the current default parameters

40

FSR Parameters Monash 13 (Default) CommentTimeShoweralphaSvalue = 01365 = 01383 Effective alphaS(mZ) valueTimeShoweralphaSorder = 1 = 1 Running orderTimeShoweralphaSuseCMW = off = off Translation from MS to CMWTimeShowerpTmin = 050 = 040 Cutoff for QCD radiationTimeShowerpTminChgQ = 050 = 040 Cutoff for QED radiationTimeShowerphiPolAsym = on = on Asymmetric azimuth distributions

Table 3 Final-state radiation (FSR) parameters

HAD Parameters Monash 13 (Default) Comment String breaks pT and z distributionsStringPTsigma = 0335 = 0304 Soft pT in string breaks (in GeV)StringPTenhancedFraction = 001 = 001 Fraction of breakups with enhanced pTStringPTenhancedWidth = 20 = 20 Enhancement factorStringZaLund = 068 = 03 Lund FF a (hard fragmentation supp)StringZbLund = 098 = 08 Lund FF b (soft fragmentation supp)StringZaExtraSquark = 00 = 00 Extra a when picking up an s quarkStringZaExtraDiquark = 097 = 050 Extra a when picking up a diquarkStringZrFactC = 132 = 100 Lund-Bowler c-quark parameterStringZrFactB = 0855 = 067 Lund-Bowler b-quark parameter Flavour composition mesonsStringFlavProbStoUD = 0217 = 019 Strangeness-to-UD ratioStringFlavmesonUDvector = 05 = 062 Light-flavour vector suppressionStringFlavmesonSvector = 055 = 0725 Strange vector suppressionStringFlavmesonCvector = 088 = 106 Charm vector suppressionStringFlavmesonBvector = 22 = 30 Bottom vector suppressionStringFlavetaSup = 060 = 063 Suppression of eta mesonsStringFlavetaPrimeSup = 012 = 012 Suppression of etarsquo mesons Flavour composition baryonsStringFlavprobQQtoQ = 0081 = 009 Diquark rate (for baryon production)StringFlavprobSQtoQQ = 0915 = 1000 Strange-diquark suppressionStringFlavprobQQ1toQQ0 = 00275 = 0027 Vector diquark suppressionStringFlavdecupletSup = 10 = 10 Spin-32 baryon suppressionStringFlavsuppressLeadingB = off = off Optional leading-baryon suppressionStringFlavpopcornSpair = 09 = 05 StringFlavpopcornSmeson = 05 = 05

Table 4 String-breaking parameters

PDF and ME Parameters Monash 13 (Default) CommentPDFpSet = 13 = 8 PDF set for the protonSigmaProcessalphaSvalue = 0130 0135 alphaS(MZ) for matrix elementsMultiPartonInteractionsalphaSvalue = 0130 0135 alphaS(MZ) for MPI

Table 5 Parton-distribution (PDF) and Matrix-Element (ME) parameters

41

ISR Parameters Monash 13 (Default) CommentSpaceShoweralphaSvalue = 01365 = 0137 Effective alphaS(mZ) valueSpaceShoweralphaSorder = 1 = 1 Running orderSpaceShoweralphaSuseCMW = off = off Translation from MS to CMWSpaceShowersamePTasMPI = off = off ISR cutoff typeSpaceShowerpT0Ref = 20 = 20 ISR pT0 cutoffSpaceShowerecmRef = 70000 = 18000 ISR pT0 reference ECM scaleSpaceShowerecmPow = 00 = 00 ISR pT0 scaling powerSpaceShowerrapidityOrder = on = on Approx coherence via y-orderingSpaceShowerphiPolAsym = on = on Azimuth asymmetries from gluon polSpaceShowerphiIntAsym = on = on Azimuth asymmetries from interferenceTimeShowerdampenBeamRecoil = on = on Recoil dampening in final-initial dipolesBeamRemnantsprimordialKTsoft = 09 = 05 Primordial kT for soft procsBeamRemnantsprimordialKThard = 18 = 20 Primordial kT for hard procsBeamRemnantshalfScaleForKT = 15 = 10 Primordial kT softhard boundaryBeamRemnantshalfMassForKT = 10 = 10 Primordial kT softhard mass boundary

Table 6 Initial-state radiation (ISR) and primordial-kT parameters

MPI Parameters Monash 13 (Default) CommentMultipartonInteractionspT0Ref = 228 = 2085 MPI pT0 IR regularization scaleMultipartonInteractionsecmRef = 70000 = 18000 MPI pT0 reference ECM scaleMultipartonInteractionsecmPow = 0215 = 019 MPI pT0 scaling powerMultipartonInteractionsbProfile = 3 = 3 Transverse matter overlap profileMultipartonInteractionsexpPow = 185 = 20 Shape parameterBeamRemnantsreconnectRange = 18 = 15 Colour ReconnectionsSigmaTotalzeroAXB = on = on Carried over from 4CSigmaDiffractivedampen = on = on Carried over from 4CSigmaDiffractivemaxXB = 650 = 650 Carried over from 4CSigmaDiffractivemaxAX = 650 = 650 Carried over from 4CSigmaDiffractivemaxXX = 650 = 650 Carried over from 4CDiffractionlargeMassSuppress = 40 = 20 High-mass diffraction suppression power

Table 7 Multi-Parton-Interaction (MPI) Colour-Reconnection (CR) and Diffractive parameters

42

B Additional Plots

B1 LEP Event-Shape Distributions

To keep the main body of the paper as uncluttered as possible we collect various plots of event-shapedistributions in figs 28 and 29 separated into light-flavour and b-tagged events on the left and rightrespectively

The experimental results come from the L3 experiment [26] However since the data points areonly available with 3-digit precision some of the least populated bins contain artifacts like uncertain-ties being reported as exactly zero etc Thus we have been forced to make the following modificationsto the data set

The statistical uncertainty was reported as zero for the last two bins of light-flavour Thrust as wellas for the last bin of the C D and BT parameters Uncertainties lt 10minus3 were derived using anapproximate statistical scaling based on the contents and uncertainties of the other bins Likewise thesystematical uncertainty for the last bin of Thrust was given as zero which we have replaced by theupper limit 5times 10minus4 The last bin of BT quoted a measured y value of zero removed in this study

For the heavy-flavour tagged event shapes more significant rounding issues were present Thusseveral of the first and last bins of each distribution either quoted zero (statistical andor systematic)uncertainties or ones with only a single digit of precision (such as 0001 for which the rounding errorcould be up to sim 50) We have interpreted all such values conservatively inserting by hand a fourthdigit on the uncertainties as large as could be consistent with rounding

B2 Additional Particle Spectra

In addition to the K and Λ spectra shown in the main body of the paper (sections 22 and 35) wehere include for reference the x spectra of φ mesons protons and Ξ baryons at LEP in figs 30 and 31the pT spectrum of Klowast mesons and the rapidity and pT spectra of φ mesons at LHC in fig 32 (withabsolute normalizations to the number of inelastic events) and the rapidity spectrum of Ξ baryons atLHC in fig 33

The transverse-momentum spectra of Klowast and φ mesons in fig 32 exhibit the same qualitativebehaviour as that of the KS mesons (fig 23) namely an excess at very soft momenta below sim 500MeV and a depletion at slightly higher momenta between 1 and 2 GeV As discussed in section 35we did not find a way to remove these undesirable features in the Monash 2013 tune suggesting thatthis is an issue that further theoretical modeling will be needed to resolve

The rapidity spectrum of Ξ baryons fig 33 shows that although the Monash tune does producemore Ξ baryons overall (as expected also from the relative increase of Ξ production at LEP cf fig 5)there is still a significant deficit of Ξ baryons at the LHC almost a factor 2 compared with the dataThis is qualitatively similar to the situation for Λ baryons (fig 24) discussed in section 35 Sincenew physics mechanisms may be required to ldquoexplainrdquo the missing baryons we conclude that furthermeasurements and better precision on both the Λ and Ξ sectors (in addition to any other baryonsthat may be accessible) would be highly interesting More explicit recommendations can be found insections 35 and 5

43

0 01 02 03 04

d(1

-T)

σ d

σ1

-310

-210

-110

1

10

2101-Thrust (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn03

01plusmn04

02plusmn05

V I

N C

I A

R O

O T

1-T (udsc)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

d(1

-T)

σ dσ

1

-310

-210

-110

1

10

2101-T (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn13

02plusmn12

02plusmn14

V I

N C

I A

R O

O T

1-T (b)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210

310C Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn03

00plusmn04

01plusmn04

V I

N C

I A

R O

O T

C0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210 C parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn17

01plusmn24

01plusmn27

V I

N C

I A

R O

O T

C (b)0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn06

01plusmn06

V I

N C

I A

R O

O T

D0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn24

02plusmn21

02plusmn26

V I

N C

I A

R O

O T

D (b)0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

Figure 28 Hadronic Z decays atradics = 912 GeV The T C and D event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

44

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn02

01plusmn03

01plusmn04

V I

N C

I A

R O

O T

WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn05

01plusmn12

01plusmn17

V I

N C

I A

R O

O T

(b)WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn02

00plusmn02

01plusmn03

V I

N C

I A

R O

O T

TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

04plusmn24

08plusmn49

08plusmn55

V I

N C

I A

R O

O T

(b)TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

Figure 29 Hadronic Z decays atradics = 912 GeV The BW and BT event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

45

0 02 04 06 08 1

dx

φgt

dn

φ1

ltn

-210

-110

1

10 )φx(

Pythia 8183Data from ALEPH_1996_S3486095d40-x01-y01

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn37

02plusmn53

03plusmn62

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

0608

112141618

Figure 30 Hadronic Z decays atradics = 912 GeV φ meson x spectrum

-5 -4 -3 -2 -1 0

dx

pgt

dn

p1

ltn

-410

-310

-210

-110

1

10

210) (Combined)px(p+

Pythia 8183Data from Zeit Phys C66 (1995) 355 PhysRev D59 (1998) 052001

ALEPH+SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn08

00plusmn09

00plusmn08

V I

N C

I A

R O

O T

px-5 -4 -3 -2 -1 0

The

ory

Dat

a

06

08

1

12

14

0 02 04

dx

Ξgt

dn

Ξ1

ltn

-110

1

10

)plusmnΞx(

Pythia 8183Data from Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn11

02plusmn13

02plusmn14

V I

N C

I A

R O

O T

Ex0 02 04

The

ory

Dat

a

06

08

1

12

14

Figure 31 Hadronic Z decays atradics = 912 GeV pplusmn and Ξplusmn x spectra

46

0 2 4 6

Td

pK

d

nIN

EL

1N

-510

-410

-310

-210

-110

(INEL |y|lt05)T

p0K

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn35

01plusmn26

01plusmn29

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 2 4 6

Td

pφ

dn

INE

L1

N-510

-410

-310

-210

-110

gt04)T

(INEL |y|lt05 pT

pφ

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn88

03plusmn84

04plusmn173

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

)dy

[mb]

-K

+K

rarrφ(σd

0

05

1

15

2 Rapidity (INEL ATLAS cuts)φ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn14

01plusmn19

01plusmn34

V I

N C

I A

R O

O T

pp 7000 GeV

|y|0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

06 08 1 12

[mb

GeV

]φ

T)

dp-

K+

Krarrφ(

σd

0

05

1

15

2

25 (INEL ATLAS cuts)

T pφ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn21

01plusmn30

02plusmn53

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p06 08 1 12

The

ory

Dat

a

06

08

1

12

14

Figure 32 pp collisions at 7 TeV Top row Klowast and φ pperp spectra compared with ALICE data [142]Bottom row φ rapidity and pperp spectrum compared with ATLAS data [143] The ATLAS cuts areφrarr K+Kminus pperpφ isin [05 12] GeV |y(φ)| lt 08 pperpK gt 023 GeV |pK | lt 08 GeV

47

0 05 1 15 2

dygt

Ξ lt

dnN

SD

1N

0

001

002

003

004)d|y|gt (NSD)Ξltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn89

01plusmn129

01plusmn192

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

0

05

1

15

2

Figure 33 pp collisions at 7 TeV Ξminus rapidity spectrum compared with CMS data [99]

48

B3 Energy Scaling of σ2rarr2(pTmin) vs σinel from 200 GeV to 100 TeV

In fig 34 we show the LO QCD 2rarr 2 cross section integrated above pTmin as a function of pTminin pp collisions at 4 different CM energies complementing and expanding on the 8-TeV CM energyshown in the main body of the paper We compare two different αs and PDF choices correspondingto those made in tunes Monash 13 (blue filled dots) and 4C (red open squares) respectively As areference for the total inelastic cross section at each energy we base ourselves on the best-fit curvein the TOTEM cross-section measurement paper [72] which in turn represents a fit produced by theCOMPETE collaboration [144] Uncertainties are rough conservative estimates based on the plot inthe TOTEM paper but they are in any case too small to significantly affect conclusions about the scaleat which the partonic cross section saturates the hadronic one

We observe that the pTmin value for which the LO QCD 2 rarr 2 partonic cross section formallybecomes equal to the total inelastic cross section (strongly suggesting that every event has at leastone such mini-jet pair) rises from values around 1 ndash 2 GeV at energies

radics lt 1 TeV to 5 GeV atradic

s = 13 TeV and finally 10 GeV atradics = 100 TeV

49

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

0 1 2 3

gtφ|dη

d|

Ch

n2

ltd

0

02

04

06

08

1gt01)

T|lt25 pηgt1 (|

Tlead| wrt pφ∆|

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn16

00plusmn19

00plusmn56

V I

N C

I A

R O

O T

pp 7000 GeV

| [rad]φ∆|0 1 2 3

The

ory

Dat

a

06

08

1

12

14

0 1 2 3

gtφ|dη

d|

Ch

n2

ltd

0

05

1

15

2

gt05)T

|lt25 pηgt5 (|Tlead

| wrt pφ∆|

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn05

00plusmn05

00plusmn70

V I

N C

I A

R O

O T

pp 7000 GeV

| [rad]φ∆|0 1 2 3

The

ory

Dat

a06

08

1

12

14

Figure 21 pp collisions at 7 TeV ∆φ of charged particles with respect to the hardest track for twodifferent hardest-track triggers compared with ATLAS data [98]

(left) and soft (right) fiducial cuts Both of the Monash and 4C tunes reproduce the data quite wellwith χ2

5 lt 1 while the older tune 2C had a higher CR strength optimized to describe Tevatrondata [96] We certainly consider the energy scaling of the effective CR strength among the mostuncertain parameters of the current min-biasunderlying-event modelling (a similar conclusion wasreached for the CR modelling in PYTHIA 6 in [97]) and intend to study the physics aspects of thisissue more closely in a forthcoming paper

For a more differential look at the event structure we consider the charged-track ∆φ distributionswith respect to the azimuthal angle of the leading track in fig 21 compared with ATLAS data [98]The plot in the left-hand pane corresponds to a requirement of pperplead ge 1 GeV while the one in theright-hand pane is for a harder trigger pperplead ge 5 GeV The former can roughly be taken as charac-teristic of min-bias events while the latter is related to the differential distribution of the underlyingevent In both cases the activity in the wide-angle region near π2 is significantly better described bythe 4C and Monash 2013 tunes (which agrees with their improved description of the overall activity)while there is a too strong peaking at low ∆φ especially for the lowest pperplead cut (left) possibly indi-cating that the structure of the min-bias events is still slightly too ldquolumpyrdquo (ie jetty) For the higherpperplead cut (right) the overcounting at very low ∆φ is already significantly milder and we observe agood agreement with the data

Turning now to the underlying event (UE) what matters most for high-pperp jet studies is that theMC models describe the UE contamination per ∆R jet area The most important UE observable fromthis perspective is thus the pperp sum density in the UE and its fluctuations For charged particles atLHC typically a pperp cut of 500 MeV is relevant since softer tracks will form helices and hence notcontribute to calorimetric jet energies Neutral particles are of course relevant across all pperp scalesIn fig 22 we show the charged pperp sum density (left with the lowest possible pperp cut of 100 MeV)and the charged-track density (right with a pperp cut of 500 MeV) in the so-called ldquoTransverse Regionrdquo(defined by 60 lt ∆φ lt 120 with respect to the leading track) inside the ATLAS acceptance of

31

0 5 10 15 20

)φ∆η

∆gt

(T

psum

lt

0

05

1

15

2

25gt01)

T|lt25 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn03

01plusmn09

02plusmn112

V I

N C

I A

R O

O T

pp 7000 GeV

(hardest track) [GeV]T1

p0 5 10 15 20

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20

)φ∆η

∆gt

(C

hlt

n

0

05

1

15

2

25gt05)

T|lt25 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn02

00plusmn04

02plusmn104

V I

N C

I A

R O

O T

pp 7000 GeV

(hardest track) [GeV]T1

p0 5 10 15 20

The

ory

Dat

a06

08

1

12

14

Figure 22 pp collisions at 7 TeV UE (ldquoTransverse regionrdquo) transverse-momentum sum density (left)and charged-track density (right) compared with ATLAS data [98]

|η| lt 25 [98] As is now well known the Tevatron extrapolations (represented here by Tune 2C)predicted a UE level which was 10 ndash 20 below the LHC data Both the current default tune 4C(which included LHC data) and the Monash 2013 tune exhibit significantly better agreement with theLHC measurements with the Monash one giving a slight additional improvement in the χ2

5 valuesWe conclude that the Monash 2013 tune parameters are appropriate for both min-bias and UE studies

35 Identified Particles at LHC

While the description of inclusive charged particles discussed in the previous section is acceptablelarger discrepancies emerge when we consider the spectra of identified particles We here focus onstrange particles in particular K0

S mesons and Λ0 hyperons in figs 23 and 24 respectively Theexperimental measurements come from CMS [99] Additional comparisons to strange-particle spectra(Klowast φ and Ξ) are collected in appendix B2

In the K0S rapidity distribution shown in the left-hand pane of fig 23 we observe that tune 4C

exhibits a mild underproduction of about 10 Though it might be tempting to speculate whether thiscould indicate some small reduction of strangeness suppression in pp collisions however we alreadynoted in section 21 that the strangeness production in ee collisions also needed to be increased byabout 10 After this adjustment we see that the overall K0

S yield in the Monash 2013 tune is fullyconsistent with the CMS measurement Nonetheless we note that the momentum distribution is stillnot satisfactorily described as shown in the right-hand pane of fig 23 Our current best guess istherefore that the overall rate of strange quarks is consistent at least in the average min-bias collision(dedicated comparisons in high-multiplicity samples would still be interesting) but that the phase-space distribution of strange hadrons needs more work Similarly to the case in ee collisions cf fig 6the model predicts too many very soft kaons though we do not currently know whether there is adynamic link between the ee and pp observations

For strange baryons we note that the increase in the Λ0 fraction in ee collisions (cf fig 5) does

32

0 05 1 15 2

dygt

K lt

dnN

SD

1n

0

02

04

06

08)d|y|gt Rapidity (NSD)

S

0ltdn(K

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn01

00plusmn09

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8 10

Td

pK

dn

NS

D1

N

-510

-410

-310

-210

-110

1

10 (|y|lt20 NSD)

T pS

0K

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn78

01plusmn34

02plusmn22

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6 8 10

The

ory

Dat

a06

08

1

12

14

Figure 23 pp collisions at 7 TeV K0S rapidity and pperp spectrum compared with CMS data [99]

0 05 1 15 2

dygt

Λ lt

dnN

SD

1N

0

01

02

03

04)d|y|gt (NSD)0Λltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn64

00plusmn78

01plusmn147

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8 10

Td

pΛ

dn

Λ1

n

-510

-410

-310

-210

-110

1

10 (|y|lt20 NSD)

T p0Λ

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn59

03plusmn66

05plusmn105

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6 8 10

The

ory

Dat

a

06

08

1

12

14

Figure 24 pp collisions at 7 TeV Λ0 rapidity and pperp spectrum compared with CMS data [99]

not result in an equivalent improvement of the Λ0 rate in pp collisions shown in fig 24 The Monash2013 tune still produces only about 23 of the observed Λ0 rate (and just over half of the observedΞminus rate cf appendix B2) We therefore believe it to be likely that an additional source of net baryonproduction is needed (at least within the limited context of the current PYTHIA modelling) in orderto describe the LHC data The momentum spectrum is likewise quite discrepant exhibiting an excessat very low momenta (stronger than that for kaons) a dip between 1ndash4 GeV and then an excess of veryhard Λ0 production The latter hard tail is somewhat milder in the Monash 2013 tune than previously

33

and it may be consistent with the trend also seen in the Λ0 spectrum at LEP cf fig 6 We concludethat baryon production still requires further modelling and tuning efforts

4 Energy Scaling

Though energy scaling these days mostly refers to the scaling of pp collisions (see eg [97]) animportant first step is to consider the scaling of observables in ee rarr γlowastZ rarr hadrons This scalingcontains information on the relative contributions of perturbative and non-perturbative fragmentationThus at low ee energies the non-perturbative components of the fragmentation model dominatewhile perturbative bremsstrahlung increases in importance towards higher ee energies In fig 25we consider the scaling of the average charged-particle multiplicity and that of charged Kaons andLambda baryons from CM energies of 14 GeV to 200 GeV obtained from measurements availableat HEPDATA Below the Z pole the measurements we include mostly come from TASSO [100]though a few points on 〈nCh〉 come from HRS (at 29 GeV [101]) and TOPAZ (at 578 GeV [102]) Atthe Z pole the data come from the four LEP experiments [38 51ndash53] with the latter extending alsoto energies above MZ [103ndash108] For completeness and as reference for future ee collider studiesmodel extrapolations for CM energies up to 1000 GeV are also shown (though still only including theeerarr γlowastZ rarr hadrons component as usual with photon ISR switched off)

From the plots in fig 25 it is clear that there are no significant differences between the energyscaling of the three ee tunes considered here (mainly reflecting that they have been tuned to samereference point at 912 GeV and that their scaling is dictated by the same underlying physics model)and that their energy dependence closely matches that observed in data However the increasedamount of non-perturbative strangeness production in the Monash tune leads to a better agreementwith the overall normalization of the Kplusmn and Λ rates at all energies

Moving to pp collisions the plots in fig 26 show the scaling of the average charged multiplicity(left column) and multiplicity distributions (right column) in min-bias collisions from 7000 GeV (toprow) to 900 GeV (middle row) and 200 GeV (bottom row) compared with data from CMS [92 109]ATLAS [91] and UA5 [110 111] We regret the omission of additional relevant min-bias measure-ments from the Tevatron and RHIC experiments here but have chosen to focus in this paper mainlyon the LHC The comparisons at 7 TeV were already discussed in the main section on pp collisionssection 3 At 900 GeV the Monash 2013 tune again gives a roughly 5 lower average central chargedmultiplicity than the 4C one with a better description of the tail towards high multiplicities At 200GeV the UA5 measurement we include here extends over the full rapidity and pperp range hence the in-terplay between diffraction and low-multiplicity non-diffractive processes is presumably (much) moreimportant We believe imperfections in this modelling to be the likely cause of the significant discrep-ancies observed at high η and for nCh le 20 at these energies Since a dedicated study of this interplayis beyond the scope of this study we limit ourselves merely to stating this observation as a point forfuture studies to help clarify

Finally in fig 27 we compare to the underlying event measured in the highly useful energyscan that was performed at the Tevatron in the last days before its shutdown [22 23] during whichextremely high min-bias statistics were collected at 300 and 900 GeV CM energy over a period of afew days As was already noted in section 3 the UE at 7 TeV is slightly larger in the Monash 2013tune than in tune 4C As can be seen from the plots here the two tunes give comparable results for allthe Tevatron energies Interestingly the UE plateau region at 900 and 1960 GeV is reached sooner inthese models than in the data translating to a roughly 10 - 20 too low UE level for leading-trackpperp values in the neighbourhood of the transition from the rise to the plateau (roughly for leading-

34

14 22 29 35 44 58 91 91 91 91 133 161 183 189 200 250 350 500 1000

gtC

hlt

n

0

20

40

60

Average Charged Multiplicity vs ECM

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN25

χ00plusmn03 00plusmn02 00plusmn02

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 22 29 35 44 58 91 91 91 91 133 161 183 189 200 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

14 22 35 44 91 91 133 161 183 189 250 350 500 1000

gtK

ltn

0

2

4

6 Multiplicity vs ECM+-Average K

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN25

χ00plusmn06 00plusmn20

00plusmn18

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 22 35 44 91 91 133 161 183 189 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

14 35 91 91 91 91 133 200 250 350 500 1000

gtΛ

ltn

0

02

04

06

08

1

12 Multiplicity vs ECM0ΛAverage

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn06

01plusmn22

01plusmn18

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 35 91 91 91 91 133 200 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

Figure 25 e+eminus rarr hadrons Energy scaling of 〈nCh〉 〈nKplusmn〉 and 〈nΛ〉 in e+eminus rarr qq eventsincluding comparisons to measurements from HEPDATA for CM energies from 14 GeV to 200 GeVAlso shown are model extrapolations up to 1000 GeV

35

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from PhysRevLett 105 (2010) 022002

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn00

00plusmn03

00plusmn71

V I

N C

I A

R O

O T

pp 7000 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

0 50 100

)C

hP

rob(

n

-710

-610

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn27

00plusmn27

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

Chn0 50 100

The

ory

Dat

a

06

08

1

12

14

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from JHEP 1002 (2010) 041

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn03

00plusmn05

00plusmn29

V I

N C

I A

R O

O T

pp 900 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

0 10 20 30 40

)C

hP

rob(

n

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn17

01plusmn25

02plusmn127

V I

N C

I A

R O

O T

pp 900 GeV

Chn0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

0 1 2 3 4 5

gtηd

ch lt

dnN

SD

1n

0

1

2

3

4

5gt (NSD)ηd

chltdn

Pythia 8185Data from ZPhys C33 (1986) 1-6

UA5PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn36

00plusmn24

00plusmn16

V I

N C

I A

R O

O T

ppbar 200 GeV

η0 1 2 3 4 5

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)C

hP

rob(

n

-410

-310

-210

-110

1

)T

|lt05 all pηChg Mult (NSD |

Pythia 8185Data from ZPhys C43 (1989) 357

UA5PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn24

00plusmn24

00plusmn08

V I

N C

I A

R O

O T

ppbar 200 GeV

Chn0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 26 Min-bias pp events from 200 to 7000 GeV Energy scaling of 〈dnChdη〉 (left) andP (nCh) (right)

36

0 10 20 30

)φ∆η

∆gt

(T

psum

lt

0

05

1

15gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn24

26plusmn33

12plusmn143

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 10 20 30

)φ∆η

∆gt

(C

hlt

n

0

05

1

15gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

04plusmn05

13plusmn08

14plusmn100

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn58

06plusmn53

08plusmn193

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn16

15plusmn20

06plusmn114

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

gt05)T

|lt10 pη (|T1

)gt vs pT

TRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn10

02plusmn07

05plusmn22

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

gt05)T

|lt10 pη (|T1

gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn20

02plusmn11

03plusmn08

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 27 The Tevatron energy scan The underlying event (left average summed-pperp density andright average track density in the transverse region as function of leading-track pperp) for pp collisionsat 300 (bottom row) 900 GeV (middle row) and 1960 GeV (top row)

37

track pperp values 2 lt pT1 lt 10 GeV) This indicates that the energy scaling of the UE modeling and inparticular the details of its transition between central and peripheral collisions is still not satisfactorilyunderstood

5 Conclusions and Exhortation

We have presented a reanalysis of the constraints on fragmentation in ee collisions and applied theresults to update the final-state fragmentation parameters in PYTHIA 8 We combine these parameterswith a tune to hadron-collider data using a new NNPDF 23 LO QCD+QED PDF set which has beenencoded so it is available as an internal PDF set in PYTHIA 8 independently of LHAPDF [112]

In this PDF set as well as in our tune the value of the strong coupling for hard-scattering matrixelements is fixed to be αs(MZ) = 013 consistent with other LO determinations of it For initial-and final-state radiation our tune uses the effective value αs(MZ) = 01365 The difference isconsistent with an effective translation between the MS and CMW schemes We note that alternative(LO NLO and NNLO) NNPDF 23 QCD+QED sets with αs(MZ) = 0119 are also available inthe code for people who want to check the impact of using a different αs(MZ) value andor higher-order PDF sets on hard-scattering events For the purpose of such studies we point out that it ispossible in PYTHIA 8 to preserve most of the features of the shower- and underlying-event tuningby changing only the PDF for the hard-scattering matrix elements leaving the PDF choice for theshower evolution and MPI framework unaltered (see the PYTHIA 8 HTML manualrsquos PDF sectionunder PDFuseHard)

The updated parameters are available as an option starting from PYTHIA 8185 by setting

Tuneee = 7 and Tunepp = 14

By no means do we claim that this should be regarded as the final word in tuning the PYTHIA 8Monte Carlo model First of all the model continues to evolve For instance developments foreseenfor the near future include updates of colour reconnections diffraction and the treatment of g rarr qqsplittings Any of these should in principle be accompanied by a reevaluation of the model constraints

Moreover despite the comprehensive view of collider data we have attempted to take in thisstudy there still remains several issues that were not addressed including initial-final interferenceand coherence effects [113 114] (probably more a modelling issue than a tuning one) reliable esti-mates of theoretical uncertainties [8 17 24 29 97 115] diffraction14 [74 116 117] and other colour-singlet phenomena such as onium production long-distance (eg forward-backward forward-centraland ldquoridgerdquo-type) correlations [88 118ndash123] B-hadron decays [124] and tuning in the presence ofmatrix-element matching at LO and NLO (see [21 29 115 125 126] for recent phenomenologi-cal studies) Especially in the latter context of matrix-element matching we expect that in manycases PYTHIA 8 will be used together with codes such as ALPGEN [127] MADGRAPH [128]aMCatNLO [129] or POWHEG [130] either using the matching algorithms of those programs them-selves or via any of PYTHIArsquos several internal (LHEF-based [131]) implementations of matchingschemes (POWHEG [85] CKKW-L [132ndash134] MLM [135 136] UMEPS [137] NL3 [138] UN-LOPS [139]) The impact of such corrections on MC tuning depends on the details of the matchingscheme (especially its treatment of unitarity) and there is in general a non-negligible possibility ofldquomis-tuningrdquo when combining a stand-alone tune with ME corrections A simple example illustrating

14In particular the constraints on fragmentation mainly come from SLD and LEP where the non-perturbative parametersare clearly defined at the shower cutoff scaleQhad whereas diffraction is dominated by soft physics for which the definitionof the effective hadronization scale is less clear The amount of MPI in hard diffractive events also requires tuning

38

this is the effective value of αs(MZ) which for a leading-order tune is typically of order 013 whilea consistent NLO correction scheme should be compatible with values closer to 012 [29] There isalso the question of the running order of αs The propagation of such changes from the level of hardmatrix elements through the shower and hadronization tuning process are still not fully explored andhence we advise users to perform simple cross-checks such as checking the distributions presented inthis paper before and after applying matrix-element corrections Parameters that appear on both sidesof the matching such as αs should also be checked for consistency [21]

We noted several issues concerning the ee data used to constrain the fragmentation modelling thatit would be good to resolve In particular we find some tensions between the identified-particle ratesextracted from 1) HEDPATA 2) Sec 46 of the PDG and 3) the Z boson summary table in the PDGas discussed in more detail in section 2 and concerning which we made some (subjective) decisionsto arrive at a set of hopefully self-consistent constraints for this work We also note that the overallprecision of the fragmentation constraints could likely be significantly improved by an FCC-ee typemachine such as Tera-Z a possibility we hope to see more fully explored in the context of future eeQCD phenomenology studies

We conclude that the new parameter set does improve significantly on the previous default valuesin several respects including better agreement with data on

1 the net strangeness fraction (has been increased by 10 reflected not only in improved kaonand hyperon yields but also in the Ds and Bs fractions)

2 the ultra-hard fragmentation tail (has been softened especially for leading baryons and for Dand B hadrons)

3 the pTZ spectrum (softened at low pTZ)

4 the minimum-bias charged multiplicity in the forward region (has increased by 10)

5 the underlying event at 7 TeV (is very slightly higher than before)

Some questions that remain open include the following We see a roughly 20 excess of verysoft kaons in both ee and pp environments cf figs 6 and 23 despite the overall kaon yields beingwell described and the overall baryon yields at LHC appear to be underestimated by at least 30despite good agreement at LEP The momentum spectra of heavier strange particles are also poorlyreproduced in particular at LHC It is interesting and exciting that some of the LHC spectra appearto be better described by allowing collective flow in a fraction of events (cf the EPOS model [140])though we believe the jury is still out on whether this accurately reflects the underlying physics Forinstance it has been argued that colour reconnections can mimick flow effects [90] and they may alsobe able to modify the yield of baryons if the creationdestruction of string junctions is allowed [141]We look forward to future discussions on these issues

We round off with an exhortation for follow-ups on this study to provide

bull Not only central tunes experiments and other user-end colleagues need more than central de-scriptions of data there is an increasing need for serious uncertainty estimates In the contextof tune variations it is important to keep in mind that the modelling uncertainties are often in-trinsically non-universal Therefore the constraints obtained by considering data uncertaintiesonly (eg in the spirit of PROFESSORrsquos eigentunes [17]) can at most constitute a lower boundon the theoretical uncertainty (similarly to the case for PDFs) A serious uncertainty estimateincludes some systematic modelling variation irrespectively of and in addition to what data

39

allows (eg in the spirit of the Perugia set of tunes for PYTHIA 6 [8]) We therefore hope thefuture will see more elaborate combinations of data- and theory-driven approaches to systematictune uncertainties

bull Not only global tunes the power of MC models lies in their ability to simultaneously describea large variety of data hence we do not mean to imply that one should give up on universalityand tune to increasingly specific corners of phase space disregarding (or de-emphasizing withlower weights) all others However as proposed in [97] one can obtain useful explicit tests ofthe universality of the underlying physics model by performing independent tunes on separateldquophysics windowsrdquo say in the forward vs central regions for different event-selection crite-ria at different collider energies or even for different collider types In this connection justmaking one global ldquobest-fitrdquo tune may obscure tensions between the descriptions of differentcomplementary data sets By performing independent tunes to each data set separately andchecking the degree of universality of the resulting parameters one obtains a powerful crosscheck on the underlying physics model If all sets produce the same or similar parameters thenuniversality is OK hence a global tune makes very good sense and the remaining uncertain-ties can presumably be reliably estimated from data alone If instead some data sets resultin significantly different tune parameters one has a powerful indication that the universality ofthe underlying modeling is breaking down which can lead to several productive actions 1) itcan be taken into account in the context of uncertainty variations 2) the nature of the data setsfor which non-universal tune parameters are obtained can implicitly indicate the nature of theproblem leading to more robust conclusions about the underlying model than merely whether atune cancannot fit the data and 3) the observations can be communicated to the model authorsin a more unambiguous way hopefully resulting in a speedier cycle of model improvements

We hope that the Monash 2013 tune parameters may serve as a useful starting point for phe-nomenology studies and for future PYTHIA 8 tuning efforts

Acknowledgments

We thank S Mrenna M Ritzmann and T Sjostrand for comments on the manuscript and L de Nooijfor pointing us to the ALICE Klowast and φ measurements [142] and to the ATLAS φ measurementsin [143] The work of J R is supported by an STFC Rutherford Fellowship STK0052271 Thiswork was supported in part by the Research Executive Agency (REA) of the European Commissionunder the Grant Agreements PITN-GA-2012-315877 (MCnet)

A Monash 2013 Tune Parameters

In tabs 3 ndash 7 we list the FSR fragmentation parameters for the Monash tune of PYTHIA Forreference we compare them to the current default parameters

40

FSR Parameters Monash 13 (Default) CommentTimeShoweralphaSvalue = 01365 = 01383 Effective alphaS(mZ) valueTimeShoweralphaSorder = 1 = 1 Running orderTimeShoweralphaSuseCMW = off = off Translation from MS to CMWTimeShowerpTmin = 050 = 040 Cutoff for QCD radiationTimeShowerpTminChgQ = 050 = 040 Cutoff for QED radiationTimeShowerphiPolAsym = on = on Asymmetric azimuth distributions

Table 3 Final-state radiation (FSR) parameters

HAD Parameters Monash 13 (Default) Comment String breaks pT and z distributionsStringPTsigma = 0335 = 0304 Soft pT in string breaks (in GeV)StringPTenhancedFraction = 001 = 001 Fraction of breakups with enhanced pTStringPTenhancedWidth = 20 = 20 Enhancement factorStringZaLund = 068 = 03 Lund FF a (hard fragmentation supp)StringZbLund = 098 = 08 Lund FF b (soft fragmentation supp)StringZaExtraSquark = 00 = 00 Extra a when picking up an s quarkStringZaExtraDiquark = 097 = 050 Extra a when picking up a diquarkStringZrFactC = 132 = 100 Lund-Bowler c-quark parameterStringZrFactB = 0855 = 067 Lund-Bowler b-quark parameter Flavour composition mesonsStringFlavProbStoUD = 0217 = 019 Strangeness-to-UD ratioStringFlavmesonUDvector = 05 = 062 Light-flavour vector suppressionStringFlavmesonSvector = 055 = 0725 Strange vector suppressionStringFlavmesonCvector = 088 = 106 Charm vector suppressionStringFlavmesonBvector = 22 = 30 Bottom vector suppressionStringFlavetaSup = 060 = 063 Suppression of eta mesonsStringFlavetaPrimeSup = 012 = 012 Suppression of etarsquo mesons Flavour composition baryonsStringFlavprobQQtoQ = 0081 = 009 Diquark rate (for baryon production)StringFlavprobSQtoQQ = 0915 = 1000 Strange-diquark suppressionStringFlavprobQQ1toQQ0 = 00275 = 0027 Vector diquark suppressionStringFlavdecupletSup = 10 = 10 Spin-32 baryon suppressionStringFlavsuppressLeadingB = off = off Optional leading-baryon suppressionStringFlavpopcornSpair = 09 = 05 StringFlavpopcornSmeson = 05 = 05

Table 4 String-breaking parameters

PDF and ME Parameters Monash 13 (Default) CommentPDFpSet = 13 = 8 PDF set for the protonSigmaProcessalphaSvalue = 0130 0135 alphaS(MZ) for matrix elementsMultiPartonInteractionsalphaSvalue = 0130 0135 alphaS(MZ) for MPI

Table 5 Parton-distribution (PDF) and Matrix-Element (ME) parameters

41

ISR Parameters Monash 13 (Default) CommentSpaceShoweralphaSvalue = 01365 = 0137 Effective alphaS(mZ) valueSpaceShoweralphaSorder = 1 = 1 Running orderSpaceShoweralphaSuseCMW = off = off Translation from MS to CMWSpaceShowersamePTasMPI = off = off ISR cutoff typeSpaceShowerpT0Ref = 20 = 20 ISR pT0 cutoffSpaceShowerecmRef = 70000 = 18000 ISR pT0 reference ECM scaleSpaceShowerecmPow = 00 = 00 ISR pT0 scaling powerSpaceShowerrapidityOrder = on = on Approx coherence via y-orderingSpaceShowerphiPolAsym = on = on Azimuth asymmetries from gluon polSpaceShowerphiIntAsym = on = on Azimuth asymmetries from interferenceTimeShowerdampenBeamRecoil = on = on Recoil dampening in final-initial dipolesBeamRemnantsprimordialKTsoft = 09 = 05 Primordial kT for soft procsBeamRemnantsprimordialKThard = 18 = 20 Primordial kT for hard procsBeamRemnantshalfScaleForKT = 15 = 10 Primordial kT softhard boundaryBeamRemnantshalfMassForKT = 10 = 10 Primordial kT softhard mass boundary

Table 6 Initial-state radiation (ISR) and primordial-kT parameters

MPI Parameters Monash 13 (Default) CommentMultipartonInteractionspT0Ref = 228 = 2085 MPI pT0 IR regularization scaleMultipartonInteractionsecmRef = 70000 = 18000 MPI pT0 reference ECM scaleMultipartonInteractionsecmPow = 0215 = 019 MPI pT0 scaling powerMultipartonInteractionsbProfile = 3 = 3 Transverse matter overlap profileMultipartonInteractionsexpPow = 185 = 20 Shape parameterBeamRemnantsreconnectRange = 18 = 15 Colour ReconnectionsSigmaTotalzeroAXB = on = on Carried over from 4CSigmaDiffractivedampen = on = on Carried over from 4CSigmaDiffractivemaxXB = 650 = 650 Carried over from 4CSigmaDiffractivemaxAX = 650 = 650 Carried over from 4CSigmaDiffractivemaxXX = 650 = 650 Carried over from 4CDiffractionlargeMassSuppress = 40 = 20 High-mass diffraction suppression power

Table 7 Multi-Parton-Interaction (MPI) Colour-Reconnection (CR) and Diffractive parameters

42

B Additional Plots

B1 LEP Event-Shape Distributions

To keep the main body of the paper as uncluttered as possible we collect various plots of event-shapedistributions in figs 28 and 29 separated into light-flavour and b-tagged events on the left and rightrespectively

The experimental results come from the L3 experiment [26] However since the data points areonly available with 3-digit precision some of the least populated bins contain artifacts like uncertain-ties being reported as exactly zero etc Thus we have been forced to make the following modificationsto the data set

The statistical uncertainty was reported as zero for the last two bins of light-flavour Thrust as wellas for the last bin of the C D and BT parameters Uncertainties lt 10minus3 were derived using anapproximate statistical scaling based on the contents and uncertainties of the other bins Likewise thesystematical uncertainty for the last bin of Thrust was given as zero which we have replaced by theupper limit 5times 10minus4 The last bin of BT quoted a measured y value of zero removed in this study

For the heavy-flavour tagged event shapes more significant rounding issues were present Thusseveral of the first and last bins of each distribution either quoted zero (statistical andor systematic)uncertainties or ones with only a single digit of precision (such as 0001 for which the rounding errorcould be up to sim 50) We have interpreted all such values conservatively inserting by hand a fourthdigit on the uncertainties as large as could be consistent with rounding

B2 Additional Particle Spectra

In addition to the K and Λ spectra shown in the main body of the paper (sections 22 and 35) wehere include for reference the x spectra of φ mesons protons and Ξ baryons at LEP in figs 30 and 31the pT spectrum of Klowast mesons and the rapidity and pT spectra of φ mesons at LHC in fig 32 (withabsolute normalizations to the number of inelastic events) and the rapidity spectrum of Ξ baryons atLHC in fig 33

The transverse-momentum spectra of Klowast and φ mesons in fig 32 exhibit the same qualitativebehaviour as that of the KS mesons (fig 23) namely an excess at very soft momenta below sim 500MeV and a depletion at slightly higher momenta between 1 and 2 GeV As discussed in section 35we did not find a way to remove these undesirable features in the Monash 2013 tune suggesting thatthis is an issue that further theoretical modeling will be needed to resolve

The rapidity spectrum of Ξ baryons fig 33 shows that although the Monash tune does producemore Ξ baryons overall (as expected also from the relative increase of Ξ production at LEP cf fig 5)there is still a significant deficit of Ξ baryons at the LHC almost a factor 2 compared with the dataThis is qualitatively similar to the situation for Λ baryons (fig 24) discussed in section 35 Sincenew physics mechanisms may be required to ldquoexplainrdquo the missing baryons we conclude that furthermeasurements and better precision on both the Λ and Ξ sectors (in addition to any other baryonsthat may be accessible) would be highly interesting More explicit recommendations can be found insections 35 and 5

43

0 01 02 03 04

d(1

-T)

σ d

σ1

-310

-210

-110

1

10

2101-Thrust (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn03

01plusmn04

02plusmn05

V I

N C

I A

R O

O T

1-T (udsc)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

d(1

-T)

σ dσ

1

-310

-210

-110

1

10

2101-T (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn13

02plusmn12

02plusmn14

V I

N C

I A

R O

O T

1-T (b)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210

310C Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn03

00plusmn04

01plusmn04

V I

N C

I A

R O

O T

C0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210 C parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn17

01plusmn24

01plusmn27

V I

N C

I A

R O

O T

C (b)0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn06

01plusmn06

V I

N C

I A

R O

O T

D0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn24

02plusmn21

02plusmn26

V I

N C

I A

R O

O T

D (b)0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

Figure 28 Hadronic Z decays atradics = 912 GeV The T C and D event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

44

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn02

01plusmn03

01plusmn04

V I

N C

I A

R O

O T

WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn05

01plusmn12

01plusmn17

V I

N C

I A

R O

O T

(b)WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn02

00plusmn02

01plusmn03

V I

N C

I A

R O

O T

TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

04plusmn24

08plusmn49

08plusmn55

V I

N C

I A

R O

O T

(b)TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

Figure 29 Hadronic Z decays atradics = 912 GeV The BW and BT event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

45

0 02 04 06 08 1

dx

φgt

dn

φ1

ltn

-210

-110

1

10 )φx(

Pythia 8183Data from ALEPH_1996_S3486095d40-x01-y01

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn37

02plusmn53

03plusmn62

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

0608

112141618

Figure 30 Hadronic Z decays atradics = 912 GeV φ meson x spectrum

-5 -4 -3 -2 -1 0

dx

pgt

dn

p1

ltn

-410

-310

-210

-110

1

10

210) (Combined)px(p+

Pythia 8183Data from Zeit Phys C66 (1995) 355 PhysRev D59 (1998) 052001

ALEPH+SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn08

00plusmn09

00plusmn08

V I

N C

I A

R O

O T

px-5 -4 -3 -2 -1 0

The

ory

Dat

a

06

08

1

12

14

0 02 04

dx

Ξgt

dn

Ξ1

ltn

-110

1

10

)plusmnΞx(

Pythia 8183Data from Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn11

02plusmn13

02plusmn14

V I

N C

I A

R O

O T

Ex0 02 04

The

ory

Dat

a

06

08

1

12

14

Figure 31 Hadronic Z decays atradics = 912 GeV pplusmn and Ξplusmn x spectra

46

0 2 4 6

Td

pK

d

nIN

EL

1N

-510

-410

-310

-210

-110

(INEL |y|lt05)T

p0K

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn35

01plusmn26

01plusmn29

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 2 4 6

Td

pφ

dn

INE

L1

N-510

-410

-310

-210

-110

gt04)T

(INEL |y|lt05 pT

pφ

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn88

03plusmn84

04plusmn173

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

)dy

[mb]

-K

+K

rarrφ(σd

0

05

1

15

2 Rapidity (INEL ATLAS cuts)φ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn14

01plusmn19

01plusmn34

V I

N C

I A

R O

O T

pp 7000 GeV

|y|0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

06 08 1 12

[mb

GeV

]φ

T)

dp-

K+

Krarrφ(

σd

0

05

1

15

2

25 (INEL ATLAS cuts)

T pφ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn21

01plusmn30

02plusmn53

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p06 08 1 12

The

ory

Dat

a

06

08

1

12

14

Figure 32 pp collisions at 7 TeV Top row Klowast and φ pperp spectra compared with ALICE data [142]Bottom row φ rapidity and pperp spectrum compared with ATLAS data [143] The ATLAS cuts areφrarr K+Kminus pperpφ isin [05 12] GeV |y(φ)| lt 08 pperpK gt 023 GeV |pK | lt 08 GeV

47

0 05 1 15 2

dygt

Ξ lt

dnN

SD

1N

0

001

002

003

004)d|y|gt (NSD)Ξltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn89

01plusmn129

01plusmn192

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

0

05

1

15

2

Figure 33 pp collisions at 7 TeV Ξminus rapidity spectrum compared with CMS data [99]

48

B3 Energy Scaling of σ2rarr2(pTmin) vs σinel from 200 GeV to 100 TeV

In fig 34 we show the LO QCD 2rarr 2 cross section integrated above pTmin as a function of pTminin pp collisions at 4 different CM energies complementing and expanding on the 8-TeV CM energyshown in the main body of the paper We compare two different αs and PDF choices correspondingto those made in tunes Monash 13 (blue filled dots) and 4C (red open squares) respectively As areference for the total inelastic cross section at each energy we base ourselves on the best-fit curvein the TOTEM cross-section measurement paper [72] which in turn represents a fit produced by theCOMPETE collaboration [144] Uncertainties are rough conservative estimates based on the plot inthe TOTEM paper but they are in any case too small to significantly affect conclusions about the scaleat which the partonic cross section saturates the hadronic one

We observe that the pTmin value for which the LO QCD 2 rarr 2 partonic cross section formallybecomes equal to the total inelastic cross section (strongly suggesting that every event has at leastone such mini-jet pair) rises from values around 1 ndash 2 GeV at energies

radics lt 1 TeV to 5 GeV atradic

s = 13 TeV and finally 10 GeV atradics = 100 TeV

49

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

0 5 10 15 20

)φ∆η

∆gt

(T

psum

lt

0

05

1

15

2

25gt01)

T|lt25 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn03

01plusmn09

02plusmn112

V I

N C

I A

R O

O T

pp 7000 GeV

(hardest track) [GeV]T1

p0 5 10 15 20

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20

)φ∆η

∆gt

(C

hlt

n

0

05

1

15

2

25gt05)

T|lt25 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from PhysRev D83 (2011) 112001

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn02

00plusmn04

02plusmn104

V I

N C

I A

R O

O T

pp 7000 GeV

(hardest track) [GeV]T1

p0 5 10 15 20

The

ory

Dat

a06

08

1

12

14

Figure 22 pp collisions at 7 TeV UE (ldquoTransverse regionrdquo) transverse-momentum sum density (left)and charged-track density (right) compared with ATLAS data [98]

|η| lt 25 [98] As is now well known the Tevatron extrapolations (represented here by Tune 2C)predicted a UE level which was 10 ndash 20 below the LHC data Both the current default tune 4C(which included LHC data) and the Monash 2013 tune exhibit significantly better agreement with theLHC measurements with the Monash one giving a slight additional improvement in the χ2

5 valuesWe conclude that the Monash 2013 tune parameters are appropriate for both min-bias and UE studies

35 Identified Particles at LHC

While the description of inclusive charged particles discussed in the previous section is acceptablelarger discrepancies emerge when we consider the spectra of identified particles We here focus onstrange particles in particular K0

S mesons and Λ0 hyperons in figs 23 and 24 respectively Theexperimental measurements come from CMS [99] Additional comparisons to strange-particle spectra(Klowast φ and Ξ) are collected in appendix B2

In the K0S rapidity distribution shown in the left-hand pane of fig 23 we observe that tune 4C

exhibits a mild underproduction of about 10 Though it might be tempting to speculate whether thiscould indicate some small reduction of strangeness suppression in pp collisions however we alreadynoted in section 21 that the strangeness production in ee collisions also needed to be increased byabout 10 After this adjustment we see that the overall K0

S yield in the Monash 2013 tune is fullyconsistent with the CMS measurement Nonetheless we note that the momentum distribution is stillnot satisfactorily described as shown in the right-hand pane of fig 23 Our current best guess istherefore that the overall rate of strange quarks is consistent at least in the average min-bias collision(dedicated comparisons in high-multiplicity samples would still be interesting) but that the phase-space distribution of strange hadrons needs more work Similarly to the case in ee collisions cf fig 6the model predicts too many very soft kaons though we do not currently know whether there is adynamic link between the ee and pp observations

For strange baryons we note that the increase in the Λ0 fraction in ee collisions (cf fig 5) does

32

0 05 1 15 2

dygt

K lt

dnN

SD

1n

0

02

04

06

08)d|y|gt Rapidity (NSD)

S

0ltdn(K

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn01

00plusmn09

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8 10

Td

pK

dn

NS

D1

N

-510

-410

-310

-210

-110

1

10 (|y|lt20 NSD)

T pS

0K

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn78

01plusmn34

02plusmn22

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6 8 10

The

ory

Dat

a06

08

1

12

14

Figure 23 pp collisions at 7 TeV K0S rapidity and pperp spectrum compared with CMS data [99]

0 05 1 15 2

dygt

Λ lt

dnN

SD

1N

0

01

02

03

04)d|y|gt (NSD)0Λltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn64

00plusmn78

01plusmn147

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8 10

Td

pΛ

dn

Λ1

n

-510

-410

-310

-210

-110

1

10 (|y|lt20 NSD)

T p0Λ

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn59

03plusmn66

05plusmn105

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6 8 10

The

ory

Dat

a

06

08

1

12

14

Figure 24 pp collisions at 7 TeV Λ0 rapidity and pperp spectrum compared with CMS data [99]

not result in an equivalent improvement of the Λ0 rate in pp collisions shown in fig 24 The Monash2013 tune still produces only about 23 of the observed Λ0 rate (and just over half of the observedΞminus rate cf appendix B2) We therefore believe it to be likely that an additional source of net baryonproduction is needed (at least within the limited context of the current PYTHIA modelling) in orderto describe the LHC data The momentum spectrum is likewise quite discrepant exhibiting an excessat very low momenta (stronger than that for kaons) a dip between 1ndash4 GeV and then an excess of veryhard Λ0 production The latter hard tail is somewhat milder in the Monash 2013 tune than previously

33

and it may be consistent with the trend also seen in the Λ0 spectrum at LEP cf fig 6 We concludethat baryon production still requires further modelling and tuning efforts

4 Energy Scaling

Though energy scaling these days mostly refers to the scaling of pp collisions (see eg [97]) animportant first step is to consider the scaling of observables in ee rarr γlowastZ rarr hadrons This scalingcontains information on the relative contributions of perturbative and non-perturbative fragmentationThus at low ee energies the non-perturbative components of the fragmentation model dominatewhile perturbative bremsstrahlung increases in importance towards higher ee energies In fig 25we consider the scaling of the average charged-particle multiplicity and that of charged Kaons andLambda baryons from CM energies of 14 GeV to 200 GeV obtained from measurements availableat HEPDATA Below the Z pole the measurements we include mostly come from TASSO [100]though a few points on 〈nCh〉 come from HRS (at 29 GeV [101]) and TOPAZ (at 578 GeV [102]) Atthe Z pole the data come from the four LEP experiments [38 51ndash53] with the latter extending alsoto energies above MZ [103ndash108] For completeness and as reference for future ee collider studiesmodel extrapolations for CM energies up to 1000 GeV are also shown (though still only including theeerarr γlowastZ rarr hadrons component as usual with photon ISR switched off)

From the plots in fig 25 it is clear that there are no significant differences between the energyscaling of the three ee tunes considered here (mainly reflecting that they have been tuned to samereference point at 912 GeV and that their scaling is dictated by the same underlying physics model)and that their energy dependence closely matches that observed in data However the increasedamount of non-perturbative strangeness production in the Monash tune leads to a better agreementwith the overall normalization of the Kplusmn and Λ rates at all energies

Moving to pp collisions the plots in fig 26 show the scaling of the average charged multiplicity(left column) and multiplicity distributions (right column) in min-bias collisions from 7000 GeV (toprow) to 900 GeV (middle row) and 200 GeV (bottom row) compared with data from CMS [92 109]ATLAS [91] and UA5 [110 111] We regret the omission of additional relevant min-bias measure-ments from the Tevatron and RHIC experiments here but have chosen to focus in this paper mainlyon the LHC The comparisons at 7 TeV were already discussed in the main section on pp collisionssection 3 At 900 GeV the Monash 2013 tune again gives a roughly 5 lower average central chargedmultiplicity than the 4C one with a better description of the tail towards high multiplicities At 200GeV the UA5 measurement we include here extends over the full rapidity and pperp range hence the in-terplay between diffraction and low-multiplicity non-diffractive processes is presumably (much) moreimportant We believe imperfections in this modelling to be the likely cause of the significant discrep-ancies observed at high η and for nCh le 20 at these energies Since a dedicated study of this interplayis beyond the scope of this study we limit ourselves merely to stating this observation as a point forfuture studies to help clarify

Finally in fig 27 we compare to the underlying event measured in the highly useful energyscan that was performed at the Tevatron in the last days before its shutdown [22 23] during whichextremely high min-bias statistics were collected at 300 and 900 GeV CM energy over a period of afew days As was already noted in section 3 the UE at 7 TeV is slightly larger in the Monash 2013tune than in tune 4C As can be seen from the plots here the two tunes give comparable results for allthe Tevatron energies Interestingly the UE plateau region at 900 and 1960 GeV is reached sooner inthese models than in the data translating to a roughly 10 - 20 too low UE level for leading-trackpperp values in the neighbourhood of the transition from the rise to the plateau (roughly for leading-

34

14 22 29 35 44 58 91 91 91 91 133 161 183 189 200 250 350 500 1000

gtC

hlt

n

0

20

40

60

Average Charged Multiplicity vs ECM

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN25

χ00plusmn03 00plusmn02 00plusmn02

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 22 29 35 44 58 91 91 91 91 133 161 183 189 200 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

14 22 35 44 91 91 133 161 183 189 250 350 500 1000

gtK

ltn

0

2

4

6 Multiplicity vs ECM+-Average K

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN25

χ00plusmn06 00plusmn20

00plusmn18

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 22 35 44 91 91 133 161 183 189 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

14 35 91 91 91 91 133 200 250 350 500 1000

gtΛ

ltn

0

02

04

06

08

1

12 Multiplicity vs ECM0ΛAverage

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn06

01plusmn22

01plusmn18

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 35 91 91 91 91 133 200 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

Figure 25 e+eminus rarr hadrons Energy scaling of 〈nCh〉 〈nKplusmn〉 and 〈nΛ〉 in e+eminus rarr qq eventsincluding comparisons to measurements from HEPDATA for CM energies from 14 GeV to 200 GeVAlso shown are model extrapolations up to 1000 GeV

35

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from PhysRevLett 105 (2010) 022002

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn00

00plusmn03

00plusmn71

V I

N C

I A

R O

O T

pp 7000 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

0 50 100

)C

hP

rob(

n

-710

-610

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn27

00plusmn27

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

Chn0 50 100

The

ory

Dat

a

06

08

1

12

14

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from JHEP 1002 (2010) 041

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn03

00plusmn05

00plusmn29

V I

N C

I A

R O

O T

pp 900 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

0 10 20 30 40

)C

hP

rob(

n

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn17

01plusmn25

02plusmn127

V I

N C

I A

R O

O T

pp 900 GeV

Chn0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

0 1 2 3 4 5

gtηd

ch lt

dnN

SD

1n

0

1

2

3

4

5gt (NSD)ηd

chltdn

Pythia 8185Data from ZPhys C33 (1986) 1-6

UA5PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn36

00plusmn24

00plusmn16

V I

N C

I A

R O

O T

ppbar 200 GeV

η0 1 2 3 4 5

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)C

hP

rob(

n

-410

-310

-210

-110

1

)T

|lt05 all pηChg Mult (NSD |

Pythia 8185Data from ZPhys C43 (1989) 357

UA5PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn24

00plusmn24

00plusmn08

V I

N C

I A

R O

O T

ppbar 200 GeV

Chn0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 26 Min-bias pp events from 200 to 7000 GeV Energy scaling of 〈dnChdη〉 (left) andP (nCh) (right)

36

0 10 20 30

)φ∆η

∆gt

(T

psum

lt

0

05

1

15gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn24

26plusmn33

12plusmn143

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 10 20 30

)φ∆η

∆gt

(C

hlt

n

0

05

1

15gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

04plusmn05

13plusmn08

14plusmn100

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn58

06plusmn53

08plusmn193

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn16

15plusmn20

06plusmn114

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

gt05)T

|lt10 pη (|T1

)gt vs pT

TRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn10

02plusmn07

05plusmn22

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

gt05)T

|lt10 pη (|T1

gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn20

02plusmn11

03plusmn08

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 27 The Tevatron energy scan The underlying event (left average summed-pperp density andright average track density in the transverse region as function of leading-track pperp) for pp collisionsat 300 (bottom row) 900 GeV (middle row) and 1960 GeV (top row)

37

track pperp values 2 lt pT1 lt 10 GeV) This indicates that the energy scaling of the UE modeling and inparticular the details of its transition between central and peripheral collisions is still not satisfactorilyunderstood

5 Conclusions and Exhortation

We have presented a reanalysis of the constraints on fragmentation in ee collisions and applied theresults to update the final-state fragmentation parameters in PYTHIA 8 We combine these parameterswith a tune to hadron-collider data using a new NNPDF 23 LO QCD+QED PDF set which has beenencoded so it is available as an internal PDF set in PYTHIA 8 independently of LHAPDF [112]

In this PDF set as well as in our tune the value of the strong coupling for hard-scattering matrixelements is fixed to be αs(MZ) = 013 consistent with other LO determinations of it For initial-and final-state radiation our tune uses the effective value αs(MZ) = 01365 The difference isconsistent with an effective translation between the MS and CMW schemes We note that alternative(LO NLO and NNLO) NNPDF 23 QCD+QED sets with αs(MZ) = 0119 are also available inthe code for people who want to check the impact of using a different αs(MZ) value andor higher-order PDF sets on hard-scattering events For the purpose of such studies we point out that it ispossible in PYTHIA 8 to preserve most of the features of the shower- and underlying-event tuningby changing only the PDF for the hard-scattering matrix elements leaving the PDF choice for theshower evolution and MPI framework unaltered (see the PYTHIA 8 HTML manualrsquos PDF sectionunder PDFuseHard)

The updated parameters are available as an option starting from PYTHIA 8185 by setting

Tuneee = 7 and Tunepp = 14

By no means do we claim that this should be regarded as the final word in tuning the PYTHIA 8Monte Carlo model First of all the model continues to evolve For instance developments foreseenfor the near future include updates of colour reconnections diffraction and the treatment of g rarr qqsplittings Any of these should in principle be accompanied by a reevaluation of the model constraints

Moreover despite the comprehensive view of collider data we have attempted to take in thisstudy there still remains several issues that were not addressed including initial-final interferenceand coherence effects [113 114] (probably more a modelling issue than a tuning one) reliable esti-mates of theoretical uncertainties [8 17 24 29 97 115] diffraction14 [74 116 117] and other colour-singlet phenomena such as onium production long-distance (eg forward-backward forward-centraland ldquoridgerdquo-type) correlations [88 118ndash123] B-hadron decays [124] and tuning in the presence ofmatrix-element matching at LO and NLO (see [21 29 115 125 126] for recent phenomenologi-cal studies) Especially in the latter context of matrix-element matching we expect that in manycases PYTHIA 8 will be used together with codes such as ALPGEN [127] MADGRAPH [128]aMCatNLO [129] or POWHEG [130] either using the matching algorithms of those programs them-selves or via any of PYTHIArsquos several internal (LHEF-based [131]) implementations of matchingschemes (POWHEG [85] CKKW-L [132ndash134] MLM [135 136] UMEPS [137] NL3 [138] UN-LOPS [139]) The impact of such corrections on MC tuning depends on the details of the matchingscheme (especially its treatment of unitarity) and there is in general a non-negligible possibility ofldquomis-tuningrdquo when combining a stand-alone tune with ME corrections A simple example illustrating

14In particular the constraints on fragmentation mainly come from SLD and LEP where the non-perturbative parametersare clearly defined at the shower cutoff scaleQhad whereas diffraction is dominated by soft physics for which the definitionof the effective hadronization scale is less clear The amount of MPI in hard diffractive events also requires tuning

38

this is the effective value of αs(MZ) which for a leading-order tune is typically of order 013 whilea consistent NLO correction scheme should be compatible with values closer to 012 [29] There isalso the question of the running order of αs The propagation of such changes from the level of hardmatrix elements through the shower and hadronization tuning process are still not fully explored andhence we advise users to perform simple cross-checks such as checking the distributions presented inthis paper before and after applying matrix-element corrections Parameters that appear on both sidesof the matching such as αs should also be checked for consistency [21]

We noted several issues concerning the ee data used to constrain the fragmentation modelling thatit would be good to resolve In particular we find some tensions between the identified-particle ratesextracted from 1) HEDPATA 2) Sec 46 of the PDG and 3) the Z boson summary table in the PDGas discussed in more detail in section 2 and concerning which we made some (subjective) decisionsto arrive at a set of hopefully self-consistent constraints for this work We also note that the overallprecision of the fragmentation constraints could likely be significantly improved by an FCC-ee typemachine such as Tera-Z a possibility we hope to see more fully explored in the context of future eeQCD phenomenology studies

We conclude that the new parameter set does improve significantly on the previous default valuesin several respects including better agreement with data on

1 the net strangeness fraction (has been increased by 10 reflected not only in improved kaonand hyperon yields but also in the Ds and Bs fractions)

2 the ultra-hard fragmentation tail (has been softened especially for leading baryons and for Dand B hadrons)

3 the pTZ spectrum (softened at low pTZ)

4 the minimum-bias charged multiplicity in the forward region (has increased by 10)

5 the underlying event at 7 TeV (is very slightly higher than before)

Some questions that remain open include the following We see a roughly 20 excess of verysoft kaons in both ee and pp environments cf figs 6 and 23 despite the overall kaon yields beingwell described and the overall baryon yields at LHC appear to be underestimated by at least 30despite good agreement at LEP The momentum spectra of heavier strange particles are also poorlyreproduced in particular at LHC It is interesting and exciting that some of the LHC spectra appearto be better described by allowing collective flow in a fraction of events (cf the EPOS model [140])though we believe the jury is still out on whether this accurately reflects the underlying physics Forinstance it has been argued that colour reconnections can mimick flow effects [90] and they may alsobe able to modify the yield of baryons if the creationdestruction of string junctions is allowed [141]We look forward to future discussions on these issues

We round off with an exhortation for follow-ups on this study to provide

bull Not only central tunes experiments and other user-end colleagues need more than central de-scriptions of data there is an increasing need for serious uncertainty estimates In the contextof tune variations it is important to keep in mind that the modelling uncertainties are often in-trinsically non-universal Therefore the constraints obtained by considering data uncertaintiesonly (eg in the spirit of PROFESSORrsquos eigentunes [17]) can at most constitute a lower boundon the theoretical uncertainty (similarly to the case for PDFs) A serious uncertainty estimateincludes some systematic modelling variation irrespectively of and in addition to what data

39

allows (eg in the spirit of the Perugia set of tunes for PYTHIA 6 [8]) We therefore hope thefuture will see more elaborate combinations of data- and theory-driven approaches to systematictune uncertainties

bull Not only global tunes the power of MC models lies in their ability to simultaneously describea large variety of data hence we do not mean to imply that one should give up on universalityand tune to increasingly specific corners of phase space disregarding (or de-emphasizing withlower weights) all others However as proposed in [97] one can obtain useful explicit tests ofthe universality of the underlying physics model by performing independent tunes on separateldquophysics windowsrdquo say in the forward vs central regions for different event-selection crite-ria at different collider energies or even for different collider types In this connection justmaking one global ldquobest-fitrdquo tune may obscure tensions between the descriptions of differentcomplementary data sets By performing independent tunes to each data set separately andchecking the degree of universality of the resulting parameters one obtains a powerful crosscheck on the underlying physics model If all sets produce the same or similar parameters thenuniversality is OK hence a global tune makes very good sense and the remaining uncertain-ties can presumably be reliably estimated from data alone If instead some data sets resultin significantly different tune parameters one has a powerful indication that the universality ofthe underlying modeling is breaking down which can lead to several productive actions 1) itcan be taken into account in the context of uncertainty variations 2) the nature of the data setsfor which non-universal tune parameters are obtained can implicitly indicate the nature of theproblem leading to more robust conclusions about the underlying model than merely whether atune cancannot fit the data and 3) the observations can be communicated to the model authorsin a more unambiguous way hopefully resulting in a speedier cycle of model improvements

We hope that the Monash 2013 tune parameters may serve as a useful starting point for phe-nomenology studies and for future PYTHIA 8 tuning efforts

Acknowledgments

We thank S Mrenna M Ritzmann and T Sjostrand for comments on the manuscript and L de Nooijfor pointing us to the ALICE Klowast and φ measurements [142] and to the ATLAS φ measurementsin [143] The work of J R is supported by an STFC Rutherford Fellowship STK0052271 Thiswork was supported in part by the Research Executive Agency (REA) of the European Commissionunder the Grant Agreements PITN-GA-2012-315877 (MCnet)

A Monash 2013 Tune Parameters

In tabs 3 ndash 7 we list the FSR fragmentation parameters for the Monash tune of PYTHIA Forreference we compare them to the current default parameters

40

FSR Parameters Monash 13 (Default) CommentTimeShoweralphaSvalue = 01365 = 01383 Effective alphaS(mZ) valueTimeShoweralphaSorder = 1 = 1 Running orderTimeShoweralphaSuseCMW = off = off Translation from MS to CMWTimeShowerpTmin = 050 = 040 Cutoff for QCD radiationTimeShowerpTminChgQ = 050 = 040 Cutoff for QED radiationTimeShowerphiPolAsym = on = on Asymmetric azimuth distributions

Table 3 Final-state radiation (FSR) parameters

HAD Parameters Monash 13 (Default) Comment String breaks pT and z distributionsStringPTsigma = 0335 = 0304 Soft pT in string breaks (in GeV)StringPTenhancedFraction = 001 = 001 Fraction of breakups with enhanced pTStringPTenhancedWidth = 20 = 20 Enhancement factorStringZaLund = 068 = 03 Lund FF a (hard fragmentation supp)StringZbLund = 098 = 08 Lund FF b (soft fragmentation supp)StringZaExtraSquark = 00 = 00 Extra a when picking up an s quarkStringZaExtraDiquark = 097 = 050 Extra a when picking up a diquarkStringZrFactC = 132 = 100 Lund-Bowler c-quark parameterStringZrFactB = 0855 = 067 Lund-Bowler b-quark parameter Flavour composition mesonsStringFlavProbStoUD = 0217 = 019 Strangeness-to-UD ratioStringFlavmesonUDvector = 05 = 062 Light-flavour vector suppressionStringFlavmesonSvector = 055 = 0725 Strange vector suppressionStringFlavmesonCvector = 088 = 106 Charm vector suppressionStringFlavmesonBvector = 22 = 30 Bottom vector suppressionStringFlavetaSup = 060 = 063 Suppression of eta mesonsStringFlavetaPrimeSup = 012 = 012 Suppression of etarsquo mesons Flavour composition baryonsStringFlavprobQQtoQ = 0081 = 009 Diquark rate (for baryon production)StringFlavprobSQtoQQ = 0915 = 1000 Strange-diquark suppressionStringFlavprobQQ1toQQ0 = 00275 = 0027 Vector diquark suppressionStringFlavdecupletSup = 10 = 10 Spin-32 baryon suppressionStringFlavsuppressLeadingB = off = off Optional leading-baryon suppressionStringFlavpopcornSpair = 09 = 05 StringFlavpopcornSmeson = 05 = 05

Table 4 String-breaking parameters

PDF and ME Parameters Monash 13 (Default) CommentPDFpSet = 13 = 8 PDF set for the protonSigmaProcessalphaSvalue = 0130 0135 alphaS(MZ) for matrix elementsMultiPartonInteractionsalphaSvalue = 0130 0135 alphaS(MZ) for MPI

Table 5 Parton-distribution (PDF) and Matrix-Element (ME) parameters

41

ISR Parameters Monash 13 (Default) CommentSpaceShoweralphaSvalue = 01365 = 0137 Effective alphaS(mZ) valueSpaceShoweralphaSorder = 1 = 1 Running orderSpaceShoweralphaSuseCMW = off = off Translation from MS to CMWSpaceShowersamePTasMPI = off = off ISR cutoff typeSpaceShowerpT0Ref = 20 = 20 ISR pT0 cutoffSpaceShowerecmRef = 70000 = 18000 ISR pT0 reference ECM scaleSpaceShowerecmPow = 00 = 00 ISR pT0 scaling powerSpaceShowerrapidityOrder = on = on Approx coherence via y-orderingSpaceShowerphiPolAsym = on = on Azimuth asymmetries from gluon polSpaceShowerphiIntAsym = on = on Azimuth asymmetries from interferenceTimeShowerdampenBeamRecoil = on = on Recoil dampening in final-initial dipolesBeamRemnantsprimordialKTsoft = 09 = 05 Primordial kT for soft procsBeamRemnantsprimordialKThard = 18 = 20 Primordial kT for hard procsBeamRemnantshalfScaleForKT = 15 = 10 Primordial kT softhard boundaryBeamRemnantshalfMassForKT = 10 = 10 Primordial kT softhard mass boundary

Table 6 Initial-state radiation (ISR) and primordial-kT parameters

MPI Parameters Monash 13 (Default) CommentMultipartonInteractionspT0Ref = 228 = 2085 MPI pT0 IR regularization scaleMultipartonInteractionsecmRef = 70000 = 18000 MPI pT0 reference ECM scaleMultipartonInteractionsecmPow = 0215 = 019 MPI pT0 scaling powerMultipartonInteractionsbProfile = 3 = 3 Transverse matter overlap profileMultipartonInteractionsexpPow = 185 = 20 Shape parameterBeamRemnantsreconnectRange = 18 = 15 Colour ReconnectionsSigmaTotalzeroAXB = on = on Carried over from 4CSigmaDiffractivedampen = on = on Carried over from 4CSigmaDiffractivemaxXB = 650 = 650 Carried over from 4CSigmaDiffractivemaxAX = 650 = 650 Carried over from 4CSigmaDiffractivemaxXX = 650 = 650 Carried over from 4CDiffractionlargeMassSuppress = 40 = 20 High-mass diffraction suppression power

Table 7 Multi-Parton-Interaction (MPI) Colour-Reconnection (CR) and Diffractive parameters

42

B Additional Plots

B1 LEP Event-Shape Distributions

To keep the main body of the paper as uncluttered as possible we collect various plots of event-shapedistributions in figs 28 and 29 separated into light-flavour and b-tagged events on the left and rightrespectively

The experimental results come from the L3 experiment [26] However since the data points areonly available with 3-digit precision some of the least populated bins contain artifacts like uncertain-ties being reported as exactly zero etc Thus we have been forced to make the following modificationsto the data set

The statistical uncertainty was reported as zero for the last two bins of light-flavour Thrust as wellas for the last bin of the C D and BT parameters Uncertainties lt 10minus3 were derived using anapproximate statistical scaling based on the contents and uncertainties of the other bins Likewise thesystematical uncertainty for the last bin of Thrust was given as zero which we have replaced by theupper limit 5times 10minus4 The last bin of BT quoted a measured y value of zero removed in this study

For the heavy-flavour tagged event shapes more significant rounding issues were present Thusseveral of the first and last bins of each distribution either quoted zero (statistical andor systematic)uncertainties or ones with only a single digit of precision (such as 0001 for which the rounding errorcould be up to sim 50) We have interpreted all such values conservatively inserting by hand a fourthdigit on the uncertainties as large as could be consistent with rounding

B2 Additional Particle Spectra

In addition to the K and Λ spectra shown in the main body of the paper (sections 22 and 35) wehere include for reference the x spectra of φ mesons protons and Ξ baryons at LEP in figs 30 and 31the pT spectrum of Klowast mesons and the rapidity and pT spectra of φ mesons at LHC in fig 32 (withabsolute normalizations to the number of inelastic events) and the rapidity spectrum of Ξ baryons atLHC in fig 33

The transverse-momentum spectra of Klowast and φ mesons in fig 32 exhibit the same qualitativebehaviour as that of the KS mesons (fig 23) namely an excess at very soft momenta below sim 500MeV and a depletion at slightly higher momenta between 1 and 2 GeV As discussed in section 35we did not find a way to remove these undesirable features in the Monash 2013 tune suggesting thatthis is an issue that further theoretical modeling will be needed to resolve

The rapidity spectrum of Ξ baryons fig 33 shows that although the Monash tune does producemore Ξ baryons overall (as expected also from the relative increase of Ξ production at LEP cf fig 5)there is still a significant deficit of Ξ baryons at the LHC almost a factor 2 compared with the dataThis is qualitatively similar to the situation for Λ baryons (fig 24) discussed in section 35 Sincenew physics mechanisms may be required to ldquoexplainrdquo the missing baryons we conclude that furthermeasurements and better precision on both the Λ and Ξ sectors (in addition to any other baryonsthat may be accessible) would be highly interesting More explicit recommendations can be found insections 35 and 5

43

0 01 02 03 04

d(1

-T)

σ d

σ1

-310

-210

-110

1

10

2101-Thrust (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn03

01plusmn04

02plusmn05

V I

N C

I A

R O

O T

1-T (udsc)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

d(1

-T)

σ dσ

1

-310

-210

-110

1

10

2101-T (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn13

02plusmn12

02plusmn14

V I

N C

I A

R O

O T

1-T (b)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210

310C Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn03

00plusmn04

01plusmn04

V I

N C

I A

R O

O T

C0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210 C parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn17

01plusmn24

01plusmn27

V I

N C

I A

R O

O T

C (b)0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn06

01plusmn06

V I

N C

I A

R O

O T

D0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn24

02plusmn21

02plusmn26

V I

N C

I A

R O

O T

D (b)0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

Figure 28 Hadronic Z decays atradics = 912 GeV The T C and D event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

44

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn02

01plusmn03

01plusmn04

V I

N C

I A

R O

O T

WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn05

01plusmn12

01plusmn17

V I

N C

I A

R O

O T

(b)WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn02

00plusmn02

01plusmn03

V I

N C

I A

R O

O T

TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

04plusmn24

08plusmn49

08plusmn55

V I

N C

I A

R O

O T

(b)TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

Figure 29 Hadronic Z decays atradics = 912 GeV The BW and BT event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

45

0 02 04 06 08 1

dx

φgt

dn

φ1

ltn

-210

-110

1

10 )φx(

Pythia 8183Data from ALEPH_1996_S3486095d40-x01-y01

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn37

02plusmn53

03plusmn62

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

0608

112141618

Figure 30 Hadronic Z decays atradics = 912 GeV φ meson x spectrum

-5 -4 -3 -2 -1 0

dx

pgt

dn

p1

ltn

-410

-310

-210

-110

1

10

210) (Combined)px(p+

Pythia 8183Data from Zeit Phys C66 (1995) 355 PhysRev D59 (1998) 052001

ALEPH+SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn08

00plusmn09

00plusmn08

V I

N C

I A

R O

O T

px-5 -4 -3 -2 -1 0

The

ory

Dat

a

06

08

1

12

14

0 02 04

dx

Ξgt

dn

Ξ1

ltn

-110

1

10

)plusmnΞx(

Pythia 8183Data from Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn11

02plusmn13

02plusmn14

V I

N C

I A

R O

O T

Ex0 02 04

The

ory

Dat

a

06

08

1

12

14

Figure 31 Hadronic Z decays atradics = 912 GeV pplusmn and Ξplusmn x spectra

46

0 2 4 6

Td

pK

d

nIN

EL

1N

-510

-410

-310

-210

-110

(INEL |y|lt05)T

p0K

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn35

01plusmn26

01plusmn29

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 2 4 6

Td

pφ

dn

INE

L1

N-510

-410

-310

-210

-110

gt04)T

(INEL |y|lt05 pT

pφ

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn88

03plusmn84

04plusmn173

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

)dy

[mb]

-K

+K

rarrφ(σd

0

05

1

15

2 Rapidity (INEL ATLAS cuts)φ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn14

01plusmn19

01plusmn34

V I

N C

I A

R O

O T

pp 7000 GeV

|y|0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

06 08 1 12

[mb

GeV

]φ

T)

dp-

K+

Krarrφ(

σd

0

05

1

15

2

25 (INEL ATLAS cuts)

T pφ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn21

01plusmn30

02plusmn53

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p06 08 1 12

The

ory

Dat

a

06

08

1

12

14

Figure 32 pp collisions at 7 TeV Top row Klowast and φ pperp spectra compared with ALICE data [142]Bottom row φ rapidity and pperp spectrum compared with ATLAS data [143] The ATLAS cuts areφrarr K+Kminus pperpφ isin [05 12] GeV |y(φ)| lt 08 pperpK gt 023 GeV |pK | lt 08 GeV

47

0 05 1 15 2

dygt

Ξ lt

dnN

SD

1N

0

001

002

003

004)d|y|gt (NSD)Ξltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn89

01plusmn129

01plusmn192

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

0

05

1

15

2

Figure 33 pp collisions at 7 TeV Ξminus rapidity spectrum compared with CMS data [99]

48

B3 Energy Scaling of σ2rarr2(pTmin) vs σinel from 200 GeV to 100 TeV

In fig 34 we show the LO QCD 2rarr 2 cross section integrated above pTmin as a function of pTminin pp collisions at 4 different CM energies complementing and expanding on the 8-TeV CM energyshown in the main body of the paper We compare two different αs and PDF choices correspondingto those made in tunes Monash 13 (blue filled dots) and 4C (red open squares) respectively As areference for the total inelastic cross section at each energy we base ourselves on the best-fit curvein the TOTEM cross-section measurement paper [72] which in turn represents a fit produced by theCOMPETE collaboration [144] Uncertainties are rough conservative estimates based on the plot inthe TOTEM paper but they are in any case too small to significantly affect conclusions about the scaleat which the partonic cross section saturates the hadronic one

We observe that the pTmin value for which the LO QCD 2 rarr 2 partonic cross section formallybecomes equal to the total inelastic cross section (strongly suggesting that every event has at leastone such mini-jet pair) rises from values around 1 ndash 2 GeV at energies

radics lt 1 TeV to 5 GeV atradic

s = 13 TeV and finally 10 GeV atradics = 100 TeV

49

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

0 05 1 15 2

dygt

K lt

dnN

SD

1n

0

02

04

06

08)d|y|gt Rapidity (NSD)

S

0ltdn(K

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn01

00plusmn09

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8 10

Td

pK

dn

NS

D1

N

-510

-410

-310

-210

-110

1

10 (|y|lt20 NSD)

T pS

0K

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn78

01plusmn34

02plusmn22

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6 8 10

The

ory

Dat

a06

08

1

12

14

Figure 23 pp collisions at 7 TeV K0S rapidity and pperp spectrum compared with CMS data [99]

0 05 1 15 2

dygt

Λ lt

dnN

SD

1N

0

01

02

03

04)d|y|gt (NSD)0Λltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn64

00plusmn78

01plusmn147

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

06

08

1

12

14

0 2 4 6 8 10

Td

pΛ

dn

Λ1

n

-510

-410

-310

-210

-110

1

10 (|y|lt20 NSD)

T p0Λ

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn59

03plusmn66

05plusmn105

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6 8 10

The

ory

Dat

a

06

08

1

12

14

Figure 24 pp collisions at 7 TeV Λ0 rapidity and pperp spectrum compared with CMS data [99]

not result in an equivalent improvement of the Λ0 rate in pp collisions shown in fig 24 The Monash2013 tune still produces only about 23 of the observed Λ0 rate (and just over half of the observedΞminus rate cf appendix B2) We therefore believe it to be likely that an additional source of net baryonproduction is needed (at least within the limited context of the current PYTHIA modelling) in orderto describe the LHC data The momentum spectrum is likewise quite discrepant exhibiting an excessat very low momenta (stronger than that for kaons) a dip between 1ndash4 GeV and then an excess of veryhard Λ0 production The latter hard tail is somewhat milder in the Monash 2013 tune than previously

33

and it may be consistent with the trend also seen in the Λ0 spectrum at LEP cf fig 6 We concludethat baryon production still requires further modelling and tuning efforts

4 Energy Scaling

Though energy scaling these days mostly refers to the scaling of pp collisions (see eg [97]) animportant first step is to consider the scaling of observables in ee rarr γlowastZ rarr hadrons This scalingcontains information on the relative contributions of perturbative and non-perturbative fragmentationThus at low ee energies the non-perturbative components of the fragmentation model dominatewhile perturbative bremsstrahlung increases in importance towards higher ee energies In fig 25we consider the scaling of the average charged-particle multiplicity and that of charged Kaons andLambda baryons from CM energies of 14 GeV to 200 GeV obtained from measurements availableat HEPDATA Below the Z pole the measurements we include mostly come from TASSO [100]though a few points on 〈nCh〉 come from HRS (at 29 GeV [101]) and TOPAZ (at 578 GeV [102]) Atthe Z pole the data come from the four LEP experiments [38 51ndash53] with the latter extending alsoto energies above MZ [103ndash108] For completeness and as reference for future ee collider studiesmodel extrapolations for CM energies up to 1000 GeV are also shown (though still only including theeerarr γlowastZ rarr hadrons component as usual with photon ISR switched off)

From the plots in fig 25 it is clear that there are no significant differences between the energyscaling of the three ee tunes considered here (mainly reflecting that they have been tuned to samereference point at 912 GeV and that their scaling is dictated by the same underlying physics model)and that their energy dependence closely matches that observed in data However the increasedamount of non-perturbative strangeness production in the Monash tune leads to a better agreementwith the overall normalization of the Kplusmn and Λ rates at all energies

Moving to pp collisions the plots in fig 26 show the scaling of the average charged multiplicity(left column) and multiplicity distributions (right column) in min-bias collisions from 7000 GeV (toprow) to 900 GeV (middle row) and 200 GeV (bottom row) compared with data from CMS [92 109]ATLAS [91] and UA5 [110 111] We regret the omission of additional relevant min-bias measure-ments from the Tevatron and RHIC experiments here but have chosen to focus in this paper mainlyon the LHC The comparisons at 7 TeV were already discussed in the main section on pp collisionssection 3 At 900 GeV the Monash 2013 tune again gives a roughly 5 lower average central chargedmultiplicity than the 4C one with a better description of the tail towards high multiplicities At 200GeV the UA5 measurement we include here extends over the full rapidity and pperp range hence the in-terplay between diffraction and low-multiplicity non-diffractive processes is presumably (much) moreimportant We believe imperfections in this modelling to be the likely cause of the significant discrep-ancies observed at high η and for nCh le 20 at these energies Since a dedicated study of this interplayis beyond the scope of this study we limit ourselves merely to stating this observation as a point forfuture studies to help clarify

Finally in fig 27 we compare to the underlying event measured in the highly useful energyscan that was performed at the Tevatron in the last days before its shutdown [22 23] during whichextremely high min-bias statistics were collected at 300 and 900 GeV CM energy over a period of afew days As was already noted in section 3 the UE at 7 TeV is slightly larger in the Monash 2013tune than in tune 4C As can be seen from the plots here the two tunes give comparable results for allthe Tevatron energies Interestingly the UE plateau region at 900 and 1960 GeV is reached sooner inthese models than in the data translating to a roughly 10 - 20 too low UE level for leading-trackpperp values in the neighbourhood of the transition from the rise to the plateau (roughly for leading-

34

14 22 29 35 44 58 91 91 91 91 133 161 183 189 200 250 350 500 1000

gtC

hlt

n

0

20

40

60

Average Charged Multiplicity vs ECM

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN25

χ00plusmn03 00plusmn02 00plusmn02

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 22 29 35 44 58 91 91 91 91 133 161 183 189 200 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

14 22 35 44 91 91 133 161 183 189 250 350 500 1000

gtK

ltn

0

2

4

6 Multiplicity vs ECM+-Average K

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN25

χ00plusmn06 00plusmn20

00plusmn18

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 22 35 44 91 91 133 161 183 189 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

14 35 91 91 91 91 133 200 250 350 500 1000

gtΛ

ltn

0

02

04

06

08

1

12 Multiplicity vs ECM0ΛAverage

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn06

01plusmn22

01plusmn18

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 35 91 91 91 91 133 200 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

Figure 25 e+eminus rarr hadrons Energy scaling of 〈nCh〉 〈nKplusmn〉 and 〈nΛ〉 in e+eminus rarr qq eventsincluding comparisons to measurements from HEPDATA for CM energies from 14 GeV to 200 GeVAlso shown are model extrapolations up to 1000 GeV

35

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from PhysRevLett 105 (2010) 022002

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn00

00plusmn03

00plusmn71

V I

N C

I A

R O

O T

pp 7000 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

0 50 100

)C

hP

rob(

n

-710

-610

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn27

00plusmn27

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

Chn0 50 100

The

ory

Dat

a

06

08

1

12

14

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from JHEP 1002 (2010) 041

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn03

00plusmn05

00plusmn29

V I

N C

I A

R O

O T

pp 900 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

0 10 20 30 40

)C

hP

rob(

n

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn17

01plusmn25

02plusmn127

V I

N C

I A

R O

O T

pp 900 GeV

Chn0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

0 1 2 3 4 5

gtηd

ch lt

dnN

SD

1n

0

1

2

3

4

5gt (NSD)ηd

chltdn

Pythia 8185Data from ZPhys C33 (1986) 1-6

UA5PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn36

00plusmn24

00plusmn16

V I

N C

I A

R O

O T

ppbar 200 GeV

η0 1 2 3 4 5

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)C

hP

rob(

n

-410

-310

-210

-110

1

)T

|lt05 all pηChg Mult (NSD |

Pythia 8185Data from ZPhys C43 (1989) 357

UA5PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn24

00plusmn24

00plusmn08

V I

N C

I A

R O

O T

ppbar 200 GeV

Chn0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 26 Min-bias pp events from 200 to 7000 GeV Energy scaling of 〈dnChdη〉 (left) andP (nCh) (right)

36

0 10 20 30

)φ∆η

∆gt

(T

psum

lt

0

05

1

15gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn24

26plusmn33

12plusmn143

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 10 20 30

)φ∆η

∆gt

(C

hlt

n

0

05

1

15gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

04plusmn05

13plusmn08

14plusmn100

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn58

06plusmn53

08plusmn193

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn16

15plusmn20

06plusmn114

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

gt05)T

|lt10 pη (|T1

)gt vs pT

TRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn10

02plusmn07

05plusmn22

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

gt05)T

|lt10 pη (|T1

gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn20

02plusmn11

03plusmn08

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 27 The Tevatron energy scan The underlying event (left average summed-pperp density andright average track density in the transverse region as function of leading-track pperp) for pp collisionsat 300 (bottom row) 900 GeV (middle row) and 1960 GeV (top row)

37

track pperp values 2 lt pT1 lt 10 GeV) This indicates that the energy scaling of the UE modeling and inparticular the details of its transition between central and peripheral collisions is still not satisfactorilyunderstood

5 Conclusions and Exhortation

We have presented a reanalysis of the constraints on fragmentation in ee collisions and applied theresults to update the final-state fragmentation parameters in PYTHIA 8 We combine these parameterswith a tune to hadron-collider data using a new NNPDF 23 LO QCD+QED PDF set which has beenencoded so it is available as an internal PDF set in PYTHIA 8 independently of LHAPDF [112]

In this PDF set as well as in our tune the value of the strong coupling for hard-scattering matrixelements is fixed to be αs(MZ) = 013 consistent with other LO determinations of it For initial-and final-state radiation our tune uses the effective value αs(MZ) = 01365 The difference isconsistent with an effective translation between the MS and CMW schemes We note that alternative(LO NLO and NNLO) NNPDF 23 QCD+QED sets with αs(MZ) = 0119 are also available inthe code for people who want to check the impact of using a different αs(MZ) value andor higher-order PDF sets on hard-scattering events For the purpose of such studies we point out that it ispossible in PYTHIA 8 to preserve most of the features of the shower- and underlying-event tuningby changing only the PDF for the hard-scattering matrix elements leaving the PDF choice for theshower evolution and MPI framework unaltered (see the PYTHIA 8 HTML manualrsquos PDF sectionunder PDFuseHard)

The updated parameters are available as an option starting from PYTHIA 8185 by setting

Tuneee = 7 and Tunepp = 14

By no means do we claim that this should be regarded as the final word in tuning the PYTHIA 8Monte Carlo model First of all the model continues to evolve For instance developments foreseenfor the near future include updates of colour reconnections diffraction and the treatment of g rarr qqsplittings Any of these should in principle be accompanied by a reevaluation of the model constraints

Moreover despite the comprehensive view of collider data we have attempted to take in thisstudy there still remains several issues that were not addressed including initial-final interferenceand coherence effects [113 114] (probably more a modelling issue than a tuning one) reliable esti-mates of theoretical uncertainties [8 17 24 29 97 115] diffraction14 [74 116 117] and other colour-singlet phenomena such as onium production long-distance (eg forward-backward forward-centraland ldquoridgerdquo-type) correlations [88 118ndash123] B-hadron decays [124] and tuning in the presence ofmatrix-element matching at LO and NLO (see [21 29 115 125 126] for recent phenomenologi-cal studies) Especially in the latter context of matrix-element matching we expect that in manycases PYTHIA 8 will be used together with codes such as ALPGEN [127] MADGRAPH [128]aMCatNLO [129] or POWHEG [130] either using the matching algorithms of those programs them-selves or via any of PYTHIArsquos several internal (LHEF-based [131]) implementations of matchingschemes (POWHEG [85] CKKW-L [132ndash134] MLM [135 136] UMEPS [137] NL3 [138] UN-LOPS [139]) The impact of such corrections on MC tuning depends on the details of the matchingscheme (especially its treatment of unitarity) and there is in general a non-negligible possibility ofldquomis-tuningrdquo when combining a stand-alone tune with ME corrections A simple example illustrating

14In particular the constraints on fragmentation mainly come from SLD and LEP where the non-perturbative parametersare clearly defined at the shower cutoff scaleQhad whereas diffraction is dominated by soft physics for which the definitionof the effective hadronization scale is less clear The amount of MPI in hard diffractive events also requires tuning

38

this is the effective value of αs(MZ) which for a leading-order tune is typically of order 013 whilea consistent NLO correction scheme should be compatible with values closer to 012 [29] There isalso the question of the running order of αs The propagation of such changes from the level of hardmatrix elements through the shower and hadronization tuning process are still not fully explored andhence we advise users to perform simple cross-checks such as checking the distributions presented inthis paper before and after applying matrix-element corrections Parameters that appear on both sidesof the matching such as αs should also be checked for consistency [21]

We noted several issues concerning the ee data used to constrain the fragmentation modelling thatit would be good to resolve In particular we find some tensions between the identified-particle ratesextracted from 1) HEDPATA 2) Sec 46 of the PDG and 3) the Z boson summary table in the PDGas discussed in more detail in section 2 and concerning which we made some (subjective) decisionsto arrive at a set of hopefully self-consistent constraints for this work We also note that the overallprecision of the fragmentation constraints could likely be significantly improved by an FCC-ee typemachine such as Tera-Z a possibility we hope to see more fully explored in the context of future eeQCD phenomenology studies

We conclude that the new parameter set does improve significantly on the previous default valuesin several respects including better agreement with data on

1 the net strangeness fraction (has been increased by 10 reflected not only in improved kaonand hyperon yields but also in the Ds and Bs fractions)

2 the ultra-hard fragmentation tail (has been softened especially for leading baryons and for Dand B hadrons)

3 the pTZ spectrum (softened at low pTZ)

4 the minimum-bias charged multiplicity in the forward region (has increased by 10)

5 the underlying event at 7 TeV (is very slightly higher than before)

Some questions that remain open include the following We see a roughly 20 excess of verysoft kaons in both ee and pp environments cf figs 6 and 23 despite the overall kaon yields beingwell described and the overall baryon yields at LHC appear to be underestimated by at least 30despite good agreement at LEP The momentum spectra of heavier strange particles are also poorlyreproduced in particular at LHC It is interesting and exciting that some of the LHC spectra appearto be better described by allowing collective flow in a fraction of events (cf the EPOS model [140])though we believe the jury is still out on whether this accurately reflects the underlying physics Forinstance it has been argued that colour reconnections can mimick flow effects [90] and they may alsobe able to modify the yield of baryons if the creationdestruction of string junctions is allowed [141]We look forward to future discussions on these issues

We round off with an exhortation for follow-ups on this study to provide

bull Not only central tunes experiments and other user-end colleagues need more than central de-scriptions of data there is an increasing need for serious uncertainty estimates In the contextof tune variations it is important to keep in mind that the modelling uncertainties are often in-trinsically non-universal Therefore the constraints obtained by considering data uncertaintiesonly (eg in the spirit of PROFESSORrsquos eigentunes [17]) can at most constitute a lower boundon the theoretical uncertainty (similarly to the case for PDFs) A serious uncertainty estimateincludes some systematic modelling variation irrespectively of and in addition to what data

39

allows (eg in the spirit of the Perugia set of tunes for PYTHIA 6 [8]) We therefore hope thefuture will see more elaborate combinations of data- and theory-driven approaches to systematictune uncertainties

bull Not only global tunes the power of MC models lies in their ability to simultaneously describea large variety of data hence we do not mean to imply that one should give up on universalityand tune to increasingly specific corners of phase space disregarding (or de-emphasizing withlower weights) all others However as proposed in [97] one can obtain useful explicit tests ofthe universality of the underlying physics model by performing independent tunes on separateldquophysics windowsrdquo say in the forward vs central regions for different event-selection crite-ria at different collider energies or even for different collider types In this connection justmaking one global ldquobest-fitrdquo tune may obscure tensions between the descriptions of differentcomplementary data sets By performing independent tunes to each data set separately andchecking the degree of universality of the resulting parameters one obtains a powerful crosscheck on the underlying physics model If all sets produce the same or similar parameters thenuniversality is OK hence a global tune makes very good sense and the remaining uncertain-ties can presumably be reliably estimated from data alone If instead some data sets resultin significantly different tune parameters one has a powerful indication that the universality ofthe underlying modeling is breaking down which can lead to several productive actions 1) itcan be taken into account in the context of uncertainty variations 2) the nature of the data setsfor which non-universal tune parameters are obtained can implicitly indicate the nature of theproblem leading to more robust conclusions about the underlying model than merely whether atune cancannot fit the data and 3) the observations can be communicated to the model authorsin a more unambiguous way hopefully resulting in a speedier cycle of model improvements

We hope that the Monash 2013 tune parameters may serve as a useful starting point for phe-nomenology studies and for future PYTHIA 8 tuning efforts

Acknowledgments

We thank S Mrenna M Ritzmann and T Sjostrand for comments on the manuscript and L de Nooijfor pointing us to the ALICE Klowast and φ measurements [142] and to the ATLAS φ measurementsin [143] The work of J R is supported by an STFC Rutherford Fellowship STK0052271 Thiswork was supported in part by the Research Executive Agency (REA) of the European Commissionunder the Grant Agreements PITN-GA-2012-315877 (MCnet)

A Monash 2013 Tune Parameters

In tabs 3 ndash 7 we list the FSR fragmentation parameters for the Monash tune of PYTHIA Forreference we compare them to the current default parameters

40

FSR Parameters Monash 13 (Default) CommentTimeShoweralphaSvalue = 01365 = 01383 Effective alphaS(mZ) valueTimeShoweralphaSorder = 1 = 1 Running orderTimeShoweralphaSuseCMW = off = off Translation from MS to CMWTimeShowerpTmin = 050 = 040 Cutoff for QCD radiationTimeShowerpTminChgQ = 050 = 040 Cutoff for QED radiationTimeShowerphiPolAsym = on = on Asymmetric azimuth distributions

Table 3 Final-state radiation (FSR) parameters

HAD Parameters Monash 13 (Default) Comment String breaks pT and z distributionsStringPTsigma = 0335 = 0304 Soft pT in string breaks (in GeV)StringPTenhancedFraction = 001 = 001 Fraction of breakups with enhanced pTStringPTenhancedWidth = 20 = 20 Enhancement factorStringZaLund = 068 = 03 Lund FF a (hard fragmentation supp)StringZbLund = 098 = 08 Lund FF b (soft fragmentation supp)StringZaExtraSquark = 00 = 00 Extra a when picking up an s quarkStringZaExtraDiquark = 097 = 050 Extra a when picking up a diquarkStringZrFactC = 132 = 100 Lund-Bowler c-quark parameterStringZrFactB = 0855 = 067 Lund-Bowler b-quark parameter Flavour composition mesonsStringFlavProbStoUD = 0217 = 019 Strangeness-to-UD ratioStringFlavmesonUDvector = 05 = 062 Light-flavour vector suppressionStringFlavmesonSvector = 055 = 0725 Strange vector suppressionStringFlavmesonCvector = 088 = 106 Charm vector suppressionStringFlavmesonBvector = 22 = 30 Bottom vector suppressionStringFlavetaSup = 060 = 063 Suppression of eta mesonsStringFlavetaPrimeSup = 012 = 012 Suppression of etarsquo mesons Flavour composition baryonsStringFlavprobQQtoQ = 0081 = 009 Diquark rate (for baryon production)StringFlavprobSQtoQQ = 0915 = 1000 Strange-diquark suppressionStringFlavprobQQ1toQQ0 = 00275 = 0027 Vector diquark suppressionStringFlavdecupletSup = 10 = 10 Spin-32 baryon suppressionStringFlavsuppressLeadingB = off = off Optional leading-baryon suppressionStringFlavpopcornSpair = 09 = 05 StringFlavpopcornSmeson = 05 = 05

Table 4 String-breaking parameters

PDF and ME Parameters Monash 13 (Default) CommentPDFpSet = 13 = 8 PDF set for the protonSigmaProcessalphaSvalue = 0130 0135 alphaS(MZ) for matrix elementsMultiPartonInteractionsalphaSvalue = 0130 0135 alphaS(MZ) for MPI

Table 5 Parton-distribution (PDF) and Matrix-Element (ME) parameters

41

ISR Parameters Monash 13 (Default) CommentSpaceShoweralphaSvalue = 01365 = 0137 Effective alphaS(mZ) valueSpaceShoweralphaSorder = 1 = 1 Running orderSpaceShoweralphaSuseCMW = off = off Translation from MS to CMWSpaceShowersamePTasMPI = off = off ISR cutoff typeSpaceShowerpT0Ref = 20 = 20 ISR pT0 cutoffSpaceShowerecmRef = 70000 = 18000 ISR pT0 reference ECM scaleSpaceShowerecmPow = 00 = 00 ISR pT0 scaling powerSpaceShowerrapidityOrder = on = on Approx coherence via y-orderingSpaceShowerphiPolAsym = on = on Azimuth asymmetries from gluon polSpaceShowerphiIntAsym = on = on Azimuth asymmetries from interferenceTimeShowerdampenBeamRecoil = on = on Recoil dampening in final-initial dipolesBeamRemnantsprimordialKTsoft = 09 = 05 Primordial kT for soft procsBeamRemnantsprimordialKThard = 18 = 20 Primordial kT for hard procsBeamRemnantshalfScaleForKT = 15 = 10 Primordial kT softhard boundaryBeamRemnantshalfMassForKT = 10 = 10 Primordial kT softhard mass boundary

Table 6 Initial-state radiation (ISR) and primordial-kT parameters

MPI Parameters Monash 13 (Default) CommentMultipartonInteractionspT0Ref = 228 = 2085 MPI pT0 IR regularization scaleMultipartonInteractionsecmRef = 70000 = 18000 MPI pT0 reference ECM scaleMultipartonInteractionsecmPow = 0215 = 019 MPI pT0 scaling powerMultipartonInteractionsbProfile = 3 = 3 Transverse matter overlap profileMultipartonInteractionsexpPow = 185 = 20 Shape parameterBeamRemnantsreconnectRange = 18 = 15 Colour ReconnectionsSigmaTotalzeroAXB = on = on Carried over from 4CSigmaDiffractivedampen = on = on Carried over from 4CSigmaDiffractivemaxXB = 650 = 650 Carried over from 4CSigmaDiffractivemaxAX = 650 = 650 Carried over from 4CSigmaDiffractivemaxXX = 650 = 650 Carried over from 4CDiffractionlargeMassSuppress = 40 = 20 High-mass diffraction suppression power

Table 7 Multi-Parton-Interaction (MPI) Colour-Reconnection (CR) and Diffractive parameters

42

B Additional Plots

B1 LEP Event-Shape Distributions

To keep the main body of the paper as uncluttered as possible we collect various plots of event-shapedistributions in figs 28 and 29 separated into light-flavour and b-tagged events on the left and rightrespectively

The experimental results come from the L3 experiment [26] However since the data points areonly available with 3-digit precision some of the least populated bins contain artifacts like uncertain-ties being reported as exactly zero etc Thus we have been forced to make the following modificationsto the data set

The statistical uncertainty was reported as zero for the last two bins of light-flavour Thrust as wellas for the last bin of the C D and BT parameters Uncertainties lt 10minus3 were derived using anapproximate statistical scaling based on the contents and uncertainties of the other bins Likewise thesystematical uncertainty for the last bin of Thrust was given as zero which we have replaced by theupper limit 5times 10minus4 The last bin of BT quoted a measured y value of zero removed in this study

For the heavy-flavour tagged event shapes more significant rounding issues were present Thusseveral of the first and last bins of each distribution either quoted zero (statistical andor systematic)uncertainties or ones with only a single digit of precision (such as 0001 for which the rounding errorcould be up to sim 50) We have interpreted all such values conservatively inserting by hand a fourthdigit on the uncertainties as large as could be consistent with rounding

B2 Additional Particle Spectra

In addition to the K and Λ spectra shown in the main body of the paper (sections 22 and 35) wehere include for reference the x spectra of φ mesons protons and Ξ baryons at LEP in figs 30 and 31the pT spectrum of Klowast mesons and the rapidity and pT spectra of φ mesons at LHC in fig 32 (withabsolute normalizations to the number of inelastic events) and the rapidity spectrum of Ξ baryons atLHC in fig 33

The transverse-momentum spectra of Klowast and φ mesons in fig 32 exhibit the same qualitativebehaviour as that of the KS mesons (fig 23) namely an excess at very soft momenta below sim 500MeV and a depletion at slightly higher momenta between 1 and 2 GeV As discussed in section 35we did not find a way to remove these undesirable features in the Monash 2013 tune suggesting thatthis is an issue that further theoretical modeling will be needed to resolve

The rapidity spectrum of Ξ baryons fig 33 shows that although the Monash tune does producemore Ξ baryons overall (as expected also from the relative increase of Ξ production at LEP cf fig 5)there is still a significant deficit of Ξ baryons at the LHC almost a factor 2 compared with the dataThis is qualitatively similar to the situation for Λ baryons (fig 24) discussed in section 35 Sincenew physics mechanisms may be required to ldquoexplainrdquo the missing baryons we conclude that furthermeasurements and better precision on both the Λ and Ξ sectors (in addition to any other baryonsthat may be accessible) would be highly interesting More explicit recommendations can be found insections 35 and 5

43

0 01 02 03 04

d(1

-T)

σ d

σ1

-310

-210

-110

1

10

2101-Thrust (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn03

01plusmn04

02plusmn05

V I

N C

I A

R O

O T

1-T (udsc)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

d(1

-T)

σ dσ

1

-310

-210

-110

1

10

2101-T (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn13

02plusmn12

02plusmn14

V I

N C

I A

R O

O T

1-T (b)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210

310C Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn03

00plusmn04

01plusmn04

V I

N C

I A

R O

O T

C0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210 C parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn17

01plusmn24

01plusmn27

V I

N C

I A

R O

O T

C (b)0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn06

01plusmn06

V I

N C

I A

R O

O T

D0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn24

02plusmn21

02plusmn26

V I

N C

I A

R O

O T

D (b)0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

Figure 28 Hadronic Z decays atradics = 912 GeV The T C and D event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

44

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn02

01plusmn03

01plusmn04

V I

N C

I A

R O

O T

WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn05

01plusmn12

01plusmn17

V I

N C

I A

R O

O T

(b)WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn02

00plusmn02

01plusmn03

V I

N C

I A

R O

O T

TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

04plusmn24

08plusmn49

08plusmn55

V I

N C

I A

R O

O T

(b)TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

Figure 29 Hadronic Z decays atradics = 912 GeV The BW and BT event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

45

0 02 04 06 08 1

dx

φgt

dn

φ1

ltn

-210

-110

1

10 )φx(

Pythia 8183Data from ALEPH_1996_S3486095d40-x01-y01

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn37

02plusmn53

03plusmn62

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

0608

112141618

Figure 30 Hadronic Z decays atradics = 912 GeV φ meson x spectrum

-5 -4 -3 -2 -1 0

dx

pgt

dn

p1

ltn

-410

-310

-210

-110

1

10

210) (Combined)px(p+

Pythia 8183Data from Zeit Phys C66 (1995) 355 PhysRev D59 (1998) 052001

ALEPH+SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn08

00plusmn09

00plusmn08

V I

N C

I A

R O

O T

px-5 -4 -3 -2 -1 0

The

ory

Dat

a

06

08

1

12

14

0 02 04

dx

Ξgt

dn

Ξ1

ltn

-110

1

10

)plusmnΞx(

Pythia 8183Data from Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn11

02plusmn13

02plusmn14

V I

N C

I A

R O

O T

Ex0 02 04

The

ory

Dat

a

06

08

1

12

14

Figure 31 Hadronic Z decays atradics = 912 GeV pplusmn and Ξplusmn x spectra

46

0 2 4 6

Td

pK

d

nIN

EL

1N

-510

-410

-310

-210

-110

(INEL |y|lt05)T

p0K

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn35

01plusmn26

01plusmn29

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 2 4 6

Td

pφ

dn

INE

L1

N-510

-410

-310

-210

-110

gt04)T

(INEL |y|lt05 pT

pφ

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn88

03plusmn84

04plusmn173

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

)dy

[mb]

-K

+K

rarrφ(σd

0

05

1

15

2 Rapidity (INEL ATLAS cuts)φ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn14

01plusmn19

01plusmn34

V I

N C

I A

R O

O T

pp 7000 GeV

|y|0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

06 08 1 12

[mb

GeV

]φ

T)

dp-

K+

Krarrφ(

σd

0

05

1

15

2

25 (INEL ATLAS cuts)

T pφ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn21

01plusmn30

02plusmn53

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p06 08 1 12

The

ory

Dat

a

06

08

1

12

14

Figure 32 pp collisions at 7 TeV Top row Klowast and φ pperp spectra compared with ALICE data [142]Bottom row φ rapidity and pperp spectrum compared with ATLAS data [143] The ATLAS cuts areφrarr K+Kminus pperpφ isin [05 12] GeV |y(φ)| lt 08 pperpK gt 023 GeV |pK | lt 08 GeV

47

0 05 1 15 2

dygt

Ξ lt

dnN

SD

1N

0

001

002

003

004)d|y|gt (NSD)Ξltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn89

01plusmn129

01plusmn192

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

0

05

1

15

2

Figure 33 pp collisions at 7 TeV Ξminus rapidity spectrum compared with CMS data [99]

48

B3 Energy Scaling of σ2rarr2(pTmin) vs σinel from 200 GeV to 100 TeV

In fig 34 we show the LO QCD 2rarr 2 cross section integrated above pTmin as a function of pTminin pp collisions at 4 different CM energies complementing and expanding on the 8-TeV CM energyshown in the main body of the paper We compare two different αs and PDF choices correspondingto those made in tunes Monash 13 (blue filled dots) and 4C (red open squares) respectively As areference for the total inelastic cross section at each energy we base ourselves on the best-fit curvein the TOTEM cross-section measurement paper [72] which in turn represents a fit produced by theCOMPETE collaboration [144] Uncertainties are rough conservative estimates based on the plot inthe TOTEM paper but they are in any case too small to significantly affect conclusions about the scaleat which the partonic cross section saturates the hadronic one

We observe that the pTmin value for which the LO QCD 2 rarr 2 partonic cross section formallybecomes equal to the total inelastic cross section (strongly suggesting that every event has at leastone such mini-jet pair) rises from values around 1 ndash 2 GeV at energies

radics lt 1 TeV to 5 GeV atradic

s = 13 TeV and finally 10 GeV atradics = 100 TeV

49

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

and it may be consistent with the trend also seen in the Λ0 spectrum at LEP cf fig 6 We concludethat baryon production still requires further modelling and tuning efforts

4 Energy Scaling

Though energy scaling these days mostly refers to the scaling of pp collisions (see eg [97]) animportant first step is to consider the scaling of observables in ee rarr γlowastZ rarr hadrons This scalingcontains information on the relative contributions of perturbative and non-perturbative fragmentationThus at low ee energies the non-perturbative components of the fragmentation model dominatewhile perturbative bremsstrahlung increases in importance towards higher ee energies In fig 25we consider the scaling of the average charged-particle multiplicity and that of charged Kaons andLambda baryons from CM energies of 14 GeV to 200 GeV obtained from measurements availableat HEPDATA Below the Z pole the measurements we include mostly come from TASSO [100]though a few points on 〈nCh〉 come from HRS (at 29 GeV [101]) and TOPAZ (at 578 GeV [102]) Atthe Z pole the data come from the four LEP experiments [38 51ndash53] with the latter extending alsoto energies above MZ [103ndash108] For completeness and as reference for future ee collider studiesmodel extrapolations for CM energies up to 1000 GeV are also shown (though still only including theeerarr γlowastZ rarr hadrons component as usual with photon ISR switched off)

From the plots in fig 25 it is clear that there are no significant differences between the energyscaling of the three ee tunes considered here (mainly reflecting that they have been tuned to samereference point at 912 GeV and that their scaling is dictated by the same underlying physics model)and that their energy dependence closely matches that observed in data However the increasedamount of non-perturbative strangeness production in the Monash tune leads to a better agreementwith the overall normalization of the Kplusmn and Λ rates at all energies

Moving to pp collisions the plots in fig 26 show the scaling of the average charged multiplicity(left column) and multiplicity distributions (right column) in min-bias collisions from 7000 GeV (toprow) to 900 GeV (middle row) and 200 GeV (bottom row) compared with data from CMS [92 109]ATLAS [91] and UA5 [110 111] We regret the omission of additional relevant min-bias measure-ments from the Tevatron and RHIC experiments here but have chosen to focus in this paper mainlyon the LHC The comparisons at 7 TeV were already discussed in the main section on pp collisionssection 3 At 900 GeV the Monash 2013 tune again gives a roughly 5 lower average central chargedmultiplicity than the 4C one with a better description of the tail towards high multiplicities At 200GeV the UA5 measurement we include here extends over the full rapidity and pperp range hence the in-terplay between diffraction and low-multiplicity non-diffractive processes is presumably (much) moreimportant We believe imperfections in this modelling to be the likely cause of the significant discrep-ancies observed at high η and for nCh le 20 at these energies Since a dedicated study of this interplayis beyond the scope of this study we limit ourselves merely to stating this observation as a point forfuture studies to help clarify

Finally in fig 27 we compare to the underlying event measured in the highly useful energyscan that was performed at the Tevatron in the last days before its shutdown [22 23] during whichextremely high min-bias statistics were collected at 300 and 900 GeV CM energy over a period of afew days As was already noted in section 3 the UE at 7 TeV is slightly larger in the Monash 2013tune than in tune 4C As can be seen from the plots here the two tunes give comparable results for allthe Tevatron energies Interestingly the UE plateau region at 900 and 1960 GeV is reached sooner inthese models than in the data translating to a roughly 10 - 20 too low UE level for leading-trackpperp values in the neighbourhood of the transition from the rise to the plateau (roughly for leading-

34

14 22 29 35 44 58 91 91 91 91 133 161 183 189 200 250 350 500 1000

gtC

hlt

n

0

20

40

60

Average Charged Multiplicity vs ECM

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN25

χ00plusmn03 00plusmn02 00plusmn02

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 22 29 35 44 58 91 91 91 91 133 161 183 189 200 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

14 22 35 44 91 91 133 161 183 189 250 350 500 1000

gtK

ltn

0

2

4

6 Multiplicity vs ECM+-Average K

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN25

χ00plusmn06 00plusmn20

00plusmn18

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 22 35 44 91 91 133 161 183 189 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

14 35 91 91 91 91 133 200 250 350 500 1000

gtΛ

ltn

0

02

04

06

08

1

12 Multiplicity vs ECM0ΛAverage

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn06

01plusmn22

01plusmn18

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 35 91 91 91 91 133 200 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

Figure 25 e+eminus rarr hadrons Energy scaling of 〈nCh〉 〈nKplusmn〉 and 〈nΛ〉 in e+eminus rarr qq eventsincluding comparisons to measurements from HEPDATA for CM energies from 14 GeV to 200 GeVAlso shown are model extrapolations up to 1000 GeV

35

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from PhysRevLett 105 (2010) 022002

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn00

00plusmn03

00plusmn71

V I

N C

I A

R O

O T

pp 7000 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

0 50 100

)C

hP

rob(

n

-710

-610

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn27

00plusmn27

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

Chn0 50 100

The

ory

Dat

a

06

08

1

12

14

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from JHEP 1002 (2010) 041

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn03

00plusmn05

00plusmn29

V I

N C

I A

R O

O T

pp 900 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

0 10 20 30 40

)C

hP

rob(

n

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn17

01plusmn25

02plusmn127

V I

N C

I A

R O

O T

pp 900 GeV

Chn0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

0 1 2 3 4 5

gtηd

ch lt

dnN

SD

1n

0

1

2

3

4

5gt (NSD)ηd

chltdn

Pythia 8185Data from ZPhys C33 (1986) 1-6

UA5PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn36

00plusmn24

00plusmn16

V I

N C

I A

R O

O T

ppbar 200 GeV

η0 1 2 3 4 5

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)C

hP

rob(

n

-410

-310

-210

-110

1

)T

|lt05 all pηChg Mult (NSD |

Pythia 8185Data from ZPhys C43 (1989) 357

UA5PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn24

00plusmn24

00plusmn08

V I

N C

I A

R O

O T

ppbar 200 GeV

Chn0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 26 Min-bias pp events from 200 to 7000 GeV Energy scaling of 〈dnChdη〉 (left) andP (nCh) (right)

36

0 10 20 30

)φ∆η

∆gt

(T

psum

lt

0

05

1

15gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn24

26plusmn33

12plusmn143

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 10 20 30

)φ∆η

∆gt

(C

hlt

n

0

05

1

15gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

04plusmn05

13plusmn08

14plusmn100

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn58

06plusmn53

08plusmn193

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn16

15plusmn20

06plusmn114

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

gt05)T

|lt10 pη (|T1

)gt vs pT

TRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn10

02plusmn07

05plusmn22

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

gt05)T

|lt10 pη (|T1

gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn20

02plusmn11

03plusmn08

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 27 The Tevatron energy scan The underlying event (left average summed-pperp density andright average track density in the transverse region as function of leading-track pperp) for pp collisionsat 300 (bottom row) 900 GeV (middle row) and 1960 GeV (top row)

37

track pperp values 2 lt pT1 lt 10 GeV) This indicates that the energy scaling of the UE modeling and inparticular the details of its transition between central and peripheral collisions is still not satisfactorilyunderstood

5 Conclusions and Exhortation

We have presented a reanalysis of the constraints on fragmentation in ee collisions and applied theresults to update the final-state fragmentation parameters in PYTHIA 8 We combine these parameterswith a tune to hadron-collider data using a new NNPDF 23 LO QCD+QED PDF set which has beenencoded so it is available as an internal PDF set in PYTHIA 8 independently of LHAPDF [112]

In this PDF set as well as in our tune the value of the strong coupling for hard-scattering matrixelements is fixed to be αs(MZ) = 013 consistent with other LO determinations of it For initial-and final-state radiation our tune uses the effective value αs(MZ) = 01365 The difference isconsistent with an effective translation between the MS and CMW schemes We note that alternative(LO NLO and NNLO) NNPDF 23 QCD+QED sets with αs(MZ) = 0119 are also available inthe code for people who want to check the impact of using a different αs(MZ) value andor higher-order PDF sets on hard-scattering events For the purpose of such studies we point out that it ispossible in PYTHIA 8 to preserve most of the features of the shower- and underlying-event tuningby changing only the PDF for the hard-scattering matrix elements leaving the PDF choice for theshower evolution and MPI framework unaltered (see the PYTHIA 8 HTML manualrsquos PDF sectionunder PDFuseHard)

The updated parameters are available as an option starting from PYTHIA 8185 by setting

Tuneee = 7 and Tunepp = 14

By no means do we claim that this should be regarded as the final word in tuning the PYTHIA 8Monte Carlo model First of all the model continues to evolve For instance developments foreseenfor the near future include updates of colour reconnections diffraction and the treatment of g rarr qqsplittings Any of these should in principle be accompanied by a reevaluation of the model constraints

Moreover despite the comprehensive view of collider data we have attempted to take in thisstudy there still remains several issues that were not addressed including initial-final interferenceand coherence effects [113 114] (probably more a modelling issue than a tuning one) reliable esti-mates of theoretical uncertainties [8 17 24 29 97 115] diffraction14 [74 116 117] and other colour-singlet phenomena such as onium production long-distance (eg forward-backward forward-centraland ldquoridgerdquo-type) correlations [88 118ndash123] B-hadron decays [124] and tuning in the presence ofmatrix-element matching at LO and NLO (see [21 29 115 125 126] for recent phenomenologi-cal studies) Especially in the latter context of matrix-element matching we expect that in manycases PYTHIA 8 will be used together with codes such as ALPGEN [127] MADGRAPH [128]aMCatNLO [129] or POWHEG [130] either using the matching algorithms of those programs them-selves or via any of PYTHIArsquos several internal (LHEF-based [131]) implementations of matchingschemes (POWHEG [85] CKKW-L [132ndash134] MLM [135 136] UMEPS [137] NL3 [138] UN-LOPS [139]) The impact of such corrections on MC tuning depends on the details of the matchingscheme (especially its treatment of unitarity) and there is in general a non-negligible possibility ofldquomis-tuningrdquo when combining a stand-alone tune with ME corrections A simple example illustrating

14In particular the constraints on fragmentation mainly come from SLD and LEP where the non-perturbative parametersare clearly defined at the shower cutoff scaleQhad whereas diffraction is dominated by soft physics for which the definitionof the effective hadronization scale is less clear The amount of MPI in hard diffractive events also requires tuning

38

this is the effective value of αs(MZ) which for a leading-order tune is typically of order 013 whilea consistent NLO correction scheme should be compatible with values closer to 012 [29] There isalso the question of the running order of αs The propagation of such changes from the level of hardmatrix elements through the shower and hadronization tuning process are still not fully explored andhence we advise users to perform simple cross-checks such as checking the distributions presented inthis paper before and after applying matrix-element corrections Parameters that appear on both sidesof the matching such as αs should also be checked for consistency [21]

We noted several issues concerning the ee data used to constrain the fragmentation modelling thatit would be good to resolve In particular we find some tensions between the identified-particle ratesextracted from 1) HEDPATA 2) Sec 46 of the PDG and 3) the Z boson summary table in the PDGas discussed in more detail in section 2 and concerning which we made some (subjective) decisionsto arrive at a set of hopefully self-consistent constraints for this work We also note that the overallprecision of the fragmentation constraints could likely be significantly improved by an FCC-ee typemachine such as Tera-Z a possibility we hope to see more fully explored in the context of future eeQCD phenomenology studies

We conclude that the new parameter set does improve significantly on the previous default valuesin several respects including better agreement with data on

1 the net strangeness fraction (has been increased by 10 reflected not only in improved kaonand hyperon yields but also in the Ds and Bs fractions)

2 the ultra-hard fragmentation tail (has been softened especially for leading baryons and for Dand B hadrons)

3 the pTZ spectrum (softened at low pTZ)

4 the minimum-bias charged multiplicity in the forward region (has increased by 10)

5 the underlying event at 7 TeV (is very slightly higher than before)

Some questions that remain open include the following We see a roughly 20 excess of verysoft kaons in both ee and pp environments cf figs 6 and 23 despite the overall kaon yields beingwell described and the overall baryon yields at LHC appear to be underestimated by at least 30despite good agreement at LEP The momentum spectra of heavier strange particles are also poorlyreproduced in particular at LHC It is interesting and exciting that some of the LHC spectra appearto be better described by allowing collective flow in a fraction of events (cf the EPOS model [140])though we believe the jury is still out on whether this accurately reflects the underlying physics Forinstance it has been argued that colour reconnections can mimick flow effects [90] and they may alsobe able to modify the yield of baryons if the creationdestruction of string junctions is allowed [141]We look forward to future discussions on these issues

We round off with an exhortation for follow-ups on this study to provide

bull Not only central tunes experiments and other user-end colleagues need more than central de-scriptions of data there is an increasing need for serious uncertainty estimates In the contextof tune variations it is important to keep in mind that the modelling uncertainties are often in-trinsically non-universal Therefore the constraints obtained by considering data uncertaintiesonly (eg in the spirit of PROFESSORrsquos eigentunes [17]) can at most constitute a lower boundon the theoretical uncertainty (similarly to the case for PDFs) A serious uncertainty estimateincludes some systematic modelling variation irrespectively of and in addition to what data

39

allows (eg in the spirit of the Perugia set of tunes for PYTHIA 6 [8]) We therefore hope thefuture will see more elaborate combinations of data- and theory-driven approaches to systematictune uncertainties

bull Not only global tunes the power of MC models lies in their ability to simultaneously describea large variety of data hence we do not mean to imply that one should give up on universalityand tune to increasingly specific corners of phase space disregarding (or de-emphasizing withlower weights) all others However as proposed in [97] one can obtain useful explicit tests ofthe universality of the underlying physics model by performing independent tunes on separateldquophysics windowsrdquo say in the forward vs central regions for different event-selection crite-ria at different collider energies or even for different collider types In this connection justmaking one global ldquobest-fitrdquo tune may obscure tensions between the descriptions of differentcomplementary data sets By performing independent tunes to each data set separately andchecking the degree of universality of the resulting parameters one obtains a powerful crosscheck on the underlying physics model If all sets produce the same or similar parameters thenuniversality is OK hence a global tune makes very good sense and the remaining uncertain-ties can presumably be reliably estimated from data alone If instead some data sets resultin significantly different tune parameters one has a powerful indication that the universality ofthe underlying modeling is breaking down which can lead to several productive actions 1) itcan be taken into account in the context of uncertainty variations 2) the nature of the data setsfor which non-universal tune parameters are obtained can implicitly indicate the nature of theproblem leading to more robust conclusions about the underlying model than merely whether atune cancannot fit the data and 3) the observations can be communicated to the model authorsin a more unambiguous way hopefully resulting in a speedier cycle of model improvements

We hope that the Monash 2013 tune parameters may serve as a useful starting point for phe-nomenology studies and for future PYTHIA 8 tuning efforts

Acknowledgments

We thank S Mrenna M Ritzmann and T Sjostrand for comments on the manuscript and L de Nooijfor pointing us to the ALICE Klowast and φ measurements [142] and to the ATLAS φ measurementsin [143] The work of J R is supported by an STFC Rutherford Fellowship STK0052271 Thiswork was supported in part by the Research Executive Agency (REA) of the European Commissionunder the Grant Agreements PITN-GA-2012-315877 (MCnet)

A Monash 2013 Tune Parameters

In tabs 3 ndash 7 we list the FSR fragmentation parameters for the Monash tune of PYTHIA Forreference we compare them to the current default parameters

40

FSR Parameters Monash 13 (Default) CommentTimeShoweralphaSvalue = 01365 = 01383 Effective alphaS(mZ) valueTimeShoweralphaSorder = 1 = 1 Running orderTimeShoweralphaSuseCMW = off = off Translation from MS to CMWTimeShowerpTmin = 050 = 040 Cutoff for QCD radiationTimeShowerpTminChgQ = 050 = 040 Cutoff for QED radiationTimeShowerphiPolAsym = on = on Asymmetric azimuth distributions

Table 3 Final-state radiation (FSR) parameters

HAD Parameters Monash 13 (Default) Comment String breaks pT and z distributionsStringPTsigma = 0335 = 0304 Soft pT in string breaks (in GeV)StringPTenhancedFraction = 001 = 001 Fraction of breakups with enhanced pTStringPTenhancedWidth = 20 = 20 Enhancement factorStringZaLund = 068 = 03 Lund FF a (hard fragmentation supp)StringZbLund = 098 = 08 Lund FF b (soft fragmentation supp)StringZaExtraSquark = 00 = 00 Extra a when picking up an s quarkStringZaExtraDiquark = 097 = 050 Extra a when picking up a diquarkStringZrFactC = 132 = 100 Lund-Bowler c-quark parameterStringZrFactB = 0855 = 067 Lund-Bowler b-quark parameter Flavour composition mesonsStringFlavProbStoUD = 0217 = 019 Strangeness-to-UD ratioStringFlavmesonUDvector = 05 = 062 Light-flavour vector suppressionStringFlavmesonSvector = 055 = 0725 Strange vector suppressionStringFlavmesonCvector = 088 = 106 Charm vector suppressionStringFlavmesonBvector = 22 = 30 Bottom vector suppressionStringFlavetaSup = 060 = 063 Suppression of eta mesonsStringFlavetaPrimeSup = 012 = 012 Suppression of etarsquo mesons Flavour composition baryonsStringFlavprobQQtoQ = 0081 = 009 Diquark rate (for baryon production)StringFlavprobSQtoQQ = 0915 = 1000 Strange-diquark suppressionStringFlavprobQQ1toQQ0 = 00275 = 0027 Vector diquark suppressionStringFlavdecupletSup = 10 = 10 Spin-32 baryon suppressionStringFlavsuppressLeadingB = off = off Optional leading-baryon suppressionStringFlavpopcornSpair = 09 = 05 StringFlavpopcornSmeson = 05 = 05

Table 4 String-breaking parameters

PDF and ME Parameters Monash 13 (Default) CommentPDFpSet = 13 = 8 PDF set for the protonSigmaProcessalphaSvalue = 0130 0135 alphaS(MZ) for matrix elementsMultiPartonInteractionsalphaSvalue = 0130 0135 alphaS(MZ) for MPI

Table 5 Parton-distribution (PDF) and Matrix-Element (ME) parameters

41

ISR Parameters Monash 13 (Default) CommentSpaceShoweralphaSvalue = 01365 = 0137 Effective alphaS(mZ) valueSpaceShoweralphaSorder = 1 = 1 Running orderSpaceShoweralphaSuseCMW = off = off Translation from MS to CMWSpaceShowersamePTasMPI = off = off ISR cutoff typeSpaceShowerpT0Ref = 20 = 20 ISR pT0 cutoffSpaceShowerecmRef = 70000 = 18000 ISR pT0 reference ECM scaleSpaceShowerecmPow = 00 = 00 ISR pT0 scaling powerSpaceShowerrapidityOrder = on = on Approx coherence via y-orderingSpaceShowerphiPolAsym = on = on Azimuth asymmetries from gluon polSpaceShowerphiIntAsym = on = on Azimuth asymmetries from interferenceTimeShowerdampenBeamRecoil = on = on Recoil dampening in final-initial dipolesBeamRemnantsprimordialKTsoft = 09 = 05 Primordial kT for soft procsBeamRemnantsprimordialKThard = 18 = 20 Primordial kT for hard procsBeamRemnantshalfScaleForKT = 15 = 10 Primordial kT softhard boundaryBeamRemnantshalfMassForKT = 10 = 10 Primordial kT softhard mass boundary

Table 6 Initial-state radiation (ISR) and primordial-kT parameters

MPI Parameters Monash 13 (Default) CommentMultipartonInteractionspT0Ref = 228 = 2085 MPI pT0 IR regularization scaleMultipartonInteractionsecmRef = 70000 = 18000 MPI pT0 reference ECM scaleMultipartonInteractionsecmPow = 0215 = 019 MPI pT0 scaling powerMultipartonInteractionsbProfile = 3 = 3 Transverse matter overlap profileMultipartonInteractionsexpPow = 185 = 20 Shape parameterBeamRemnantsreconnectRange = 18 = 15 Colour ReconnectionsSigmaTotalzeroAXB = on = on Carried over from 4CSigmaDiffractivedampen = on = on Carried over from 4CSigmaDiffractivemaxXB = 650 = 650 Carried over from 4CSigmaDiffractivemaxAX = 650 = 650 Carried over from 4CSigmaDiffractivemaxXX = 650 = 650 Carried over from 4CDiffractionlargeMassSuppress = 40 = 20 High-mass diffraction suppression power

Table 7 Multi-Parton-Interaction (MPI) Colour-Reconnection (CR) and Diffractive parameters

42

B Additional Plots

B1 LEP Event-Shape Distributions

To keep the main body of the paper as uncluttered as possible we collect various plots of event-shapedistributions in figs 28 and 29 separated into light-flavour and b-tagged events on the left and rightrespectively

The experimental results come from the L3 experiment [26] However since the data points areonly available with 3-digit precision some of the least populated bins contain artifacts like uncertain-ties being reported as exactly zero etc Thus we have been forced to make the following modificationsto the data set

The statistical uncertainty was reported as zero for the last two bins of light-flavour Thrust as wellas for the last bin of the C D and BT parameters Uncertainties lt 10minus3 were derived using anapproximate statistical scaling based on the contents and uncertainties of the other bins Likewise thesystematical uncertainty for the last bin of Thrust was given as zero which we have replaced by theupper limit 5times 10minus4 The last bin of BT quoted a measured y value of zero removed in this study

For the heavy-flavour tagged event shapes more significant rounding issues were present Thusseveral of the first and last bins of each distribution either quoted zero (statistical andor systematic)uncertainties or ones with only a single digit of precision (such as 0001 for which the rounding errorcould be up to sim 50) We have interpreted all such values conservatively inserting by hand a fourthdigit on the uncertainties as large as could be consistent with rounding

B2 Additional Particle Spectra

In addition to the K and Λ spectra shown in the main body of the paper (sections 22 and 35) wehere include for reference the x spectra of φ mesons protons and Ξ baryons at LEP in figs 30 and 31the pT spectrum of Klowast mesons and the rapidity and pT spectra of φ mesons at LHC in fig 32 (withabsolute normalizations to the number of inelastic events) and the rapidity spectrum of Ξ baryons atLHC in fig 33

The transverse-momentum spectra of Klowast and φ mesons in fig 32 exhibit the same qualitativebehaviour as that of the KS mesons (fig 23) namely an excess at very soft momenta below sim 500MeV and a depletion at slightly higher momenta between 1 and 2 GeV As discussed in section 35we did not find a way to remove these undesirable features in the Monash 2013 tune suggesting thatthis is an issue that further theoretical modeling will be needed to resolve

The rapidity spectrum of Ξ baryons fig 33 shows that although the Monash tune does producemore Ξ baryons overall (as expected also from the relative increase of Ξ production at LEP cf fig 5)there is still a significant deficit of Ξ baryons at the LHC almost a factor 2 compared with the dataThis is qualitatively similar to the situation for Λ baryons (fig 24) discussed in section 35 Sincenew physics mechanisms may be required to ldquoexplainrdquo the missing baryons we conclude that furthermeasurements and better precision on both the Λ and Ξ sectors (in addition to any other baryonsthat may be accessible) would be highly interesting More explicit recommendations can be found insections 35 and 5

43

0 01 02 03 04

d(1

-T)

σ d

σ1

-310

-210

-110

1

10

2101-Thrust (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn03

01plusmn04

02plusmn05

V I

N C

I A

R O

O T

1-T (udsc)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

d(1

-T)

σ dσ

1

-310

-210

-110

1

10

2101-T (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn13

02plusmn12

02plusmn14

V I

N C

I A

R O

O T

1-T (b)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210

310C Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn03

00plusmn04

01plusmn04

V I

N C

I A

R O

O T

C0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210 C parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn17

01plusmn24

01plusmn27

V I

N C

I A

R O

O T

C (b)0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn06

01plusmn06

V I

N C

I A

R O

O T

D0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn24

02plusmn21

02plusmn26

V I

N C

I A

R O

O T

D (b)0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

Figure 28 Hadronic Z decays atradics = 912 GeV The T C and D event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

44

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn02

01plusmn03

01plusmn04

V I

N C

I A

R O

O T

WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn05

01plusmn12

01plusmn17

V I

N C

I A

R O

O T

(b)WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn02

00plusmn02

01plusmn03

V I

N C

I A

R O

O T

TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

04plusmn24

08plusmn49

08plusmn55

V I

N C

I A

R O

O T

(b)TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

Figure 29 Hadronic Z decays atradics = 912 GeV The BW and BT event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

45

0 02 04 06 08 1

dx

φgt

dn

φ1

ltn

-210

-110

1

10 )φx(

Pythia 8183Data from ALEPH_1996_S3486095d40-x01-y01

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn37

02plusmn53

03plusmn62

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

0608

112141618

Figure 30 Hadronic Z decays atradics = 912 GeV φ meson x spectrum

-5 -4 -3 -2 -1 0

dx

pgt

dn

p1

ltn

-410

-310

-210

-110

1

10

210) (Combined)px(p+

Pythia 8183Data from Zeit Phys C66 (1995) 355 PhysRev D59 (1998) 052001

ALEPH+SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn08

00plusmn09

00plusmn08

V I

N C

I A

R O

O T

px-5 -4 -3 -2 -1 0

The

ory

Dat

a

06

08

1

12

14

0 02 04

dx

Ξgt

dn

Ξ1

ltn

-110

1

10

)plusmnΞx(

Pythia 8183Data from Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn11

02plusmn13

02plusmn14

V I

N C

I A

R O

O T

Ex0 02 04

The

ory

Dat

a

06

08

1

12

14

Figure 31 Hadronic Z decays atradics = 912 GeV pplusmn and Ξplusmn x spectra

46

0 2 4 6

Td

pK

d

nIN

EL

1N

-510

-410

-310

-210

-110

(INEL |y|lt05)T

p0K

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn35

01plusmn26

01plusmn29

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 2 4 6

Td

pφ

dn

INE

L1

N-510

-410

-310

-210

-110

gt04)T

(INEL |y|lt05 pT

pφ

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn88

03plusmn84

04plusmn173

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

)dy

[mb]

-K

+K

rarrφ(σd

0

05

1

15

2 Rapidity (INEL ATLAS cuts)φ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn14

01plusmn19

01plusmn34

V I

N C

I A

R O

O T

pp 7000 GeV

|y|0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

06 08 1 12

[mb

GeV

]φ

T)

dp-

K+

Krarrφ(

σd

0

05

1

15

2

25 (INEL ATLAS cuts)

T pφ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn21

01plusmn30

02plusmn53

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p06 08 1 12

The

ory

Dat

a

06

08

1

12

14

Figure 32 pp collisions at 7 TeV Top row Klowast and φ pperp spectra compared with ALICE data [142]Bottom row φ rapidity and pperp spectrum compared with ATLAS data [143] The ATLAS cuts areφrarr K+Kminus pperpφ isin [05 12] GeV |y(φ)| lt 08 pperpK gt 023 GeV |pK | lt 08 GeV

47

0 05 1 15 2

dygt

Ξ lt

dnN

SD

1N

0

001

002

003

004)d|y|gt (NSD)Ξltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn89

01plusmn129

01plusmn192

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

0

05

1

15

2

Figure 33 pp collisions at 7 TeV Ξminus rapidity spectrum compared with CMS data [99]

48

B3 Energy Scaling of σ2rarr2(pTmin) vs σinel from 200 GeV to 100 TeV

In fig 34 we show the LO QCD 2rarr 2 cross section integrated above pTmin as a function of pTminin pp collisions at 4 different CM energies complementing and expanding on the 8-TeV CM energyshown in the main body of the paper We compare two different αs and PDF choices correspondingto those made in tunes Monash 13 (blue filled dots) and 4C (red open squares) respectively As areference for the total inelastic cross section at each energy we base ourselves on the best-fit curvein the TOTEM cross-section measurement paper [72] which in turn represents a fit produced by theCOMPETE collaboration [144] Uncertainties are rough conservative estimates based on the plot inthe TOTEM paper but they are in any case too small to significantly affect conclusions about the scaleat which the partonic cross section saturates the hadronic one

We observe that the pTmin value for which the LO QCD 2 rarr 2 partonic cross section formallybecomes equal to the total inelastic cross section (strongly suggesting that every event has at leastone such mini-jet pair) rises from values around 1 ndash 2 GeV at energies

radics lt 1 TeV to 5 GeV atradic

s = 13 TeV and finally 10 GeV atradics = 100 TeV

49

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

14 22 29 35 44 58 91 91 91 91 133 161 183 189 200 250 350 500 1000

gtC

hlt

n

0

20

40

60

Average Charged Multiplicity vs ECM

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN25

χ00plusmn03 00plusmn02 00plusmn02

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 22 29 35 44 58 91 91 91 91 133 161 183 189 200 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

14 22 35 44 91 91 133 161 183 189 250 350 500 1000

gtK

ltn

0

2

4

6 Multiplicity vs ECM+-Average K

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN25

χ00plusmn06 00plusmn20

00plusmn18

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 22 35 44 91 91 133 161 183 189 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

14 35 91 91 91 91 133 200 250 350 500 1000

gtΛ

ltn

0

02

04

06

08

1

12 Multiplicity vs ECM0ΛAverage

Pythia 8185Data from HEPDATA

HEPDATAPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn06

01plusmn22

01plusmn18

V I

N C

I A

R O

O T

hadronsrarree

(not to scale)cmE

14 35 91 91 91 91 133 200 250 350 500 1000

The

ory

Dat

a

06

08

1

12

14

Figure 25 e+eminus rarr hadrons Energy scaling of 〈nCh〉 〈nKplusmn〉 and 〈nΛ〉 in e+eminus rarr qq eventsincluding comparisons to measurements from HEPDATA for CM energies from 14 GeV to 200 GeVAlso shown are model extrapolations up to 1000 GeV

35

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from PhysRevLett 105 (2010) 022002

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn00

00plusmn03

00plusmn71

V I

N C

I A

R O

O T

pp 7000 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

0 50 100

)C

hP

rob(

n

-710

-610

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn27

00plusmn27

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

Chn0 50 100

The

ory

Dat

a

06

08

1

12

14

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from JHEP 1002 (2010) 041

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn03

00plusmn05

00plusmn29

V I

N C

I A

R O

O T

pp 900 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

0 10 20 30 40

)C

hP

rob(

n

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn17

01plusmn25

02plusmn127

V I

N C

I A

R O

O T

pp 900 GeV

Chn0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

0 1 2 3 4 5

gtηd

ch lt

dnN

SD

1n

0

1

2

3

4

5gt (NSD)ηd

chltdn

Pythia 8185Data from ZPhys C33 (1986) 1-6

UA5PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn36

00plusmn24

00plusmn16

V I

N C

I A

R O

O T

ppbar 200 GeV

η0 1 2 3 4 5

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)C

hP

rob(

n

-410

-310

-210

-110

1

)T

|lt05 all pηChg Mult (NSD |

Pythia 8185Data from ZPhys C43 (1989) 357

UA5PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn24

00plusmn24

00plusmn08

V I

N C

I A

R O

O T

ppbar 200 GeV

Chn0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 26 Min-bias pp events from 200 to 7000 GeV Energy scaling of 〈dnChdη〉 (left) andP (nCh) (right)

36

0 10 20 30

)φ∆η

∆gt

(T

psum

lt

0

05

1

15gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn24

26plusmn33

12plusmn143

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 10 20 30

)φ∆η

∆gt

(C

hlt

n

0

05

1

15gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

04plusmn05

13plusmn08

14plusmn100

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn58

06plusmn53

08plusmn193

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn16

15plusmn20

06plusmn114

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

gt05)T

|lt10 pη (|T1

)gt vs pT

TRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn10

02plusmn07

05plusmn22

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

gt05)T

|lt10 pη (|T1

gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn20

02plusmn11

03plusmn08

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 27 The Tevatron energy scan The underlying event (left average summed-pperp density andright average track density in the transverse region as function of leading-track pperp) for pp collisionsat 300 (bottom row) 900 GeV (middle row) and 1960 GeV (top row)

37

track pperp values 2 lt pT1 lt 10 GeV) This indicates that the energy scaling of the UE modeling and inparticular the details of its transition between central and peripheral collisions is still not satisfactorilyunderstood

5 Conclusions and Exhortation

We have presented a reanalysis of the constraints on fragmentation in ee collisions and applied theresults to update the final-state fragmentation parameters in PYTHIA 8 We combine these parameterswith a tune to hadron-collider data using a new NNPDF 23 LO QCD+QED PDF set which has beenencoded so it is available as an internal PDF set in PYTHIA 8 independently of LHAPDF [112]

In this PDF set as well as in our tune the value of the strong coupling for hard-scattering matrixelements is fixed to be αs(MZ) = 013 consistent with other LO determinations of it For initial-and final-state radiation our tune uses the effective value αs(MZ) = 01365 The difference isconsistent with an effective translation between the MS and CMW schemes We note that alternative(LO NLO and NNLO) NNPDF 23 QCD+QED sets with αs(MZ) = 0119 are also available inthe code for people who want to check the impact of using a different αs(MZ) value andor higher-order PDF sets on hard-scattering events For the purpose of such studies we point out that it ispossible in PYTHIA 8 to preserve most of the features of the shower- and underlying-event tuningby changing only the PDF for the hard-scattering matrix elements leaving the PDF choice for theshower evolution and MPI framework unaltered (see the PYTHIA 8 HTML manualrsquos PDF sectionunder PDFuseHard)

The updated parameters are available as an option starting from PYTHIA 8185 by setting

Tuneee = 7 and Tunepp = 14

By no means do we claim that this should be regarded as the final word in tuning the PYTHIA 8Monte Carlo model First of all the model continues to evolve For instance developments foreseenfor the near future include updates of colour reconnections diffraction and the treatment of g rarr qqsplittings Any of these should in principle be accompanied by a reevaluation of the model constraints

Moreover despite the comprehensive view of collider data we have attempted to take in thisstudy there still remains several issues that were not addressed including initial-final interferenceand coherence effects [113 114] (probably more a modelling issue than a tuning one) reliable esti-mates of theoretical uncertainties [8 17 24 29 97 115] diffraction14 [74 116 117] and other colour-singlet phenomena such as onium production long-distance (eg forward-backward forward-centraland ldquoridgerdquo-type) correlations [88 118ndash123] B-hadron decays [124] and tuning in the presence ofmatrix-element matching at LO and NLO (see [21 29 115 125 126] for recent phenomenologi-cal studies) Especially in the latter context of matrix-element matching we expect that in manycases PYTHIA 8 will be used together with codes such as ALPGEN [127] MADGRAPH [128]aMCatNLO [129] or POWHEG [130] either using the matching algorithms of those programs them-selves or via any of PYTHIArsquos several internal (LHEF-based [131]) implementations of matchingschemes (POWHEG [85] CKKW-L [132ndash134] MLM [135 136] UMEPS [137] NL3 [138] UN-LOPS [139]) The impact of such corrections on MC tuning depends on the details of the matchingscheme (especially its treatment of unitarity) and there is in general a non-negligible possibility ofldquomis-tuningrdquo when combining a stand-alone tune with ME corrections A simple example illustrating

14In particular the constraints on fragmentation mainly come from SLD and LEP where the non-perturbative parametersare clearly defined at the shower cutoff scaleQhad whereas diffraction is dominated by soft physics for which the definitionof the effective hadronization scale is less clear The amount of MPI in hard diffractive events also requires tuning

38

this is the effective value of αs(MZ) which for a leading-order tune is typically of order 013 whilea consistent NLO correction scheme should be compatible with values closer to 012 [29] There isalso the question of the running order of αs The propagation of such changes from the level of hardmatrix elements through the shower and hadronization tuning process are still not fully explored andhence we advise users to perform simple cross-checks such as checking the distributions presented inthis paper before and after applying matrix-element corrections Parameters that appear on both sidesof the matching such as αs should also be checked for consistency [21]

We noted several issues concerning the ee data used to constrain the fragmentation modelling thatit would be good to resolve In particular we find some tensions between the identified-particle ratesextracted from 1) HEDPATA 2) Sec 46 of the PDG and 3) the Z boson summary table in the PDGas discussed in more detail in section 2 and concerning which we made some (subjective) decisionsto arrive at a set of hopefully self-consistent constraints for this work We also note that the overallprecision of the fragmentation constraints could likely be significantly improved by an FCC-ee typemachine such as Tera-Z a possibility we hope to see more fully explored in the context of future eeQCD phenomenology studies

We conclude that the new parameter set does improve significantly on the previous default valuesin several respects including better agreement with data on

1 the net strangeness fraction (has been increased by 10 reflected not only in improved kaonand hyperon yields but also in the Ds and Bs fractions)

2 the ultra-hard fragmentation tail (has been softened especially for leading baryons and for Dand B hadrons)

3 the pTZ spectrum (softened at low pTZ)

4 the minimum-bias charged multiplicity in the forward region (has increased by 10)

5 the underlying event at 7 TeV (is very slightly higher than before)

Some questions that remain open include the following We see a roughly 20 excess of verysoft kaons in both ee and pp environments cf figs 6 and 23 despite the overall kaon yields beingwell described and the overall baryon yields at LHC appear to be underestimated by at least 30despite good agreement at LEP The momentum spectra of heavier strange particles are also poorlyreproduced in particular at LHC It is interesting and exciting that some of the LHC spectra appearto be better described by allowing collective flow in a fraction of events (cf the EPOS model [140])though we believe the jury is still out on whether this accurately reflects the underlying physics Forinstance it has been argued that colour reconnections can mimick flow effects [90] and they may alsobe able to modify the yield of baryons if the creationdestruction of string junctions is allowed [141]We look forward to future discussions on these issues

We round off with an exhortation for follow-ups on this study to provide

bull Not only central tunes experiments and other user-end colleagues need more than central de-scriptions of data there is an increasing need for serious uncertainty estimates In the contextof tune variations it is important to keep in mind that the modelling uncertainties are often in-trinsically non-universal Therefore the constraints obtained by considering data uncertaintiesonly (eg in the spirit of PROFESSORrsquos eigentunes [17]) can at most constitute a lower boundon the theoretical uncertainty (similarly to the case for PDFs) A serious uncertainty estimateincludes some systematic modelling variation irrespectively of and in addition to what data

39

allows (eg in the spirit of the Perugia set of tunes for PYTHIA 6 [8]) We therefore hope thefuture will see more elaborate combinations of data- and theory-driven approaches to systematictune uncertainties

bull Not only global tunes the power of MC models lies in their ability to simultaneously describea large variety of data hence we do not mean to imply that one should give up on universalityand tune to increasingly specific corners of phase space disregarding (or de-emphasizing withlower weights) all others However as proposed in [97] one can obtain useful explicit tests ofthe universality of the underlying physics model by performing independent tunes on separateldquophysics windowsrdquo say in the forward vs central regions for different event-selection crite-ria at different collider energies or even for different collider types In this connection justmaking one global ldquobest-fitrdquo tune may obscure tensions between the descriptions of differentcomplementary data sets By performing independent tunes to each data set separately andchecking the degree of universality of the resulting parameters one obtains a powerful crosscheck on the underlying physics model If all sets produce the same or similar parameters thenuniversality is OK hence a global tune makes very good sense and the remaining uncertain-ties can presumably be reliably estimated from data alone If instead some data sets resultin significantly different tune parameters one has a powerful indication that the universality ofthe underlying modeling is breaking down which can lead to several productive actions 1) itcan be taken into account in the context of uncertainty variations 2) the nature of the data setsfor which non-universal tune parameters are obtained can implicitly indicate the nature of theproblem leading to more robust conclusions about the underlying model than merely whether atune cancannot fit the data and 3) the observations can be communicated to the model authorsin a more unambiguous way hopefully resulting in a speedier cycle of model improvements

We hope that the Monash 2013 tune parameters may serve as a useful starting point for phe-nomenology studies and for future PYTHIA 8 tuning efforts

Acknowledgments

We thank S Mrenna M Ritzmann and T Sjostrand for comments on the manuscript and L de Nooijfor pointing us to the ALICE Klowast and φ measurements [142] and to the ATLAS φ measurementsin [143] The work of J R is supported by an STFC Rutherford Fellowship STK0052271 Thiswork was supported in part by the Research Executive Agency (REA) of the European Commissionunder the Grant Agreements PITN-GA-2012-315877 (MCnet)

A Monash 2013 Tune Parameters

In tabs 3 ndash 7 we list the FSR fragmentation parameters for the Monash tune of PYTHIA Forreference we compare them to the current default parameters

40

FSR Parameters Monash 13 (Default) CommentTimeShoweralphaSvalue = 01365 = 01383 Effective alphaS(mZ) valueTimeShoweralphaSorder = 1 = 1 Running orderTimeShoweralphaSuseCMW = off = off Translation from MS to CMWTimeShowerpTmin = 050 = 040 Cutoff for QCD radiationTimeShowerpTminChgQ = 050 = 040 Cutoff for QED radiationTimeShowerphiPolAsym = on = on Asymmetric azimuth distributions

Table 3 Final-state radiation (FSR) parameters

HAD Parameters Monash 13 (Default) Comment String breaks pT and z distributionsStringPTsigma = 0335 = 0304 Soft pT in string breaks (in GeV)StringPTenhancedFraction = 001 = 001 Fraction of breakups with enhanced pTStringPTenhancedWidth = 20 = 20 Enhancement factorStringZaLund = 068 = 03 Lund FF a (hard fragmentation supp)StringZbLund = 098 = 08 Lund FF b (soft fragmentation supp)StringZaExtraSquark = 00 = 00 Extra a when picking up an s quarkStringZaExtraDiquark = 097 = 050 Extra a when picking up a diquarkStringZrFactC = 132 = 100 Lund-Bowler c-quark parameterStringZrFactB = 0855 = 067 Lund-Bowler b-quark parameter Flavour composition mesonsStringFlavProbStoUD = 0217 = 019 Strangeness-to-UD ratioStringFlavmesonUDvector = 05 = 062 Light-flavour vector suppressionStringFlavmesonSvector = 055 = 0725 Strange vector suppressionStringFlavmesonCvector = 088 = 106 Charm vector suppressionStringFlavmesonBvector = 22 = 30 Bottom vector suppressionStringFlavetaSup = 060 = 063 Suppression of eta mesonsStringFlavetaPrimeSup = 012 = 012 Suppression of etarsquo mesons Flavour composition baryonsStringFlavprobQQtoQ = 0081 = 009 Diquark rate (for baryon production)StringFlavprobSQtoQQ = 0915 = 1000 Strange-diquark suppressionStringFlavprobQQ1toQQ0 = 00275 = 0027 Vector diquark suppressionStringFlavdecupletSup = 10 = 10 Spin-32 baryon suppressionStringFlavsuppressLeadingB = off = off Optional leading-baryon suppressionStringFlavpopcornSpair = 09 = 05 StringFlavpopcornSmeson = 05 = 05

Table 4 String-breaking parameters

PDF and ME Parameters Monash 13 (Default) CommentPDFpSet = 13 = 8 PDF set for the protonSigmaProcessalphaSvalue = 0130 0135 alphaS(MZ) for matrix elementsMultiPartonInteractionsalphaSvalue = 0130 0135 alphaS(MZ) for MPI

Table 5 Parton-distribution (PDF) and Matrix-Element (ME) parameters

41

ISR Parameters Monash 13 (Default) CommentSpaceShoweralphaSvalue = 01365 = 0137 Effective alphaS(mZ) valueSpaceShoweralphaSorder = 1 = 1 Running orderSpaceShoweralphaSuseCMW = off = off Translation from MS to CMWSpaceShowersamePTasMPI = off = off ISR cutoff typeSpaceShowerpT0Ref = 20 = 20 ISR pT0 cutoffSpaceShowerecmRef = 70000 = 18000 ISR pT0 reference ECM scaleSpaceShowerecmPow = 00 = 00 ISR pT0 scaling powerSpaceShowerrapidityOrder = on = on Approx coherence via y-orderingSpaceShowerphiPolAsym = on = on Azimuth asymmetries from gluon polSpaceShowerphiIntAsym = on = on Azimuth asymmetries from interferenceTimeShowerdampenBeamRecoil = on = on Recoil dampening in final-initial dipolesBeamRemnantsprimordialKTsoft = 09 = 05 Primordial kT for soft procsBeamRemnantsprimordialKThard = 18 = 20 Primordial kT for hard procsBeamRemnantshalfScaleForKT = 15 = 10 Primordial kT softhard boundaryBeamRemnantshalfMassForKT = 10 = 10 Primordial kT softhard mass boundary

Table 6 Initial-state radiation (ISR) and primordial-kT parameters

MPI Parameters Monash 13 (Default) CommentMultipartonInteractionspT0Ref = 228 = 2085 MPI pT0 IR regularization scaleMultipartonInteractionsecmRef = 70000 = 18000 MPI pT0 reference ECM scaleMultipartonInteractionsecmPow = 0215 = 019 MPI pT0 scaling powerMultipartonInteractionsbProfile = 3 = 3 Transverse matter overlap profileMultipartonInteractionsexpPow = 185 = 20 Shape parameterBeamRemnantsreconnectRange = 18 = 15 Colour ReconnectionsSigmaTotalzeroAXB = on = on Carried over from 4CSigmaDiffractivedampen = on = on Carried over from 4CSigmaDiffractivemaxXB = 650 = 650 Carried over from 4CSigmaDiffractivemaxAX = 650 = 650 Carried over from 4CSigmaDiffractivemaxXX = 650 = 650 Carried over from 4CDiffractionlargeMassSuppress = 40 = 20 High-mass diffraction suppression power

Table 7 Multi-Parton-Interaction (MPI) Colour-Reconnection (CR) and Diffractive parameters

42

B Additional Plots

B1 LEP Event-Shape Distributions

To keep the main body of the paper as uncluttered as possible we collect various plots of event-shapedistributions in figs 28 and 29 separated into light-flavour and b-tagged events on the left and rightrespectively

The experimental results come from the L3 experiment [26] However since the data points areonly available with 3-digit precision some of the least populated bins contain artifacts like uncertain-ties being reported as exactly zero etc Thus we have been forced to make the following modificationsto the data set

The statistical uncertainty was reported as zero for the last two bins of light-flavour Thrust as wellas for the last bin of the C D and BT parameters Uncertainties lt 10minus3 were derived using anapproximate statistical scaling based on the contents and uncertainties of the other bins Likewise thesystematical uncertainty for the last bin of Thrust was given as zero which we have replaced by theupper limit 5times 10minus4 The last bin of BT quoted a measured y value of zero removed in this study

For the heavy-flavour tagged event shapes more significant rounding issues were present Thusseveral of the first and last bins of each distribution either quoted zero (statistical andor systematic)uncertainties or ones with only a single digit of precision (such as 0001 for which the rounding errorcould be up to sim 50) We have interpreted all such values conservatively inserting by hand a fourthdigit on the uncertainties as large as could be consistent with rounding

B2 Additional Particle Spectra

In addition to the K and Λ spectra shown in the main body of the paper (sections 22 and 35) wehere include for reference the x spectra of φ mesons protons and Ξ baryons at LEP in figs 30 and 31the pT spectrum of Klowast mesons and the rapidity and pT spectra of φ mesons at LHC in fig 32 (withabsolute normalizations to the number of inelastic events) and the rapidity spectrum of Ξ baryons atLHC in fig 33

The transverse-momentum spectra of Klowast and φ mesons in fig 32 exhibit the same qualitativebehaviour as that of the KS mesons (fig 23) namely an excess at very soft momenta below sim 500MeV and a depletion at slightly higher momenta between 1 and 2 GeV As discussed in section 35we did not find a way to remove these undesirable features in the Monash 2013 tune suggesting thatthis is an issue that further theoretical modeling will be needed to resolve

The rapidity spectrum of Ξ baryons fig 33 shows that although the Monash tune does producemore Ξ baryons overall (as expected also from the relative increase of Ξ production at LEP cf fig 5)there is still a significant deficit of Ξ baryons at the LHC almost a factor 2 compared with the dataThis is qualitatively similar to the situation for Λ baryons (fig 24) discussed in section 35 Sincenew physics mechanisms may be required to ldquoexplainrdquo the missing baryons we conclude that furthermeasurements and better precision on both the Λ and Ξ sectors (in addition to any other baryonsthat may be accessible) would be highly interesting More explicit recommendations can be found insections 35 and 5

43

0 01 02 03 04

d(1

-T)

σ d

σ1

-310

-210

-110

1

10

2101-Thrust (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn03

01plusmn04

02plusmn05

V I

N C

I A

R O

O T

1-T (udsc)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

d(1

-T)

σ dσ

1

-310

-210

-110

1

10

2101-T (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn13

02plusmn12

02plusmn14

V I

N C

I A

R O

O T

1-T (b)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210

310C Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn03

00plusmn04

01plusmn04

V I

N C

I A

R O

O T

C0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210 C parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn17

01plusmn24

01plusmn27

V I

N C

I A

R O

O T

C (b)0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn06

01plusmn06

V I

N C

I A

R O

O T

D0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn24

02plusmn21

02plusmn26

V I

N C

I A

R O

O T

D (b)0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

Figure 28 Hadronic Z decays atradics = 912 GeV The T C and D event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

44

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn02

01plusmn03

01plusmn04

V I

N C

I A

R O

O T

WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn05

01plusmn12

01plusmn17

V I

N C

I A

R O

O T

(b)WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn02

00plusmn02

01plusmn03

V I

N C

I A

R O

O T

TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

04plusmn24

08plusmn49

08plusmn55

V I

N C

I A

R O

O T

(b)TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

Figure 29 Hadronic Z decays atradics = 912 GeV The BW and BT event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

45

0 02 04 06 08 1

dx

φgt

dn

φ1

ltn

-210

-110

1

10 )φx(

Pythia 8183Data from ALEPH_1996_S3486095d40-x01-y01

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn37

02plusmn53

03plusmn62

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

0608

112141618

Figure 30 Hadronic Z decays atradics = 912 GeV φ meson x spectrum

-5 -4 -3 -2 -1 0

dx

pgt

dn

p1

ltn

-410

-310

-210

-110

1

10

210) (Combined)px(p+

Pythia 8183Data from Zeit Phys C66 (1995) 355 PhysRev D59 (1998) 052001

ALEPH+SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn08

00plusmn09

00plusmn08

V I

N C

I A

R O

O T

px-5 -4 -3 -2 -1 0

The

ory

Dat

a

06

08

1

12

14

0 02 04

dx

Ξgt

dn

Ξ1

ltn

-110

1

10

)plusmnΞx(

Pythia 8183Data from Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn11

02plusmn13

02plusmn14

V I

N C

I A

R O

O T

Ex0 02 04

The

ory

Dat

a

06

08

1

12

14

Figure 31 Hadronic Z decays atradics = 912 GeV pplusmn and Ξplusmn x spectra

46

0 2 4 6

Td

pK

d

nIN

EL

1N

-510

-410

-310

-210

-110

(INEL |y|lt05)T

p0K

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn35

01plusmn26

01plusmn29

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 2 4 6

Td

pφ

dn

INE

L1

N-510

-410

-310

-210

-110

gt04)T

(INEL |y|lt05 pT

pφ

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn88

03plusmn84

04plusmn173

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

)dy

[mb]

-K

+K

rarrφ(σd

0

05

1

15

2 Rapidity (INEL ATLAS cuts)φ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn14

01plusmn19

01plusmn34

V I

N C

I A

R O

O T

pp 7000 GeV

|y|0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

06 08 1 12

[mb

GeV

]φ

T)

dp-

K+

Krarrφ(

σd

0

05

1

15

2

25 (INEL ATLAS cuts)

T pφ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn21

01plusmn30

02plusmn53

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p06 08 1 12

The

ory

Dat

a

06

08

1

12

14

Figure 32 pp collisions at 7 TeV Top row Klowast and φ pperp spectra compared with ALICE data [142]Bottom row φ rapidity and pperp spectrum compared with ATLAS data [143] The ATLAS cuts areφrarr K+Kminus pperpφ isin [05 12] GeV |y(φ)| lt 08 pperpK gt 023 GeV |pK | lt 08 GeV

47

0 05 1 15 2

dygt

Ξ lt

dnN

SD

1N

0

001

002

003

004)d|y|gt (NSD)Ξltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn89

01plusmn129

01plusmn192

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

0

05

1

15

2

Figure 33 pp collisions at 7 TeV Ξminus rapidity spectrum compared with CMS data [99]

48

B3 Energy Scaling of σ2rarr2(pTmin) vs σinel from 200 GeV to 100 TeV

In fig 34 we show the LO QCD 2rarr 2 cross section integrated above pTmin as a function of pTminin pp collisions at 4 different CM energies complementing and expanding on the 8-TeV CM energyshown in the main body of the paper We compare two different αs and PDF choices correspondingto those made in tunes Monash 13 (blue filled dots) and 4C (red open squares) respectively As areference for the total inelastic cross section at each energy we base ourselves on the best-fit curvein the TOTEM cross-section measurement paper [72] which in turn represents a fit produced by theCOMPETE collaboration [144] Uncertainties are rough conservative estimates based on the plot inthe TOTEM paper but they are in any case too small to significantly affect conclusions about the scaleat which the partonic cross section saturates the hadronic one

We observe that the pTmin value for which the LO QCD 2 rarr 2 partonic cross section formallybecomes equal to the total inelastic cross section (strongly suggesting that every event has at leastone such mini-jet pair) rises from values around 1 ndash 2 GeV at energies

radics lt 1 TeV to 5 GeV atradic

s = 13 TeV and finally 10 GeV atradics = 100 TeV

49

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from PhysRevLett 105 (2010) 022002

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn00

00plusmn03

00plusmn71

V I

N C

I A

R O

O T

pp 7000 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

0 50 100

)C

hP

rob(

n

-710

-610

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn27

00plusmn27

00plusmn96

V I

N C

I A

R O

O T

pp 7000 GeV

Chn0 50 100

The

ory

Dat

a

06

08

1

12

14

-2 -1 0 1 2

gtηd

ch lt

dnN

SD

1n

0

2

4

6

8

10

12gt (NSD)ηd

chltdn

Pythia 8185Data from JHEP 1002 (2010) 041

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn03

00plusmn05

00plusmn29

V I

N C

I A

R O

O T

pp 900 GeV

η-2 -1 0 1 2

The

ory

Dat

a

06

08

1

12

14

0 10 20 30 40

)C

hP

rob(

n

-510

-410

-310

-210

-110

1|lt25)ηgt05 |

T 1 pge

ChChg Mult (n

Pythia 8185Data from New JPhys 13 (2011) 053033

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn17

01plusmn25

02plusmn127

V I

N C

I A

R O

O T

pp 900 GeV

Chn0 10 20 30 40

The

ory

Dat

a

06

08

1

12

14

0 1 2 3 4 5

gtηd

ch lt

dnN

SD

1n

0

1

2

3

4

5gt (NSD)ηd

chltdn

Pythia 8185Data from ZPhys C33 (1986) 1-6

UA5PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn36

00plusmn24

00plusmn16

V I

N C

I A

R O

O T

ppbar 200 GeV

η0 1 2 3 4 5

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)C

hP

rob(

n

-410

-310

-210

-110

1

)T

|lt05 all pηChg Mult (NSD |

Pythia 8185Data from ZPhys C43 (1989) 357

UA5PY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

00plusmn24

00plusmn24

00plusmn08

V I

N C

I A

R O

O T

ppbar 200 GeV

Chn0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 26 Min-bias pp events from 200 to 7000 GeV Energy scaling of 〈dnChdη〉 (left) andP (nCh) (right)

36

0 10 20 30

)φ∆η

∆gt

(T

psum

lt

0

05

1

15gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn24

26plusmn33

12plusmn143

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 10 20 30

)φ∆η

∆gt

(C

hlt

n

0

05

1

15gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

04plusmn05

13plusmn08

14plusmn100

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn58

06plusmn53

08plusmn193

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn16

15plusmn20

06plusmn114

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

gt05)T

|lt10 pη (|T1

)gt vs pT

TRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn10

02plusmn07

05plusmn22

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

gt05)T

|lt10 pη (|T1

gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn20

02plusmn11

03plusmn08

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 27 The Tevatron energy scan The underlying event (left average summed-pperp density andright average track density in the transverse region as function of leading-track pperp) for pp collisionsat 300 (bottom row) 900 GeV (middle row) and 1960 GeV (top row)

37

track pperp values 2 lt pT1 lt 10 GeV) This indicates that the energy scaling of the UE modeling and inparticular the details of its transition between central and peripheral collisions is still not satisfactorilyunderstood

5 Conclusions and Exhortation

We have presented a reanalysis of the constraints on fragmentation in ee collisions and applied theresults to update the final-state fragmentation parameters in PYTHIA 8 We combine these parameterswith a tune to hadron-collider data using a new NNPDF 23 LO QCD+QED PDF set which has beenencoded so it is available as an internal PDF set in PYTHIA 8 independently of LHAPDF [112]

In this PDF set as well as in our tune the value of the strong coupling for hard-scattering matrixelements is fixed to be αs(MZ) = 013 consistent with other LO determinations of it For initial-and final-state radiation our tune uses the effective value αs(MZ) = 01365 The difference isconsistent with an effective translation between the MS and CMW schemes We note that alternative(LO NLO and NNLO) NNPDF 23 QCD+QED sets with αs(MZ) = 0119 are also available inthe code for people who want to check the impact of using a different αs(MZ) value andor higher-order PDF sets on hard-scattering events For the purpose of such studies we point out that it ispossible in PYTHIA 8 to preserve most of the features of the shower- and underlying-event tuningby changing only the PDF for the hard-scattering matrix elements leaving the PDF choice for theshower evolution and MPI framework unaltered (see the PYTHIA 8 HTML manualrsquos PDF sectionunder PDFuseHard)

The updated parameters are available as an option starting from PYTHIA 8185 by setting

Tuneee = 7 and Tunepp = 14

By no means do we claim that this should be regarded as the final word in tuning the PYTHIA 8Monte Carlo model First of all the model continues to evolve For instance developments foreseenfor the near future include updates of colour reconnections diffraction and the treatment of g rarr qqsplittings Any of these should in principle be accompanied by a reevaluation of the model constraints

Moreover despite the comprehensive view of collider data we have attempted to take in thisstudy there still remains several issues that were not addressed including initial-final interferenceand coherence effects [113 114] (probably more a modelling issue than a tuning one) reliable esti-mates of theoretical uncertainties [8 17 24 29 97 115] diffraction14 [74 116 117] and other colour-singlet phenomena such as onium production long-distance (eg forward-backward forward-centraland ldquoridgerdquo-type) correlations [88 118ndash123] B-hadron decays [124] and tuning in the presence ofmatrix-element matching at LO and NLO (see [21 29 115 125 126] for recent phenomenologi-cal studies) Especially in the latter context of matrix-element matching we expect that in manycases PYTHIA 8 will be used together with codes such as ALPGEN [127] MADGRAPH [128]aMCatNLO [129] or POWHEG [130] either using the matching algorithms of those programs them-selves or via any of PYTHIArsquos several internal (LHEF-based [131]) implementations of matchingschemes (POWHEG [85] CKKW-L [132ndash134] MLM [135 136] UMEPS [137] NL3 [138] UN-LOPS [139]) The impact of such corrections on MC tuning depends on the details of the matchingscheme (especially its treatment of unitarity) and there is in general a non-negligible possibility ofldquomis-tuningrdquo when combining a stand-alone tune with ME corrections A simple example illustrating

14In particular the constraints on fragmentation mainly come from SLD and LEP where the non-perturbative parametersare clearly defined at the shower cutoff scaleQhad whereas diffraction is dominated by soft physics for which the definitionof the effective hadronization scale is less clear The amount of MPI in hard diffractive events also requires tuning

38

this is the effective value of αs(MZ) which for a leading-order tune is typically of order 013 whilea consistent NLO correction scheme should be compatible with values closer to 012 [29] There isalso the question of the running order of αs The propagation of such changes from the level of hardmatrix elements through the shower and hadronization tuning process are still not fully explored andhence we advise users to perform simple cross-checks such as checking the distributions presented inthis paper before and after applying matrix-element corrections Parameters that appear on both sidesof the matching such as αs should also be checked for consistency [21]

We noted several issues concerning the ee data used to constrain the fragmentation modelling thatit would be good to resolve In particular we find some tensions between the identified-particle ratesextracted from 1) HEDPATA 2) Sec 46 of the PDG and 3) the Z boson summary table in the PDGas discussed in more detail in section 2 and concerning which we made some (subjective) decisionsto arrive at a set of hopefully self-consistent constraints for this work We also note that the overallprecision of the fragmentation constraints could likely be significantly improved by an FCC-ee typemachine such as Tera-Z a possibility we hope to see more fully explored in the context of future eeQCD phenomenology studies

We conclude that the new parameter set does improve significantly on the previous default valuesin several respects including better agreement with data on

1 the net strangeness fraction (has been increased by 10 reflected not only in improved kaonand hyperon yields but also in the Ds and Bs fractions)

2 the ultra-hard fragmentation tail (has been softened especially for leading baryons and for Dand B hadrons)

3 the pTZ spectrum (softened at low pTZ)

4 the minimum-bias charged multiplicity in the forward region (has increased by 10)

5 the underlying event at 7 TeV (is very slightly higher than before)

Some questions that remain open include the following We see a roughly 20 excess of verysoft kaons in both ee and pp environments cf figs 6 and 23 despite the overall kaon yields beingwell described and the overall baryon yields at LHC appear to be underestimated by at least 30despite good agreement at LEP The momentum spectra of heavier strange particles are also poorlyreproduced in particular at LHC It is interesting and exciting that some of the LHC spectra appearto be better described by allowing collective flow in a fraction of events (cf the EPOS model [140])though we believe the jury is still out on whether this accurately reflects the underlying physics Forinstance it has been argued that colour reconnections can mimick flow effects [90] and they may alsobe able to modify the yield of baryons if the creationdestruction of string junctions is allowed [141]We look forward to future discussions on these issues

We round off with an exhortation for follow-ups on this study to provide

bull Not only central tunes experiments and other user-end colleagues need more than central de-scriptions of data there is an increasing need for serious uncertainty estimates In the contextof tune variations it is important to keep in mind that the modelling uncertainties are often in-trinsically non-universal Therefore the constraints obtained by considering data uncertaintiesonly (eg in the spirit of PROFESSORrsquos eigentunes [17]) can at most constitute a lower boundon the theoretical uncertainty (similarly to the case for PDFs) A serious uncertainty estimateincludes some systematic modelling variation irrespectively of and in addition to what data

39

allows (eg in the spirit of the Perugia set of tunes for PYTHIA 6 [8]) We therefore hope thefuture will see more elaborate combinations of data- and theory-driven approaches to systematictune uncertainties

bull Not only global tunes the power of MC models lies in their ability to simultaneously describea large variety of data hence we do not mean to imply that one should give up on universalityand tune to increasingly specific corners of phase space disregarding (or de-emphasizing withlower weights) all others However as proposed in [97] one can obtain useful explicit tests ofthe universality of the underlying physics model by performing independent tunes on separateldquophysics windowsrdquo say in the forward vs central regions for different event-selection crite-ria at different collider energies or even for different collider types In this connection justmaking one global ldquobest-fitrdquo tune may obscure tensions between the descriptions of differentcomplementary data sets By performing independent tunes to each data set separately andchecking the degree of universality of the resulting parameters one obtains a powerful crosscheck on the underlying physics model If all sets produce the same or similar parameters thenuniversality is OK hence a global tune makes very good sense and the remaining uncertain-ties can presumably be reliably estimated from data alone If instead some data sets resultin significantly different tune parameters one has a powerful indication that the universality ofthe underlying modeling is breaking down which can lead to several productive actions 1) itcan be taken into account in the context of uncertainty variations 2) the nature of the data setsfor which non-universal tune parameters are obtained can implicitly indicate the nature of theproblem leading to more robust conclusions about the underlying model than merely whether atune cancannot fit the data and 3) the observations can be communicated to the model authorsin a more unambiguous way hopefully resulting in a speedier cycle of model improvements

We hope that the Monash 2013 tune parameters may serve as a useful starting point for phe-nomenology studies and for future PYTHIA 8 tuning efforts

Acknowledgments

We thank S Mrenna M Ritzmann and T Sjostrand for comments on the manuscript and L de Nooijfor pointing us to the ALICE Klowast and φ measurements [142] and to the ATLAS φ measurementsin [143] The work of J R is supported by an STFC Rutherford Fellowship STK0052271 Thiswork was supported in part by the Research Executive Agency (REA) of the European Commissionunder the Grant Agreements PITN-GA-2012-315877 (MCnet)

A Monash 2013 Tune Parameters

In tabs 3 ndash 7 we list the FSR fragmentation parameters for the Monash tune of PYTHIA Forreference we compare them to the current default parameters

40

FSR Parameters Monash 13 (Default) CommentTimeShoweralphaSvalue = 01365 = 01383 Effective alphaS(mZ) valueTimeShoweralphaSorder = 1 = 1 Running orderTimeShoweralphaSuseCMW = off = off Translation from MS to CMWTimeShowerpTmin = 050 = 040 Cutoff for QCD radiationTimeShowerpTminChgQ = 050 = 040 Cutoff for QED radiationTimeShowerphiPolAsym = on = on Asymmetric azimuth distributions

Table 3 Final-state radiation (FSR) parameters

HAD Parameters Monash 13 (Default) Comment String breaks pT and z distributionsStringPTsigma = 0335 = 0304 Soft pT in string breaks (in GeV)StringPTenhancedFraction = 001 = 001 Fraction of breakups with enhanced pTStringPTenhancedWidth = 20 = 20 Enhancement factorStringZaLund = 068 = 03 Lund FF a (hard fragmentation supp)StringZbLund = 098 = 08 Lund FF b (soft fragmentation supp)StringZaExtraSquark = 00 = 00 Extra a when picking up an s quarkStringZaExtraDiquark = 097 = 050 Extra a when picking up a diquarkStringZrFactC = 132 = 100 Lund-Bowler c-quark parameterStringZrFactB = 0855 = 067 Lund-Bowler b-quark parameter Flavour composition mesonsStringFlavProbStoUD = 0217 = 019 Strangeness-to-UD ratioStringFlavmesonUDvector = 05 = 062 Light-flavour vector suppressionStringFlavmesonSvector = 055 = 0725 Strange vector suppressionStringFlavmesonCvector = 088 = 106 Charm vector suppressionStringFlavmesonBvector = 22 = 30 Bottom vector suppressionStringFlavetaSup = 060 = 063 Suppression of eta mesonsStringFlavetaPrimeSup = 012 = 012 Suppression of etarsquo mesons Flavour composition baryonsStringFlavprobQQtoQ = 0081 = 009 Diquark rate (for baryon production)StringFlavprobSQtoQQ = 0915 = 1000 Strange-diquark suppressionStringFlavprobQQ1toQQ0 = 00275 = 0027 Vector diquark suppressionStringFlavdecupletSup = 10 = 10 Spin-32 baryon suppressionStringFlavsuppressLeadingB = off = off Optional leading-baryon suppressionStringFlavpopcornSpair = 09 = 05 StringFlavpopcornSmeson = 05 = 05

Table 4 String-breaking parameters

PDF and ME Parameters Monash 13 (Default) CommentPDFpSet = 13 = 8 PDF set for the protonSigmaProcessalphaSvalue = 0130 0135 alphaS(MZ) for matrix elementsMultiPartonInteractionsalphaSvalue = 0130 0135 alphaS(MZ) for MPI

Table 5 Parton-distribution (PDF) and Matrix-Element (ME) parameters

41

ISR Parameters Monash 13 (Default) CommentSpaceShoweralphaSvalue = 01365 = 0137 Effective alphaS(mZ) valueSpaceShoweralphaSorder = 1 = 1 Running orderSpaceShoweralphaSuseCMW = off = off Translation from MS to CMWSpaceShowersamePTasMPI = off = off ISR cutoff typeSpaceShowerpT0Ref = 20 = 20 ISR pT0 cutoffSpaceShowerecmRef = 70000 = 18000 ISR pT0 reference ECM scaleSpaceShowerecmPow = 00 = 00 ISR pT0 scaling powerSpaceShowerrapidityOrder = on = on Approx coherence via y-orderingSpaceShowerphiPolAsym = on = on Azimuth asymmetries from gluon polSpaceShowerphiIntAsym = on = on Azimuth asymmetries from interferenceTimeShowerdampenBeamRecoil = on = on Recoil dampening in final-initial dipolesBeamRemnantsprimordialKTsoft = 09 = 05 Primordial kT for soft procsBeamRemnantsprimordialKThard = 18 = 20 Primordial kT for hard procsBeamRemnantshalfScaleForKT = 15 = 10 Primordial kT softhard boundaryBeamRemnantshalfMassForKT = 10 = 10 Primordial kT softhard mass boundary

Table 6 Initial-state radiation (ISR) and primordial-kT parameters

MPI Parameters Monash 13 (Default) CommentMultipartonInteractionspT0Ref = 228 = 2085 MPI pT0 IR regularization scaleMultipartonInteractionsecmRef = 70000 = 18000 MPI pT0 reference ECM scaleMultipartonInteractionsecmPow = 0215 = 019 MPI pT0 scaling powerMultipartonInteractionsbProfile = 3 = 3 Transverse matter overlap profileMultipartonInteractionsexpPow = 185 = 20 Shape parameterBeamRemnantsreconnectRange = 18 = 15 Colour ReconnectionsSigmaTotalzeroAXB = on = on Carried over from 4CSigmaDiffractivedampen = on = on Carried over from 4CSigmaDiffractivemaxXB = 650 = 650 Carried over from 4CSigmaDiffractivemaxAX = 650 = 650 Carried over from 4CSigmaDiffractivemaxXX = 650 = 650 Carried over from 4CDiffractionlargeMassSuppress = 40 = 20 High-mass diffraction suppression power

Table 7 Multi-Parton-Interaction (MPI) Colour-Reconnection (CR) and Diffractive parameters

42

B Additional Plots

B1 LEP Event-Shape Distributions

To keep the main body of the paper as uncluttered as possible we collect various plots of event-shapedistributions in figs 28 and 29 separated into light-flavour and b-tagged events on the left and rightrespectively

The experimental results come from the L3 experiment [26] However since the data points areonly available with 3-digit precision some of the least populated bins contain artifacts like uncertain-ties being reported as exactly zero etc Thus we have been forced to make the following modificationsto the data set

The statistical uncertainty was reported as zero for the last two bins of light-flavour Thrust as wellas for the last bin of the C D and BT parameters Uncertainties lt 10minus3 were derived using anapproximate statistical scaling based on the contents and uncertainties of the other bins Likewise thesystematical uncertainty for the last bin of Thrust was given as zero which we have replaced by theupper limit 5times 10minus4 The last bin of BT quoted a measured y value of zero removed in this study

For the heavy-flavour tagged event shapes more significant rounding issues were present Thusseveral of the first and last bins of each distribution either quoted zero (statistical andor systematic)uncertainties or ones with only a single digit of precision (such as 0001 for which the rounding errorcould be up to sim 50) We have interpreted all such values conservatively inserting by hand a fourthdigit on the uncertainties as large as could be consistent with rounding

B2 Additional Particle Spectra

In addition to the K and Λ spectra shown in the main body of the paper (sections 22 and 35) wehere include for reference the x spectra of φ mesons protons and Ξ baryons at LEP in figs 30 and 31the pT spectrum of Klowast mesons and the rapidity and pT spectra of φ mesons at LHC in fig 32 (withabsolute normalizations to the number of inelastic events) and the rapidity spectrum of Ξ baryons atLHC in fig 33

The transverse-momentum spectra of Klowast and φ mesons in fig 32 exhibit the same qualitativebehaviour as that of the KS mesons (fig 23) namely an excess at very soft momenta below sim 500MeV and a depletion at slightly higher momenta between 1 and 2 GeV As discussed in section 35we did not find a way to remove these undesirable features in the Monash 2013 tune suggesting thatthis is an issue that further theoretical modeling will be needed to resolve

The rapidity spectrum of Ξ baryons fig 33 shows that although the Monash tune does producemore Ξ baryons overall (as expected also from the relative increase of Ξ production at LEP cf fig 5)there is still a significant deficit of Ξ baryons at the LHC almost a factor 2 compared with the dataThis is qualitatively similar to the situation for Λ baryons (fig 24) discussed in section 35 Sincenew physics mechanisms may be required to ldquoexplainrdquo the missing baryons we conclude that furthermeasurements and better precision on both the Λ and Ξ sectors (in addition to any other baryonsthat may be accessible) would be highly interesting More explicit recommendations can be found insections 35 and 5

43

0 01 02 03 04

d(1

-T)

σ d

σ1

-310

-210

-110

1

10

2101-Thrust (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn03

01plusmn04

02plusmn05

V I

N C

I A

R O

O T

1-T (udsc)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

d(1

-T)

σ dσ

1

-310

-210

-110

1

10

2101-T (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn13

02plusmn12

02plusmn14

V I

N C

I A

R O

O T

1-T (b)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210

310C Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn03

00plusmn04

01plusmn04

V I

N C

I A

R O

O T

C0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210 C parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn17

01plusmn24

01plusmn27

V I

N C

I A

R O

O T

C (b)0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn06

01plusmn06

V I

N C

I A

R O

O T

D0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn24

02plusmn21

02plusmn26

V I

N C

I A

R O

O T

D (b)0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

Figure 28 Hadronic Z decays atradics = 912 GeV The T C and D event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

44

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn02

01plusmn03

01plusmn04

V I

N C

I A

R O

O T

WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn05

01plusmn12

01plusmn17

V I

N C

I A

R O

O T

(b)WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn02

00plusmn02

01plusmn03

V I

N C

I A

R O

O T

TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

04plusmn24

08plusmn49

08plusmn55

V I

N C

I A

R O

O T

(b)TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

Figure 29 Hadronic Z decays atradics = 912 GeV The BW and BT event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

45

0 02 04 06 08 1

dx

φgt

dn

φ1

ltn

-210

-110

1

10 )φx(

Pythia 8183Data from ALEPH_1996_S3486095d40-x01-y01

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn37

02plusmn53

03plusmn62

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

0608

112141618

Figure 30 Hadronic Z decays atradics = 912 GeV φ meson x spectrum

-5 -4 -3 -2 -1 0

dx

pgt

dn

p1

ltn

-410

-310

-210

-110

1

10

210) (Combined)px(p+

Pythia 8183Data from Zeit Phys C66 (1995) 355 PhysRev D59 (1998) 052001

ALEPH+SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn08

00plusmn09

00plusmn08

V I

N C

I A

R O

O T

px-5 -4 -3 -2 -1 0

The

ory

Dat

a

06

08

1

12

14

0 02 04

dx

Ξgt

dn

Ξ1

ltn

-110

1

10

)plusmnΞx(

Pythia 8183Data from Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn11

02plusmn13

02plusmn14

V I

N C

I A

R O

O T

Ex0 02 04

The

ory

Dat

a

06

08

1

12

14

Figure 31 Hadronic Z decays atradics = 912 GeV pplusmn and Ξplusmn x spectra

46

0 2 4 6

Td

pK

d

nIN

EL

1N

-510

-410

-310

-210

-110

(INEL |y|lt05)T

p0K

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn35

01plusmn26

01plusmn29

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 2 4 6

Td

pφ

dn

INE

L1

N-510

-410

-310

-210

-110

gt04)T

(INEL |y|lt05 pT

pφ

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn88

03plusmn84

04plusmn173

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

)dy

[mb]

-K

+K

rarrφ(σd

0

05

1

15

2 Rapidity (INEL ATLAS cuts)φ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn14

01plusmn19

01plusmn34

V I

N C

I A

R O

O T

pp 7000 GeV

|y|0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

06 08 1 12

[mb

GeV

]φ

T)

dp-

K+

Krarrφ(

σd

0

05

1

15

2

25 (INEL ATLAS cuts)

T pφ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn21

01plusmn30

02plusmn53

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p06 08 1 12

The

ory

Dat

a

06

08

1

12

14

Figure 32 pp collisions at 7 TeV Top row Klowast and φ pperp spectra compared with ALICE data [142]Bottom row φ rapidity and pperp spectrum compared with ATLAS data [143] The ATLAS cuts areφrarr K+Kminus pperpφ isin [05 12] GeV |y(φ)| lt 08 pperpK gt 023 GeV |pK | lt 08 GeV

47

0 05 1 15 2

dygt

Ξ lt

dnN

SD

1N

0

001

002

003

004)d|y|gt (NSD)Ξltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn89

01plusmn129

01plusmn192

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

0

05

1

15

2

Figure 33 pp collisions at 7 TeV Ξminus rapidity spectrum compared with CMS data [99]

48

B3 Energy Scaling of σ2rarr2(pTmin) vs σinel from 200 GeV to 100 TeV

In fig 34 we show the LO QCD 2rarr 2 cross section integrated above pTmin as a function of pTminin pp collisions at 4 different CM energies complementing and expanding on the 8-TeV CM energyshown in the main body of the paper We compare two different αs and PDF choices correspondingto those made in tunes Monash 13 (blue filled dots) and 4C (red open squares) respectively As areference for the total inelastic cross section at each energy we base ourselves on the best-fit curvein the TOTEM cross-section measurement paper [72] which in turn represents a fit produced by theCOMPETE collaboration [144] Uncertainties are rough conservative estimates based on the plot inthe TOTEM paper but they are in any case too small to significantly affect conclusions about the scaleat which the partonic cross section saturates the hadronic one

We observe that the pTmin value for which the LO QCD 2 rarr 2 partonic cross section formallybecomes equal to the total inelastic cross section (strongly suggesting that every event has at leastone such mini-jet pair) rises from values around 1 ndash 2 GeV at energies

radics lt 1 TeV to 5 GeV atradic

s = 13 TeV and finally 10 GeV atradics = 100 TeV

49

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

0 10 20 30

)φ∆η

∆gt

(T

psum

lt

0

05

1

15gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn24

26plusmn33

12plusmn143

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 10 20 30

)φ∆η

∆gt

(C

hlt

n

0

05

1

15gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

04plusmn05

13plusmn08

14plusmn100

V I

N C

I A

R O

O T

ppbar 1960 GeV

(hardest track) [GeV]T1

p0 10 20 30

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1)gt vs p

TTRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn58

06plusmn53

08plusmn193

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15 20 25

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

08

1gt05)

T|lt10 pη (|

T1gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn16

15plusmn20

06plusmn114

V I

N C

I A

R O

O T

ppbar 900 GeV

(hardest track) [GeV]T1

p0 5 10 15 20 25

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(T

psum

lt

0

02

04

06

gt05)T

|lt10 pη (|T1

)gt vs pT

TRNS ltSum(p

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn10

02plusmn07

05plusmn22

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

0 5 10 15

)φ∆η

∆gt

(C

hlt

n

0

02

04

06

gt05)T

|lt10 pη (|T1

gt vs pChTRNS ltn

Pythia 8185Data from CDF Note 10874

CDFPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

02plusmn20

02plusmn11

03plusmn08

V I

N C

I A

R O

O T

ppbar 300 GeV

(hardest track) [GeV]T1

p0 5 10 15

The

ory

Dat

a

06

08

1

12

14

Figure 27 The Tevatron energy scan The underlying event (left average summed-pperp density andright average track density in the transverse region as function of leading-track pperp) for pp collisionsat 300 (bottom row) 900 GeV (middle row) and 1960 GeV (top row)

37

track pperp values 2 lt pT1 lt 10 GeV) This indicates that the energy scaling of the UE modeling and inparticular the details of its transition between central and peripheral collisions is still not satisfactorilyunderstood

5 Conclusions and Exhortation

We have presented a reanalysis of the constraints on fragmentation in ee collisions and applied theresults to update the final-state fragmentation parameters in PYTHIA 8 We combine these parameterswith a tune to hadron-collider data using a new NNPDF 23 LO QCD+QED PDF set which has beenencoded so it is available as an internal PDF set in PYTHIA 8 independently of LHAPDF [112]

In this PDF set as well as in our tune the value of the strong coupling for hard-scattering matrixelements is fixed to be αs(MZ) = 013 consistent with other LO determinations of it For initial-and final-state radiation our tune uses the effective value αs(MZ) = 01365 The difference isconsistent with an effective translation between the MS and CMW schemes We note that alternative(LO NLO and NNLO) NNPDF 23 QCD+QED sets with αs(MZ) = 0119 are also available inthe code for people who want to check the impact of using a different αs(MZ) value andor higher-order PDF sets on hard-scattering events For the purpose of such studies we point out that it ispossible in PYTHIA 8 to preserve most of the features of the shower- and underlying-event tuningby changing only the PDF for the hard-scattering matrix elements leaving the PDF choice for theshower evolution and MPI framework unaltered (see the PYTHIA 8 HTML manualrsquos PDF sectionunder PDFuseHard)

The updated parameters are available as an option starting from PYTHIA 8185 by setting

Tuneee = 7 and Tunepp = 14

By no means do we claim that this should be regarded as the final word in tuning the PYTHIA 8Monte Carlo model First of all the model continues to evolve For instance developments foreseenfor the near future include updates of colour reconnections diffraction and the treatment of g rarr qqsplittings Any of these should in principle be accompanied by a reevaluation of the model constraints

Moreover despite the comprehensive view of collider data we have attempted to take in thisstudy there still remains several issues that were not addressed including initial-final interferenceand coherence effects [113 114] (probably more a modelling issue than a tuning one) reliable esti-mates of theoretical uncertainties [8 17 24 29 97 115] diffraction14 [74 116 117] and other colour-singlet phenomena such as onium production long-distance (eg forward-backward forward-centraland ldquoridgerdquo-type) correlations [88 118ndash123] B-hadron decays [124] and tuning in the presence ofmatrix-element matching at LO and NLO (see [21 29 115 125 126] for recent phenomenologi-cal studies) Especially in the latter context of matrix-element matching we expect that in manycases PYTHIA 8 will be used together with codes such as ALPGEN [127] MADGRAPH [128]aMCatNLO [129] or POWHEG [130] either using the matching algorithms of those programs them-selves or via any of PYTHIArsquos several internal (LHEF-based [131]) implementations of matchingschemes (POWHEG [85] CKKW-L [132ndash134] MLM [135 136] UMEPS [137] NL3 [138] UN-LOPS [139]) The impact of such corrections on MC tuning depends on the details of the matchingscheme (especially its treatment of unitarity) and there is in general a non-negligible possibility ofldquomis-tuningrdquo when combining a stand-alone tune with ME corrections A simple example illustrating

14In particular the constraints on fragmentation mainly come from SLD and LEP where the non-perturbative parametersare clearly defined at the shower cutoff scaleQhad whereas diffraction is dominated by soft physics for which the definitionof the effective hadronization scale is less clear The amount of MPI in hard diffractive events also requires tuning

38

this is the effective value of αs(MZ) which for a leading-order tune is typically of order 013 whilea consistent NLO correction scheme should be compatible with values closer to 012 [29] There isalso the question of the running order of αs The propagation of such changes from the level of hardmatrix elements through the shower and hadronization tuning process are still not fully explored andhence we advise users to perform simple cross-checks such as checking the distributions presented inthis paper before and after applying matrix-element corrections Parameters that appear on both sidesof the matching such as αs should also be checked for consistency [21]

We noted several issues concerning the ee data used to constrain the fragmentation modelling thatit would be good to resolve In particular we find some tensions between the identified-particle ratesextracted from 1) HEDPATA 2) Sec 46 of the PDG and 3) the Z boson summary table in the PDGas discussed in more detail in section 2 and concerning which we made some (subjective) decisionsto arrive at a set of hopefully self-consistent constraints for this work We also note that the overallprecision of the fragmentation constraints could likely be significantly improved by an FCC-ee typemachine such as Tera-Z a possibility we hope to see more fully explored in the context of future eeQCD phenomenology studies

We conclude that the new parameter set does improve significantly on the previous default valuesin several respects including better agreement with data on

1 the net strangeness fraction (has been increased by 10 reflected not only in improved kaonand hyperon yields but also in the Ds and Bs fractions)

2 the ultra-hard fragmentation tail (has been softened especially for leading baryons and for Dand B hadrons)

3 the pTZ spectrum (softened at low pTZ)

4 the minimum-bias charged multiplicity in the forward region (has increased by 10)

5 the underlying event at 7 TeV (is very slightly higher than before)

Some questions that remain open include the following We see a roughly 20 excess of verysoft kaons in both ee and pp environments cf figs 6 and 23 despite the overall kaon yields beingwell described and the overall baryon yields at LHC appear to be underestimated by at least 30despite good agreement at LEP The momentum spectra of heavier strange particles are also poorlyreproduced in particular at LHC It is interesting and exciting that some of the LHC spectra appearto be better described by allowing collective flow in a fraction of events (cf the EPOS model [140])though we believe the jury is still out on whether this accurately reflects the underlying physics Forinstance it has been argued that colour reconnections can mimick flow effects [90] and they may alsobe able to modify the yield of baryons if the creationdestruction of string junctions is allowed [141]We look forward to future discussions on these issues

We round off with an exhortation for follow-ups on this study to provide

bull Not only central tunes experiments and other user-end colleagues need more than central de-scriptions of data there is an increasing need for serious uncertainty estimates In the contextof tune variations it is important to keep in mind that the modelling uncertainties are often in-trinsically non-universal Therefore the constraints obtained by considering data uncertaintiesonly (eg in the spirit of PROFESSORrsquos eigentunes [17]) can at most constitute a lower boundon the theoretical uncertainty (similarly to the case for PDFs) A serious uncertainty estimateincludes some systematic modelling variation irrespectively of and in addition to what data

39

allows (eg in the spirit of the Perugia set of tunes for PYTHIA 6 [8]) We therefore hope thefuture will see more elaborate combinations of data- and theory-driven approaches to systematictune uncertainties

bull Not only global tunes the power of MC models lies in their ability to simultaneously describea large variety of data hence we do not mean to imply that one should give up on universalityand tune to increasingly specific corners of phase space disregarding (or de-emphasizing withlower weights) all others However as proposed in [97] one can obtain useful explicit tests ofthe universality of the underlying physics model by performing independent tunes on separateldquophysics windowsrdquo say in the forward vs central regions for different event-selection crite-ria at different collider energies or even for different collider types In this connection justmaking one global ldquobest-fitrdquo tune may obscure tensions between the descriptions of differentcomplementary data sets By performing independent tunes to each data set separately andchecking the degree of universality of the resulting parameters one obtains a powerful crosscheck on the underlying physics model If all sets produce the same or similar parameters thenuniversality is OK hence a global tune makes very good sense and the remaining uncertain-ties can presumably be reliably estimated from data alone If instead some data sets resultin significantly different tune parameters one has a powerful indication that the universality ofthe underlying modeling is breaking down which can lead to several productive actions 1) itcan be taken into account in the context of uncertainty variations 2) the nature of the data setsfor which non-universal tune parameters are obtained can implicitly indicate the nature of theproblem leading to more robust conclusions about the underlying model than merely whether atune cancannot fit the data and 3) the observations can be communicated to the model authorsin a more unambiguous way hopefully resulting in a speedier cycle of model improvements

We hope that the Monash 2013 tune parameters may serve as a useful starting point for phe-nomenology studies and for future PYTHIA 8 tuning efforts

Acknowledgments

We thank S Mrenna M Ritzmann and T Sjostrand for comments on the manuscript and L de Nooijfor pointing us to the ALICE Klowast and φ measurements [142] and to the ATLAS φ measurementsin [143] The work of J R is supported by an STFC Rutherford Fellowship STK0052271 Thiswork was supported in part by the Research Executive Agency (REA) of the European Commissionunder the Grant Agreements PITN-GA-2012-315877 (MCnet)

A Monash 2013 Tune Parameters

In tabs 3 ndash 7 we list the FSR fragmentation parameters for the Monash tune of PYTHIA Forreference we compare them to the current default parameters

40

FSR Parameters Monash 13 (Default) CommentTimeShoweralphaSvalue = 01365 = 01383 Effective alphaS(mZ) valueTimeShoweralphaSorder = 1 = 1 Running orderTimeShoweralphaSuseCMW = off = off Translation from MS to CMWTimeShowerpTmin = 050 = 040 Cutoff for QCD radiationTimeShowerpTminChgQ = 050 = 040 Cutoff for QED radiationTimeShowerphiPolAsym = on = on Asymmetric azimuth distributions

Table 3 Final-state radiation (FSR) parameters

HAD Parameters Monash 13 (Default) Comment String breaks pT and z distributionsStringPTsigma = 0335 = 0304 Soft pT in string breaks (in GeV)StringPTenhancedFraction = 001 = 001 Fraction of breakups with enhanced pTStringPTenhancedWidth = 20 = 20 Enhancement factorStringZaLund = 068 = 03 Lund FF a (hard fragmentation supp)StringZbLund = 098 = 08 Lund FF b (soft fragmentation supp)StringZaExtraSquark = 00 = 00 Extra a when picking up an s quarkStringZaExtraDiquark = 097 = 050 Extra a when picking up a diquarkStringZrFactC = 132 = 100 Lund-Bowler c-quark parameterStringZrFactB = 0855 = 067 Lund-Bowler b-quark parameter Flavour composition mesonsStringFlavProbStoUD = 0217 = 019 Strangeness-to-UD ratioStringFlavmesonUDvector = 05 = 062 Light-flavour vector suppressionStringFlavmesonSvector = 055 = 0725 Strange vector suppressionStringFlavmesonCvector = 088 = 106 Charm vector suppressionStringFlavmesonBvector = 22 = 30 Bottom vector suppressionStringFlavetaSup = 060 = 063 Suppression of eta mesonsStringFlavetaPrimeSup = 012 = 012 Suppression of etarsquo mesons Flavour composition baryonsStringFlavprobQQtoQ = 0081 = 009 Diquark rate (for baryon production)StringFlavprobSQtoQQ = 0915 = 1000 Strange-diquark suppressionStringFlavprobQQ1toQQ0 = 00275 = 0027 Vector diquark suppressionStringFlavdecupletSup = 10 = 10 Spin-32 baryon suppressionStringFlavsuppressLeadingB = off = off Optional leading-baryon suppressionStringFlavpopcornSpair = 09 = 05 StringFlavpopcornSmeson = 05 = 05

Table 4 String-breaking parameters

PDF and ME Parameters Monash 13 (Default) CommentPDFpSet = 13 = 8 PDF set for the protonSigmaProcessalphaSvalue = 0130 0135 alphaS(MZ) for matrix elementsMultiPartonInteractionsalphaSvalue = 0130 0135 alphaS(MZ) for MPI

Table 5 Parton-distribution (PDF) and Matrix-Element (ME) parameters

41

ISR Parameters Monash 13 (Default) CommentSpaceShoweralphaSvalue = 01365 = 0137 Effective alphaS(mZ) valueSpaceShoweralphaSorder = 1 = 1 Running orderSpaceShoweralphaSuseCMW = off = off Translation from MS to CMWSpaceShowersamePTasMPI = off = off ISR cutoff typeSpaceShowerpT0Ref = 20 = 20 ISR pT0 cutoffSpaceShowerecmRef = 70000 = 18000 ISR pT0 reference ECM scaleSpaceShowerecmPow = 00 = 00 ISR pT0 scaling powerSpaceShowerrapidityOrder = on = on Approx coherence via y-orderingSpaceShowerphiPolAsym = on = on Azimuth asymmetries from gluon polSpaceShowerphiIntAsym = on = on Azimuth asymmetries from interferenceTimeShowerdampenBeamRecoil = on = on Recoil dampening in final-initial dipolesBeamRemnantsprimordialKTsoft = 09 = 05 Primordial kT for soft procsBeamRemnantsprimordialKThard = 18 = 20 Primordial kT for hard procsBeamRemnantshalfScaleForKT = 15 = 10 Primordial kT softhard boundaryBeamRemnantshalfMassForKT = 10 = 10 Primordial kT softhard mass boundary

Table 6 Initial-state radiation (ISR) and primordial-kT parameters

MPI Parameters Monash 13 (Default) CommentMultipartonInteractionspT0Ref = 228 = 2085 MPI pT0 IR regularization scaleMultipartonInteractionsecmRef = 70000 = 18000 MPI pT0 reference ECM scaleMultipartonInteractionsecmPow = 0215 = 019 MPI pT0 scaling powerMultipartonInteractionsbProfile = 3 = 3 Transverse matter overlap profileMultipartonInteractionsexpPow = 185 = 20 Shape parameterBeamRemnantsreconnectRange = 18 = 15 Colour ReconnectionsSigmaTotalzeroAXB = on = on Carried over from 4CSigmaDiffractivedampen = on = on Carried over from 4CSigmaDiffractivemaxXB = 650 = 650 Carried over from 4CSigmaDiffractivemaxAX = 650 = 650 Carried over from 4CSigmaDiffractivemaxXX = 650 = 650 Carried over from 4CDiffractionlargeMassSuppress = 40 = 20 High-mass diffraction suppression power

Table 7 Multi-Parton-Interaction (MPI) Colour-Reconnection (CR) and Diffractive parameters

42

B Additional Plots

B1 LEP Event-Shape Distributions

To keep the main body of the paper as uncluttered as possible we collect various plots of event-shapedistributions in figs 28 and 29 separated into light-flavour and b-tagged events on the left and rightrespectively

The experimental results come from the L3 experiment [26] However since the data points areonly available with 3-digit precision some of the least populated bins contain artifacts like uncertain-ties being reported as exactly zero etc Thus we have been forced to make the following modificationsto the data set

The statistical uncertainty was reported as zero for the last two bins of light-flavour Thrust as wellas for the last bin of the C D and BT parameters Uncertainties lt 10minus3 were derived using anapproximate statistical scaling based on the contents and uncertainties of the other bins Likewise thesystematical uncertainty for the last bin of Thrust was given as zero which we have replaced by theupper limit 5times 10minus4 The last bin of BT quoted a measured y value of zero removed in this study

For the heavy-flavour tagged event shapes more significant rounding issues were present Thusseveral of the first and last bins of each distribution either quoted zero (statistical andor systematic)uncertainties or ones with only a single digit of precision (such as 0001 for which the rounding errorcould be up to sim 50) We have interpreted all such values conservatively inserting by hand a fourthdigit on the uncertainties as large as could be consistent with rounding

B2 Additional Particle Spectra

In addition to the K and Λ spectra shown in the main body of the paper (sections 22 and 35) wehere include for reference the x spectra of φ mesons protons and Ξ baryons at LEP in figs 30 and 31the pT spectrum of Klowast mesons and the rapidity and pT spectra of φ mesons at LHC in fig 32 (withabsolute normalizations to the number of inelastic events) and the rapidity spectrum of Ξ baryons atLHC in fig 33

The transverse-momentum spectra of Klowast and φ mesons in fig 32 exhibit the same qualitativebehaviour as that of the KS mesons (fig 23) namely an excess at very soft momenta below sim 500MeV and a depletion at slightly higher momenta between 1 and 2 GeV As discussed in section 35we did not find a way to remove these undesirable features in the Monash 2013 tune suggesting thatthis is an issue that further theoretical modeling will be needed to resolve

The rapidity spectrum of Ξ baryons fig 33 shows that although the Monash tune does producemore Ξ baryons overall (as expected also from the relative increase of Ξ production at LEP cf fig 5)there is still a significant deficit of Ξ baryons at the LHC almost a factor 2 compared with the dataThis is qualitatively similar to the situation for Λ baryons (fig 24) discussed in section 35 Sincenew physics mechanisms may be required to ldquoexplainrdquo the missing baryons we conclude that furthermeasurements and better precision on both the Λ and Ξ sectors (in addition to any other baryonsthat may be accessible) would be highly interesting More explicit recommendations can be found insections 35 and 5

43

0 01 02 03 04

d(1

-T)

σ d

σ1

-310

-210

-110

1

10

2101-Thrust (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn03

01plusmn04

02plusmn05

V I

N C

I A

R O

O T

1-T (udsc)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

d(1

-T)

σ dσ

1

-310

-210

-110

1

10

2101-T (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn13

02plusmn12

02plusmn14

V I

N C

I A

R O

O T

1-T (b)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210

310C Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn03

00plusmn04

01plusmn04

V I

N C

I A

R O

O T

C0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210 C parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn17

01plusmn24

01plusmn27

V I

N C

I A

R O

O T

C (b)0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn06

01plusmn06

V I

N C

I A

R O

O T

D0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn24

02plusmn21

02plusmn26

V I

N C

I A

R O

O T

D (b)0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

Figure 28 Hadronic Z decays atradics = 912 GeV The T C and D event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

44

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn02

01plusmn03

01plusmn04

V I

N C

I A

R O

O T

WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn05

01plusmn12

01plusmn17

V I

N C

I A

R O

O T

(b)WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn02

00plusmn02

01plusmn03

V I

N C

I A

R O

O T

TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

04plusmn24

08plusmn49

08plusmn55

V I

N C

I A

R O

O T

(b)TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

Figure 29 Hadronic Z decays atradics = 912 GeV The BW and BT event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

45

0 02 04 06 08 1

dx

φgt

dn

φ1

ltn

-210

-110

1

10 )φx(

Pythia 8183Data from ALEPH_1996_S3486095d40-x01-y01

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn37

02plusmn53

03plusmn62

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

0608

112141618

Figure 30 Hadronic Z decays atradics = 912 GeV φ meson x spectrum

-5 -4 -3 -2 -1 0

dx

pgt

dn

p1

ltn

-410

-310

-210

-110

1

10

210) (Combined)px(p+

Pythia 8183Data from Zeit Phys C66 (1995) 355 PhysRev D59 (1998) 052001

ALEPH+SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn08

00plusmn09

00plusmn08

V I

N C

I A

R O

O T

px-5 -4 -3 -2 -1 0

The

ory

Dat

a

06

08

1

12

14

0 02 04

dx

Ξgt

dn

Ξ1

ltn

-110

1

10

)plusmnΞx(

Pythia 8183Data from Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn11

02plusmn13

02plusmn14

V I

N C

I A

R O

O T

Ex0 02 04

The

ory

Dat

a

06

08

1

12

14

Figure 31 Hadronic Z decays atradics = 912 GeV pplusmn and Ξplusmn x spectra

46

0 2 4 6

Td

pK

d

nIN

EL

1N

-510

-410

-310

-210

-110

(INEL |y|lt05)T

p0K

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn35

01plusmn26

01plusmn29

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 2 4 6

Td

pφ

dn

INE

L1

N-510

-410

-310

-210

-110

gt04)T

(INEL |y|lt05 pT

pφ

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn88

03plusmn84

04plusmn173

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

)dy

[mb]

-K

+K

rarrφ(σd

0

05

1

15

2 Rapidity (INEL ATLAS cuts)φ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn14

01plusmn19

01plusmn34

V I

N C

I A

R O

O T

pp 7000 GeV

|y|0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

06 08 1 12

[mb

GeV

]φ

T)

dp-

K+

Krarrφ(

σd

0

05

1

15

2

25 (INEL ATLAS cuts)

T pφ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn21

01plusmn30

02plusmn53

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p06 08 1 12

The

ory

Dat

a

06

08

1

12

14

Figure 32 pp collisions at 7 TeV Top row Klowast and φ pperp spectra compared with ALICE data [142]Bottom row φ rapidity and pperp spectrum compared with ATLAS data [143] The ATLAS cuts areφrarr K+Kminus pperpφ isin [05 12] GeV |y(φ)| lt 08 pperpK gt 023 GeV |pK | lt 08 GeV

47

0 05 1 15 2

dygt

Ξ lt

dnN

SD

1N

0

001

002

003

004)d|y|gt (NSD)Ξltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn89

01plusmn129

01plusmn192

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

0

05

1

15

2

Figure 33 pp collisions at 7 TeV Ξminus rapidity spectrum compared with CMS data [99]

48

B3 Energy Scaling of σ2rarr2(pTmin) vs σinel from 200 GeV to 100 TeV

In fig 34 we show the LO QCD 2rarr 2 cross section integrated above pTmin as a function of pTminin pp collisions at 4 different CM energies complementing and expanding on the 8-TeV CM energyshown in the main body of the paper We compare two different αs and PDF choices correspondingto those made in tunes Monash 13 (blue filled dots) and 4C (red open squares) respectively As areference for the total inelastic cross section at each energy we base ourselves on the best-fit curvein the TOTEM cross-section measurement paper [72] which in turn represents a fit produced by theCOMPETE collaboration [144] Uncertainties are rough conservative estimates based on the plot inthe TOTEM paper but they are in any case too small to significantly affect conclusions about the scaleat which the partonic cross section saturates the hadronic one

We observe that the pTmin value for which the LO QCD 2 rarr 2 partonic cross section formallybecomes equal to the total inelastic cross section (strongly suggesting that every event has at leastone such mini-jet pair) rises from values around 1 ndash 2 GeV at energies

radics lt 1 TeV to 5 GeV atradic

s = 13 TeV and finally 10 GeV atradics = 100 TeV

49

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

track pperp values 2 lt pT1 lt 10 GeV) This indicates that the energy scaling of the UE modeling and inparticular the details of its transition between central and peripheral collisions is still not satisfactorilyunderstood

5 Conclusions and Exhortation

We have presented a reanalysis of the constraints on fragmentation in ee collisions and applied theresults to update the final-state fragmentation parameters in PYTHIA 8 We combine these parameterswith a tune to hadron-collider data using a new NNPDF 23 LO QCD+QED PDF set which has beenencoded so it is available as an internal PDF set in PYTHIA 8 independently of LHAPDF [112]

In this PDF set as well as in our tune the value of the strong coupling for hard-scattering matrixelements is fixed to be αs(MZ) = 013 consistent with other LO determinations of it For initial-and final-state radiation our tune uses the effective value αs(MZ) = 01365 The difference isconsistent with an effective translation between the MS and CMW schemes We note that alternative(LO NLO and NNLO) NNPDF 23 QCD+QED sets with αs(MZ) = 0119 are also available inthe code for people who want to check the impact of using a different αs(MZ) value andor higher-order PDF sets on hard-scattering events For the purpose of such studies we point out that it ispossible in PYTHIA 8 to preserve most of the features of the shower- and underlying-event tuningby changing only the PDF for the hard-scattering matrix elements leaving the PDF choice for theshower evolution and MPI framework unaltered (see the PYTHIA 8 HTML manualrsquos PDF sectionunder PDFuseHard)

The updated parameters are available as an option starting from PYTHIA 8185 by setting

Tuneee = 7 and Tunepp = 14

By no means do we claim that this should be regarded as the final word in tuning the PYTHIA 8Monte Carlo model First of all the model continues to evolve For instance developments foreseenfor the near future include updates of colour reconnections diffraction and the treatment of g rarr qqsplittings Any of these should in principle be accompanied by a reevaluation of the model constraints

Moreover despite the comprehensive view of collider data we have attempted to take in thisstudy there still remains several issues that were not addressed including initial-final interferenceand coherence effects [113 114] (probably more a modelling issue than a tuning one) reliable esti-mates of theoretical uncertainties [8 17 24 29 97 115] diffraction14 [74 116 117] and other colour-singlet phenomena such as onium production long-distance (eg forward-backward forward-centraland ldquoridgerdquo-type) correlations [88 118ndash123] B-hadron decays [124] and tuning in the presence ofmatrix-element matching at LO and NLO (see [21 29 115 125 126] for recent phenomenologi-cal studies) Especially in the latter context of matrix-element matching we expect that in manycases PYTHIA 8 will be used together with codes such as ALPGEN [127] MADGRAPH [128]aMCatNLO [129] or POWHEG [130] either using the matching algorithms of those programs them-selves or via any of PYTHIArsquos several internal (LHEF-based [131]) implementations of matchingschemes (POWHEG [85] CKKW-L [132ndash134] MLM [135 136] UMEPS [137] NL3 [138] UN-LOPS [139]) The impact of such corrections on MC tuning depends on the details of the matchingscheme (especially its treatment of unitarity) and there is in general a non-negligible possibility ofldquomis-tuningrdquo when combining a stand-alone tune with ME corrections A simple example illustrating

14In particular the constraints on fragmentation mainly come from SLD and LEP where the non-perturbative parametersare clearly defined at the shower cutoff scaleQhad whereas diffraction is dominated by soft physics for which the definitionof the effective hadronization scale is less clear The amount of MPI in hard diffractive events also requires tuning

38

this is the effective value of αs(MZ) which for a leading-order tune is typically of order 013 whilea consistent NLO correction scheme should be compatible with values closer to 012 [29] There isalso the question of the running order of αs The propagation of such changes from the level of hardmatrix elements through the shower and hadronization tuning process are still not fully explored andhence we advise users to perform simple cross-checks such as checking the distributions presented inthis paper before and after applying matrix-element corrections Parameters that appear on both sidesof the matching such as αs should also be checked for consistency [21]

We noted several issues concerning the ee data used to constrain the fragmentation modelling thatit would be good to resolve In particular we find some tensions between the identified-particle ratesextracted from 1) HEDPATA 2) Sec 46 of the PDG and 3) the Z boson summary table in the PDGas discussed in more detail in section 2 and concerning which we made some (subjective) decisionsto arrive at a set of hopefully self-consistent constraints for this work We also note that the overallprecision of the fragmentation constraints could likely be significantly improved by an FCC-ee typemachine such as Tera-Z a possibility we hope to see more fully explored in the context of future eeQCD phenomenology studies

We conclude that the new parameter set does improve significantly on the previous default valuesin several respects including better agreement with data on

1 the net strangeness fraction (has been increased by 10 reflected not only in improved kaonand hyperon yields but also in the Ds and Bs fractions)

2 the ultra-hard fragmentation tail (has been softened especially for leading baryons and for Dand B hadrons)

3 the pTZ spectrum (softened at low pTZ)

4 the minimum-bias charged multiplicity in the forward region (has increased by 10)

5 the underlying event at 7 TeV (is very slightly higher than before)

Some questions that remain open include the following We see a roughly 20 excess of verysoft kaons in both ee and pp environments cf figs 6 and 23 despite the overall kaon yields beingwell described and the overall baryon yields at LHC appear to be underestimated by at least 30despite good agreement at LEP The momentum spectra of heavier strange particles are also poorlyreproduced in particular at LHC It is interesting and exciting that some of the LHC spectra appearto be better described by allowing collective flow in a fraction of events (cf the EPOS model [140])though we believe the jury is still out on whether this accurately reflects the underlying physics Forinstance it has been argued that colour reconnections can mimick flow effects [90] and they may alsobe able to modify the yield of baryons if the creationdestruction of string junctions is allowed [141]We look forward to future discussions on these issues

We round off with an exhortation for follow-ups on this study to provide

bull Not only central tunes experiments and other user-end colleagues need more than central de-scriptions of data there is an increasing need for serious uncertainty estimates In the contextof tune variations it is important to keep in mind that the modelling uncertainties are often in-trinsically non-universal Therefore the constraints obtained by considering data uncertaintiesonly (eg in the spirit of PROFESSORrsquos eigentunes [17]) can at most constitute a lower boundon the theoretical uncertainty (similarly to the case for PDFs) A serious uncertainty estimateincludes some systematic modelling variation irrespectively of and in addition to what data

39

allows (eg in the spirit of the Perugia set of tunes for PYTHIA 6 [8]) We therefore hope thefuture will see more elaborate combinations of data- and theory-driven approaches to systematictune uncertainties

bull Not only global tunes the power of MC models lies in their ability to simultaneously describea large variety of data hence we do not mean to imply that one should give up on universalityand tune to increasingly specific corners of phase space disregarding (or de-emphasizing withlower weights) all others However as proposed in [97] one can obtain useful explicit tests ofthe universality of the underlying physics model by performing independent tunes on separateldquophysics windowsrdquo say in the forward vs central regions for different event-selection crite-ria at different collider energies or even for different collider types In this connection justmaking one global ldquobest-fitrdquo tune may obscure tensions between the descriptions of differentcomplementary data sets By performing independent tunes to each data set separately andchecking the degree of universality of the resulting parameters one obtains a powerful crosscheck on the underlying physics model If all sets produce the same or similar parameters thenuniversality is OK hence a global tune makes very good sense and the remaining uncertain-ties can presumably be reliably estimated from data alone If instead some data sets resultin significantly different tune parameters one has a powerful indication that the universality ofthe underlying modeling is breaking down which can lead to several productive actions 1) itcan be taken into account in the context of uncertainty variations 2) the nature of the data setsfor which non-universal tune parameters are obtained can implicitly indicate the nature of theproblem leading to more robust conclusions about the underlying model than merely whether atune cancannot fit the data and 3) the observations can be communicated to the model authorsin a more unambiguous way hopefully resulting in a speedier cycle of model improvements

We hope that the Monash 2013 tune parameters may serve as a useful starting point for phe-nomenology studies and for future PYTHIA 8 tuning efforts

Acknowledgments

We thank S Mrenna M Ritzmann and T Sjostrand for comments on the manuscript and L de Nooijfor pointing us to the ALICE Klowast and φ measurements [142] and to the ATLAS φ measurementsin [143] The work of J R is supported by an STFC Rutherford Fellowship STK0052271 Thiswork was supported in part by the Research Executive Agency (REA) of the European Commissionunder the Grant Agreements PITN-GA-2012-315877 (MCnet)

A Monash 2013 Tune Parameters

In tabs 3 ndash 7 we list the FSR fragmentation parameters for the Monash tune of PYTHIA Forreference we compare them to the current default parameters

40

FSR Parameters Monash 13 (Default) CommentTimeShoweralphaSvalue = 01365 = 01383 Effective alphaS(mZ) valueTimeShoweralphaSorder = 1 = 1 Running orderTimeShoweralphaSuseCMW = off = off Translation from MS to CMWTimeShowerpTmin = 050 = 040 Cutoff for QCD radiationTimeShowerpTminChgQ = 050 = 040 Cutoff for QED radiationTimeShowerphiPolAsym = on = on Asymmetric azimuth distributions

Table 3 Final-state radiation (FSR) parameters

HAD Parameters Monash 13 (Default) Comment String breaks pT and z distributionsStringPTsigma = 0335 = 0304 Soft pT in string breaks (in GeV)StringPTenhancedFraction = 001 = 001 Fraction of breakups with enhanced pTStringPTenhancedWidth = 20 = 20 Enhancement factorStringZaLund = 068 = 03 Lund FF a (hard fragmentation supp)StringZbLund = 098 = 08 Lund FF b (soft fragmentation supp)StringZaExtraSquark = 00 = 00 Extra a when picking up an s quarkStringZaExtraDiquark = 097 = 050 Extra a when picking up a diquarkStringZrFactC = 132 = 100 Lund-Bowler c-quark parameterStringZrFactB = 0855 = 067 Lund-Bowler b-quark parameter Flavour composition mesonsStringFlavProbStoUD = 0217 = 019 Strangeness-to-UD ratioStringFlavmesonUDvector = 05 = 062 Light-flavour vector suppressionStringFlavmesonSvector = 055 = 0725 Strange vector suppressionStringFlavmesonCvector = 088 = 106 Charm vector suppressionStringFlavmesonBvector = 22 = 30 Bottom vector suppressionStringFlavetaSup = 060 = 063 Suppression of eta mesonsStringFlavetaPrimeSup = 012 = 012 Suppression of etarsquo mesons Flavour composition baryonsStringFlavprobQQtoQ = 0081 = 009 Diquark rate (for baryon production)StringFlavprobSQtoQQ = 0915 = 1000 Strange-diquark suppressionStringFlavprobQQ1toQQ0 = 00275 = 0027 Vector diquark suppressionStringFlavdecupletSup = 10 = 10 Spin-32 baryon suppressionStringFlavsuppressLeadingB = off = off Optional leading-baryon suppressionStringFlavpopcornSpair = 09 = 05 StringFlavpopcornSmeson = 05 = 05

Table 4 String-breaking parameters

PDF and ME Parameters Monash 13 (Default) CommentPDFpSet = 13 = 8 PDF set for the protonSigmaProcessalphaSvalue = 0130 0135 alphaS(MZ) for matrix elementsMultiPartonInteractionsalphaSvalue = 0130 0135 alphaS(MZ) for MPI

Table 5 Parton-distribution (PDF) and Matrix-Element (ME) parameters

41

ISR Parameters Monash 13 (Default) CommentSpaceShoweralphaSvalue = 01365 = 0137 Effective alphaS(mZ) valueSpaceShoweralphaSorder = 1 = 1 Running orderSpaceShoweralphaSuseCMW = off = off Translation from MS to CMWSpaceShowersamePTasMPI = off = off ISR cutoff typeSpaceShowerpT0Ref = 20 = 20 ISR pT0 cutoffSpaceShowerecmRef = 70000 = 18000 ISR pT0 reference ECM scaleSpaceShowerecmPow = 00 = 00 ISR pT0 scaling powerSpaceShowerrapidityOrder = on = on Approx coherence via y-orderingSpaceShowerphiPolAsym = on = on Azimuth asymmetries from gluon polSpaceShowerphiIntAsym = on = on Azimuth asymmetries from interferenceTimeShowerdampenBeamRecoil = on = on Recoil dampening in final-initial dipolesBeamRemnantsprimordialKTsoft = 09 = 05 Primordial kT for soft procsBeamRemnantsprimordialKThard = 18 = 20 Primordial kT for hard procsBeamRemnantshalfScaleForKT = 15 = 10 Primordial kT softhard boundaryBeamRemnantshalfMassForKT = 10 = 10 Primordial kT softhard mass boundary

Table 6 Initial-state radiation (ISR) and primordial-kT parameters

MPI Parameters Monash 13 (Default) CommentMultipartonInteractionspT0Ref = 228 = 2085 MPI pT0 IR regularization scaleMultipartonInteractionsecmRef = 70000 = 18000 MPI pT0 reference ECM scaleMultipartonInteractionsecmPow = 0215 = 019 MPI pT0 scaling powerMultipartonInteractionsbProfile = 3 = 3 Transverse matter overlap profileMultipartonInteractionsexpPow = 185 = 20 Shape parameterBeamRemnantsreconnectRange = 18 = 15 Colour ReconnectionsSigmaTotalzeroAXB = on = on Carried over from 4CSigmaDiffractivedampen = on = on Carried over from 4CSigmaDiffractivemaxXB = 650 = 650 Carried over from 4CSigmaDiffractivemaxAX = 650 = 650 Carried over from 4CSigmaDiffractivemaxXX = 650 = 650 Carried over from 4CDiffractionlargeMassSuppress = 40 = 20 High-mass diffraction suppression power

Table 7 Multi-Parton-Interaction (MPI) Colour-Reconnection (CR) and Diffractive parameters

42

B Additional Plots

B1 LEP Event-Shape Distributions

To keep the main body of the paper as uncluttered as possible we collect various plots of event-shapedistributions in figs 28 and 29 separated into light-flavour and b-tagged events on the left and rightrespectively

The experimental results come from the L3 experiment [26] However since the data points areonly available with 3-digit precision some of the least populated bins contain artifacts like uncertain-ties being reported as exactly zero etc Thus we have been forced to make the following modificationsto the data set

The statistical uncertainty was reported as zero for the last two bins of light-flavour Thrust as wellas for the last bin of the C D and BT parameters Uncertainties lt 10minus3 were derived using anapproximate statistical scaling based on the contents and uncertainties of the other bins Likewise thesystematical uncertainty for the last bin of Thrust was given as zero which we have replaced by theupper limit 5times 10minus4 The last bin of BT quoted a measured y value of zero removed in this study

For the heavy-flavour tagged event shapes more significant rounding issues were present Thusseveral of the first and last bins of each distribution either quoted zero (statistical andor systematic)uncertainties or ones with only a single digit of precision (such as 0001 for which the rounding errorcould be up to sim 50) We have interpreted all such values conservatively inserting by hand a fourthdigit on the uncertainties as large as could be consistent with rounding

B2 Additional Particle Spectra

In addition to the K and Λ spectra shown in the main body of the paper (sections 22 and 35) wehere include for reference the x spectra of φ mesons protons and Ξ baryons at LEP in figs 30 and 31the pT spectrum of Klowast mesons and the rapidity and pT spectra of φ mesons at LHC in fig 32 (withabsolute normalizations to the number of inelastic events) and the rapidity spectrum of Ξ baryons atLHC in fig 33

The transverse-momentum spectra of Klowast and φ mesons in fig 32 exhibit the same qualitativebehaviour as that of the KS mesons (fig 23) namely an excess at very soft momenta below sim 500MeV and a depletion at slightly higher momenta between 1 and 2 GeV As discussed in section 35we did not find a way to remove these undesirable features in the Monash 2013 tune suggesting thatthis is an issue that further theoretical modeling will be needed to resolve

The rapidity spectrum of Ξ baryons fig 33 shows that although the Monash tune does producemore Ξ baryons overall (as expected also from the relative increase of Ξ production at LEP cf fig 5)there is still a significant deficit of Ξ baryons at the LHC almost a factor 2 compared with the dataThis is qualitatively similar to the situation for Λ baryons (fig 24) discussed in section 35 Sincenew physics mechanisms may be required to ldquoexplainrdquo the missing baryons we conclude that furthermeasurements and better precision on both the Λ and Ξ sectors (in addition to any other baryonsthat may be accessible) would be highly interesting More explicit recommendations can be found insections 35 and 5

43

0 01 02 03 04

d(1

-T)

σ d

σ1

-310

-210

-110

1

10

2101-Thrust (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn03

01plusmn04

02plusmn05

V I

N C

I A

R O

O T

1-T (udsc)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

d(1

-T)

σ dσ

1

-310

-210

-110

1

10

2101-T (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn13

02plusmn12

02plusmn14

V I

N C

I A

R O

O T

1-T (b)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210

310C Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn03

00plusmn04

01plusmn04

V I

N C

I A

R O

O T

C0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210 C parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn17

01plusmn24

01plusmn27

V I

N C

I A

R O

O T

C (b)0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn06

01plusmn06

V I

N C

I A

R O

O T

D0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn24

02plusmn21

02plusmn26

V I

N C

I A

R O

O T

D (b)0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

Figure 28 Hadronic Z decays atradics = 912 GeV The T C and D event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

44

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn02

01plusmn03

01plusmn04

V I

N C

I A

R O

O T

WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn05

01plusmn12

01plusmn17

V I

N C

I A

R O

O T

(b)WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn02

00plusmn02

01plusmn03

V I

N C

I A

R O

O T

TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

04plusmn24

08plusmn49

08plusmn55

V I

N C

I A

R O

O T

(b)TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

Figure 29 Hadronic Z decays atradics = 912 GeV The BW and BT event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

45

0 02 04 06 08 1

dx

φgt

dn

φ1

ltn

-210

-110

1

10 )φx(

Pythia 8183Data from ALEPH_1996_S3486095d40-x01-y01

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn37

02plusmn53

03plusmn62

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

0608

112141618

Figure 30 Hadronic Z decays atradics = 912 GeV φ meson x spectrum

-5 -4 -3 -2 -1 0

dx

pgt

dn

p1

ltn

-410

-310

-210

-110

1

10

210) (Combined)px(p+

Pythia 8183Data from Zeit Phys C66 (1995) 355 PhysRev D59 (1998) 052001

ALEPH+SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn08

00plusmn09

00plusmn08

V I

N C

I A

R O

O T

px-5 -4 -3 -2 -1 0

The

ory

Dat

a

06

08

1

12

14

0 02 04

dx

Ξgt

dn

Ξ1

ltn

-110

1

10

)plusmnΞx(

Pythia 8183Data from Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn11

02plusmn13

02plusmn14

V I

N C

I A

R O

O T

Ex0 02 04

The

ory

Dat

a

06

08

1

12

14

Figure 31 Hadronic Z decays atradics = 912 GeV pplusmn and Ξplusmn x spectra

46

0 2 4 6

Td

pK

d

nIN

EL

1N

-510

-410

-310

-210

-110

(INEL |y|lt05)T

p0K

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn35

01plusmn26

01plusmn29

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 2 4 6

Td

pφ

dn

INE

L1

N-510

-410

-310

-210

-110

gt04)T

(INEL |y|lt05 pT

pφ

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn88

03plusmn84

04plusmn173

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

)dy

[mb]

-K

+K

rarrφ(σd

0

05

1

15

2 Rapidity (INEL ATLAS cuts)φ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn14

01plusmn19

01plusmn34

V I

N C

I A

R O

O T

pp 7000 GeV

|y|0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

06 08 1 12

[mb

GeV

]φ

T)

dp-

K+

Krarrφ(

σd

0

05

1

15

2

25 (INEL ATLAS cuts)

T pφ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn21

01plusmn30

02plusmn53

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p06 08 1 12

The

ory

Dat

a

06

08

1

12

14

Figure 32 pp collisions at 7 TeV Top row Klowast and φ pperp spectra compared with ALICE data [142]Bottom row φ rapidity and pperp spectrum compared with ATLAS data [143] The ATLAS cuts areφrarr K+Kminus pperpφ isin [05 12] GeV |y(φ)| lt 08 pperpK gt 023 GeV |pK | lt 08 GeV

47

0 05 1 15 2

dygt

Ξ lt

dnN

SD

1N

0

001

002

003

004)d|y|gt (NSD)Ξltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn89

01plusmn129

01plusmn192

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

0

05

1

15

2

Figure 33 pp collisions at 7 TeV Ξminus rapidity spectrum compared with CMS data [99]

48

B3 Energy Scaling of σ2rarr2(pTmin) vs σinel from 200 GeV to 100 TeV

In fig 34 we show the LO QCD 2rarr 2 cross section integrated above pTmin as a function of pTminin pp collisions at 4 different CM energies complementing and expanding on the 8-TeV CM energyshown in the main body of the paper We compare two different αs and PDF choices correspondingto those made in tunes Monash 13 (blue filled dots) and 4C (red open squares) respectively As areference for the total inelastic cross section at each energy we base ourselves on the best-fit curvein the TOTEM cross-section measurement paper [72] which in turn represents a fit produced by theCOMPETE collaboration [144] Uncertainties are rough conservative estimates based on the plot inthe TOTEM paper but they are in any case too small to significantly affect conclusions about the scaleat which the partonic cross section saturates the hadronic one

We observe that the pTmin value for which the LO QCD 2 rarr 2 partonic cross section formallybecomes equal to the total inelastic cross section (strongly suggesting that every event has at leastone such mini-jet pair) rises from values around 1 ndash 2 GeV at energies

radics lt 1 TeV to 5 GeV atradic

s = 13 TeV and finally 10 GeV atradics = 100 TeV

49

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

this is the effective value of αs(MZ) which for a leading-order tune is typically of order 013 whilea consistent NLO correction scheme should be compatible with values closer to 012 [29] There isalso the question of the running order of αs The propagation of such changes from the level of hardmatrix elements through the shower and hadronization tuning process are still not fully explored andhence we advise users to perform simple cross-checks such as checking the distributions presented inthis paper before and after applying matrix-element corrections Parameters that appear on both sidesof the matching such as αs should also be checked for consistency [21]

We noted several issues concerning the ee data used to constrain the fragmentation modelling thatit would be good to resolve In particular we find some tensions between the identified-particle ratesextracted from 1) HEDPATA 2) Sec 46 of the PDG and 3) the Z boson summary table in the PDGas discussed in more detail in section 2 and concerning which we made some (subjective) decisionsto arrive at a set of hopefully self-consistent constraints for this work We also note that the overallprecision of the fragmentation constraints could likely be significantly improved by an FCC-ee typemachine such as Tera-Z a possibility we hope to see more fully explored in the context of future eeQCD phenomenology studies

We conclude that the new parameter set does improve significantly on the previous default valuesin several respects including better agreement with data on

1 the net strangeness fraction (has been increased by 10 reflected not only in improved kaonand hyperon yields but also in the Ds and Bs fractions)

2 the ultra-hard fragmentation tail (has been softened especially for leading baryons and for Dand B hadrons)

3 the pTZ spectrum (softened at low pTZ)

4 the minimum-bias charged multiplicity in the forward region (has increased by 10)

5 the underlying event at 7 TeV (is very slightly higher than before)

Some questions that remain open include the following We see a roughly 20 excess of verysoft kaons in both ee and pp environments cf figs 6 and 23 despite the overall kaon yields beingwell described and the overall baryon yields at LHC appear to be underestimated by at least 30despite good agreement at LEP The momentum spectra of heavier strange particles are also poorlyreproduced in particular at LHC It is interesting and exciting that some of the LHC spectra appearto be better described by allowing collective flow in a fraction of events (cf the EPOS model [140])though we believe the jury is still out on whether this accurately reflects the underlying physics Forinstance it has been argued that colour reconnections can mimick flow effects [90] and they may alsobe able to modify the yield of baryons if the creationdestruction of string junctions is allowed [141]We look forward to future discussions on these issues

We round off with an exhortation for follow-ups on this study to provide

bull Not only central tunes experiments and other user-end colleagues need more than central de-scriptions of data there is an increasing need for serious uncertainty estimates In the contextof tune variations it is important to keep in mind that the modelling uncertainties are often in-trinsically non-universal Therefore the constraints obtained by considering data uncertaintiesonly (eg in the spirit of PROFESSORrsquos eigentunes [17]) can at most constitute a lower boundon the theoretical uncertainty (similarly to the case for PDFs) A serious uncertainty estimateincludes some systematic modelling variation irrespectively of and in addition to what data

39

allows (eg in the spirit of the Perugia set of tunes for PYTHIA 6 [8]) We therefore hope thefuture will see more elaborate combinations of data- and theory-driven approaches to systematictune uncertainties

bull Not only global tunes the power of MC models lies in their ability to simultaneously describea large variety of data hence we do not mean to imply that one should give up on universalityand tune to increasingly specific corners of phase space disregarding (or de-emphasizing withlower weights) all others However as proposed in [97] one can obtain useful explicit tests ofthe universality of the underlying physics model by performing independent tunes on separateldquophysics windowsrdquo say in the forward vs central regions for different event-selection crite-ria at different collider energies or even for different collider types In this connection justmaking one global ldquobest-fitrdquo tune may obscure tensions between the descriptions of differentcomplementary data sets By performing independent tunes to each data set separately andchecking the degree of universality of the resulting parameters one obtains a powerful crosscheck on the underlying physics model If all sets produce the same or similar parameters thenuniversality is OK hence a global tune makes very good sense and the remaining uncertain-ties can presumably be reliably estimated from data alone If instead some data sets resultin significantly different tune parameters one has a powerful indication that the universality ofthe underlying modeling is breaking down which can lead to several productive actions 1) itcan be taken into account in the context of uncertainty variations 2) the nature of the data setsfor which non-universal tune parameters are obtained can implicitly indicate the nature of theproblem leading to more robust conclusions about the underlying model than merely whether atune cancannot fit the data and 3) the observations can be communicated to the model authorsin a more unambiguous way hopefully resulting in a speedier cycle of model improvements

We hope that the Monash 2013 tune parameters may serve as a useful starting point for phe-nomenology studies and for future PYTHIA 8 tuning efforts

Acknowledgments

We thank S Mrenna M Ritzmann and T Sjostrand for comments on the manuscript and L de Nooijfor pointing us to the ALICE Klowast and φ measurements [142] and to the ATLAS φ measurementsin [143] The work of J R is supported by an STFC Rutherford Fellowship STK0052271 Thiswork was supported in part by the Research Executive Agency (REA) of the European Commissionunder the Grant Agreements PITN-GA-2012-315877 (MCnet)

A Monash 2013 Tune Parameters

In tabs 3 ndash 7 we list the FSR fragmentation parameters for the Monash tune of PYTHIA Forreference we compare them to the current default parameters

40

FSR Parameters Monash 13 (Default) CommentTimeShoweralphaSvalue = 01365 = 01383 Effective alphaS(mZ) valueTimeShoweralphaSorder = 1 = 1 Running orderTimeShoweralphaSuseCMW = off = off Translation from MS to CMWTimeShowerpTmin = 050 = 040 Cutoff for QCD radiationTimeShowerpTminChgQ = 050 = 040 Cutoff for QED radiationTimeShowerphiPolAsym = on = on Asymmetric azimuth distributions

Table 3 Final-state radiation (FSR) parameters

HAD Parameters Monash 13 (Default) Comment String breaks pT and z distributionsStringPTsigma = 0335 = 0304 Soft pT in string breaks (in GeV)StringPTenhancedFraction = 001 = 001 Fraction of breakups with enhanced pTStringPTenhancedWidth = 20 = 20 Enhancement factorStringZaLund = 068 = 03 Lund FF a (hard fragmentation supp)StringZbLund = 098 = 08 Lund FF b (soft fragmentation supp)StringZaExtraSquark = 00 = 00 Extra a when picking up an s quarkStringZaExtraDiquark = 097 = 050 Extra a when picking up a diquarkStringZrFactC = 132 = 100 Lund-Bowler c-quark parameterStringZrFactB = 0855 = 067 Lund-Bowler b-quark parameter Flavour composition mesonsStringFlavProbStoUD = 0217 = 019 Strangeness-to-UD ratioStringFlavmesonUDvector = 05 = 062 Light-flavour vector suppressionStringFlavmesonSvector = 055 = 0725 Strange vector suppressionStringFlavmesonCvector = 088 = 106 Charm vector suppressionStringFlavmesonBvector = 22 = 30 Bottom vector suppressionStringFlavetaSup = 060 = 063 Suppression of eta mesonsStringFlavetaPrimeSup = 012 = 012 Suppression of etarsquo mesons Flavour composition baryonsStringFlavprobQQtoQ = 0081 = 009 Diquark rate (for baryon production)StringFlavprobSQtoQQ = 0915 = 1000 Strange-diquark suppressionStringFlavprobQQ1toQQ0 = 00275 = 0027 Vector diquark suppressionStringFlavdecupletSup = 10 = 10 Spin-32 baryon suppressionStringFlavsuppressLeadingB = off = off Optional leading-baryon suppressionStringFlavpopcornSpair = 09 = 05 StringFlavpopcornSmeson = 05 = 05

Table 4 String-breaking parameters

PDF and ME Parameters Monash 13 (Default) CommentPDFpSet = 13 = 8 PDF set for the protonSigmaProcessalphaSvalue = 0130 0135 alphaS(MZ) for matrix elementsMultiPartonInteractionsalphaSvalue = 0130 0135 alphaS(MZ) for MPI

Table 5 Parton-distribution (PDF) and Matrix-Element (ME) parameters

41

ISR Parameters Monash 13 (Default) CommentSpaceShoweralphaSvalue = 01365 = 0137 Effective alphaS(mZ) valueSpaceShoweralphaSorder = 1 = 1 Running orderSpaceShoweralphaSuseCMW = off = off Translation from MS to CMWSpaceShowersamePTasMPI = off = off ISR cutoff typeSpaceShowerpT0Ref = 20 = 20 ISR pT0 cutoffSpaceShowerecmRef = 70000 = 18000 ISR pT0 reference ECM scaleSpaceShowerecmPow = 00 = 00 ISR pT0 scaling powerSpaceShowerrapidityOrder = on = on Approx coherence via y-orderingSpaceShowerphiPolAsym = on = on Azimuth asymmetries from gluon polSpaceShowerphiIntAsym = on = on Azimuth asymmetries from interferenceTimeShowerdampenBeamRecoil = on = on Recoil dampening in final-initial dipolesBeamRemnantsprimordialKTsoft = 09 = 05 Primordial kT for soft procsBeamRemnantsprimordialKThard = 18 = 20 Primordial kT for hard procsBeamRemnantshalfScaleForKT = 15 = 10 Primordial kT softhard boundaryBeamRemnantshalfMassForKT = 10 = 10 Primordial kT softhard mass boundary

Table 6 Initial-state radiation (ISR) and primordial-kT parameters

MPI Parameters Monash 13 (Default) CommentMultipartonInteractionspT0Ref = 228 = 2085 MPI pT0 IR regularization scaleMultipartonInteractionsecmRef = 70000 = 18000 MPI pT0 reference ECM scaleMultipartonInteractionsecmPow = 0215 = 019 MPI pT0 scaling powerMultipartonInteractionsbProfile = 3 = 3 Transverse matter overlap profileMultipartonInteractionsexpPow = 185 = 20 Shape parameterBeamRemnantsreconnectRange = 18 = 15 Colour ReconnectionsSigmaTotalzeroAXB = on = on Carried over from 4CSigmaDiffractivedampen = on = on Carried over from 4CSigmaDiffractivemaxXB = 650 = 650 Carried over from 4CSigmaDiffractivemaxAX = 650 = 650 Carried over from 4CSigmaDiffractivemaxXX = 650 = 650 Carried over from 4CDiffractionlargeMassSuppress = 40 = 20 High-mass diffraction suppression power

Table 7 Multi-Parton-Interaction (MPI) Colour-Reconnection (CR) and Diffractive parameters

42

B Additional Plots

B1 LEP Event-Shape Distributions

To keep the main body of the paper as uncluttered as possible we collect various plots of event-shapedistributions in figs 28 and 29 separated into light-flavour and b-tagged events on the left and rightrespectively

The experimental results come from the L3 experiment [26] However since the data points areonly available with 3-digit precision some of the least populated bins contain artifacts like uncertain-ties being reported as exactly zero etc Thus we have been forced to make the following modificationsto the data set

The statistical uncertainty was reported as zero for the last two bins of light-flavour Thrust as wellas for the last bin of the C D and BT parameters Uncertainties lt 10minus3 were derived using anapproximate statistical scaling based on the contents and uncertainties of the other bins Likewise thesystematical uncertainty for the last bin of Thrust was given as zero which we have replaced by theupper limit 5times 10minus4 The last bin of BT quoted a measured y value of zero removed in this study

For the heavy-flavour tagged event shapes more significant rounding issues were present Thusseveral of the first and last bins of each distribution either quoted zero (statistical andor systematic)uncertainties or ones with only a single digit of precision (such as 0001 for which the rounding errorcould be up to sim 50) We have interpreted all such values conservatively inserting by hand a fourthdigit on the uncertainties as large as could be consistent with rounding

B2 Additional Particle Spectra

In addition to the K and Λ spectra shown in the main body of the paper (sections 22 and 35) wehere include for reference the x spectra of φ mesons protons and Ξ baryons at LEP in figs 30 and 31the pT spectrum of Klowast mesons and the rapidity and pT spectra of φ mesons at LHC in fig 32 (withabsolute normalizations to the number of inelastic events) and the rapidity spectrum of Ξ baryons atLHC in fig 33

The transverse-momentum spectra of Klowast and φ mesons in fig 32 exhibit the same qualitativebehaviour as that of the KS mesons (fig 23) namely an excess at very soft momenta below sim 500MeV and a depletion at slightly higher momenta between 1 and 2 GeV As discussed in section 35we did not find a way to remove these undesirable features in the Monash 2013 tune suggesting thatthis is an issue that further theoretical modeling will be needed to resolve

The rapidity spectrum of Ξ baryons fig 33 shows that although the Monash tune does producemore Ξ baryons overall (as expected also from the relative increase of Ξ production at LEP cf fig 5)there is still a significant deficit of Ξ baryons at the LHC almost a factor 2 compared with the dataThis is qualitatively similar to the situation for Λ baryons (fig 24) discussed in section 35 Sincenew physics mechanisms may be required to ldquoexplainrdquo the missing baryons we conclude that furthermeasurements and better precision on both the Λ and Ξ sectors (in addition to any other baryonsthat may be accessible) would be highly interesting More explicit recommendations can be found insections 35 and 5

43

0 01 02 03 04

d(1

-T)

σ d

σ1

-310

-210

-110

1

10

2101-Thrust (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn03

01plusmn04

02plusmn05

V I

N C

I A

R O

O T

1-T (udsc)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

d(1

-T)

σ dσ

1

-310

-210

-110

1

10

2101-T (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn13

02plusmn12

02plusmn14

V I

N C

I A

R O

O T

1-T (b)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210

310C Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn03

00plusmn04

01plusmn04

V I

N C

I A

R O

O T

C0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210 C parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn17

01plusmn24

01plusmn27

V I

N C

I A

R O

O T

C (b)0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn06

01plusmn06

V I

N C

I A

R O

O T

D0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn24

02plusmn21

02plusmn26

V I

N C

I A

R O

O T

D (b)0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

Figure 28 Hadronic Z decays atradics = 912 GeV The T C and D event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

44

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn02

01plusmn03

01plusmn04

V I

N C

I A

R O

O T

WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn05

01plusmn12

01plusmn17

V I

N C

I A

R O

O T

(b)WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn02

00plusmn02

01plusmn03

V I

N C

I A

R O

O T

TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

04plusmn24

08plusmn49

08plusmn55

V I

N C

I A

R O

O T

(b)TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

Figure 29 Hadronic Z decays atradics = 912 GeV The BW and BT event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

45

0 02 04 06 08 1

dx

φgt

dn

φ1

ltn

-210

-110

1

10 )φx(

Pythia 8183Data from ALEPH_1996_S3486095d40-x01-y01

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn37

02plusmn53

03plusmn62

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

0608

112141618

Figure 30 Hadronic Z decays atradics = 912 GeV φ meson x spectrum

-5 -4 -3 -2 -1 0

dx

pgt

dn

p1

ltn

-410

-310

-210

-110

1

10

210) (Combined)px(p+

Pythia 8183Data from Zeit Phys C66 (1995) 355 PhysRev D59 (1998) 052001

ALEPH+SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn08

00plusmn09

00plusmn08

V I

N C

I A

R O

O T

px-5 -4 -3 -2 -1 0

The

ory

Dat

a

06

08

1

12

14

0 02 04

dx

Ξgt

dn

Ξ1

ltn

-110

1

10

)plusmnΞx(

Pythia 8183Data from Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn11

02plusmn13

02plusmn14

V I

N C

I A

R O

O T

Ex0 02 04

The

ory

Dat

a

06

08

1

12

14

Figure 31 Hadronic Z decays atradics = 912 GeV pplusmn and Ξplusmn x spectra

46

0 2 4 6

Td

pK

d

nIN

EL

1N

-510

-410

-310

-210

-110

(INEL |y|lt05)T

p0K

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn35

01plusmn26

01plusmn29

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 2 4 6

Td

pφ

dn

INE

L1

N-510

-410

-310

-210

-110

gt04)T

(INEL |y|lt05 pT

pφ

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn88

03plusmn84

04plusmn173

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

)dy

[mb]

-K

+K

rarrφ(σd

0

05

1

15

2 Rapidity (INEL ATLAS cuts)φ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn14

01plusmn19

01plusmn34

V I

N C

I A

R O

O T

pp 7000 GeV

|y|0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

06 08 1 12

[mb

GeV

]φ

T)

dp-

K+

Krarrφ(

σd

0

05

1

15

2

25 (INEL ATLAS cuts)

T pφ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn21

01plusmn30

02plusmn53

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p06 08 1 12

The

ory

Dat

a

06

08

1

12

14

Figure 32 pp collisions at 7 TeV Top row Klowast and φ pperp spectra compared with ALICE data [142]Bottom row φ rapidity and pperp spectrum compared with ATLAS data [143] The ATLAS cuts areφrarr K+Kminus pperpφ isin [05 12] GeV |y(φ)| lt 08 pperpK gt 023 GeV |pK | lt 08 GeV

47

0 05 1 15 2

dygt

Ξ lt

dnN

SD

1N

0

001

002

003

004)d|y|gt (NSD)Ξltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn89

01plusmn129

01plusmn192

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

0

05

1

15

2

Figure 33 pp collisions at 7 TeV Ξminus rapidity spectrum compared with CMS data [99]

48

B3 Energy Scaling of σ2rarr2(pTmin) vs σinel from 200 GeV to 100 TeV

In fig 34 we show the LO QCD 2rarr 2 cross section integrated above pTmin as a function of pTminin pp collisions at 4 different CM energies complementing and expanding on the 8-TeV CM energyshown in the main body of the paper We compare two different αs and PDF choices correspondingto those made in tunes Monash 13 (blue filled dots) and 4C (red open squares) respectively As areference for the total inelastic cross section at each energy we base ourselves on the best-fit curvein the TOTEM cross-section measurement paper [72] which in turn represents a fit produced by theCOMPETE collaboration [144] Uncertainties are rough conservative estimates based on the plot inthe TOTEM paper but they are in any case too small to significantly affect conclusions about the scaleat which the partonic cross section saturates the hadronic one

We observe that the pTmin value for which the LO QCD 2 rarr 2 partonic cross section formallybecomes equal to the total inelastic cross section (strongly suggesting that every event has at leastone such mini-jet pair) rises from values around 1 ndash 2 GeV at energies

radics lt 1 TeV to 5 GeV atradic

s = 13 TeV and finally 10 GeV atradics = 100 TeV

49

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

allows (eg in the spirit of the Perugia set of tunes for PYTHIA 6 [8]) We therefore hope thefuture will see more elaborate combinations of data- and theory-driven approaches to systematictune uncertainties

bull Not only global tunes the power of MC models lies in their ability to simultaneously describea large variety of data hence we do not mean to imply that one should give up on universalityand tune to increasingly specific corners of phase space disregarding (or de-emphasizing withlower weights) all others However as proposed in [97] one can obtain useful explicit tests ofthe universality of the underlying physics model by performing independent tunes on separateldquophysics windowsrdquo say in the forward vs central regions for different event-selection crite-ria at different collider energies or even for different collider types In this connection justmaking one global ldquobest-fitrdquo tune may obscure tensions between the descriptions of differentcomplementary data sets By performing independent tunes to each data set separately andchecking the degree of universality of the resulting parameters one obtains a powerful crosscheck on the underlying physics model If all sets produce the same or similar parameters thenuniversality is OK hence a global tune makes very good sense and the remaining uncertain-ties can presumably be reliably estimated from data alone If instead some data sets resultin significantly different tune parameters one has a powerful indication that the universality ofthe underlying modeling is breaking down which can lead to several productive actions 1) itcan be taken into account in the context of uncertainty variations 2) the nature of the data setsfor which non-universal tune parameters are obtained can implicitly indicate the nature of theproblem leading to more robust conclusions about the underlying model than merely whether atune cancannot fit the data and 3) the observations can be communicated to the model authorsin a more unambiguous way hopefully resulting in a speedier cycle of model improvements

We hope that the Monash 2013 tune parameters may serve as a useful starting point for phe-nomenology studies and for future PYTHIA 8 tuning efforts

Acknowledgments

We thank S Mrenna M Ritzmann and T Sjostrand for comments on the manuscript and L de Nooijfor pointing us to the ALICE Klowast and φ measurements [142] and to the ATLAS φ measurementsin [143] The work of J R is supported by an STFC Rutherford Fellowship STK0052271 Thiswork was supported in part by the Research Executive Agency (REA) of the European Commissionunder the Grant Agreements PITN-GA-2012-315877 (MCnet)

A Monash 2013 Tune Parameters

In tabs 3 ndash 7 we list the FSR fragmentation parameters for the Monash tune of PYTHIA Forreference we compare them to the current default parameters

40

FSR Parameters Monash 13 (Default) CommentTimeShoweralphaSvalue = 01365 = 01383 Effective alphaS(mZ) valueTimeShoweralphaSorder = 1 = 1 Running orderTimeShoweralphaSuseCMW = off = off Translation from MS to CMWTimeShowerpTmin = 050 = 040 Cutoff for QCD radiationTimeShowerpTminChgQ = 050 = 040 Cutoff for QED radiationTimeShowerphiPolAsym = on = on Asymmetric azimuth distributions

Table 3 Final-state radiation (FSR) parameters

HAD Parameters Monash 13 (Default) Comment String breaks pT and z distributionsStringPTsigma = 0335 = 0304 Soft pT in string breaks (in GeV)StringPTenhancedFraction = 001 = 001 Fraction of breakups with enhanced pTStringPTenhancedWidth = 20 = 20 Enhancement factorStringZaLund = 068 = 03 Lund FF a (hard fragmentation supp)StringZbLund = 098 = 08 Lund FF b (soft fragmentation supp)StringZaExtraSquark = 00 = 00 Extra a when picking up an s quarkStringZaExtraDiquark = 097 = 050 Extra a when picking up a diquarkStringZrFactC = 132 = 100 Lund-Bowler c-quark parameterStringZrFactB = 0855 = 067 Lund-Bowler b-quark parameter Flavour composition mesonsStringFlavProbStoUD = 0217 = 019 Strangeness-to-UD ratioStringFlavmesonUDvector = 05 = 062 Light-flavour vector suppressionStringFlavmesonSvector = 055 = 0725 Strange vector suppressionStringFlavmesonCvector = 088 = 106 Charm vector suppressionStringFlavmesonBvector = 22 = 30 Bottom vector suppressionStringFlavetaSup = 060 = 063 Suppression of eta mesonsStringFlavetaPrimeSup = 012 = 012 Suppression of etarsquo mesons Flavour composition baryonsStringFlavprobQQtoQ = 0081 = 009 Diquark rate (for baryon production)StringFlavprobSQtoQQ = 0915 = 1000 Strange-diquark suppressionStringFlavprobQQ1toQQ0 = 00275 = 0027 Vector diquark suppressionStringFlavdecupletSup = 10 = 10 Spin-32 baryon suppressionStringFlavsuppressLeadingB = off = off Optional leading-baryon suppressionStringFlavpopcornSpair = 09 = 05 StringFlavpopcornSmeson = 05 = 05

Table 4 String-breaking parameters

PDF and ME Parameters Monash 13 (Default) CommentPDFpSet = 13 = 8 PDF set for the protonSigmaProcessalphaSvalue = 0130 0135 alphaS(MZ) for matrix elementsMultiPartonInteractionsalphaSvalue = 0130 0135 alphaS(MZ) for MPI

Table 5 Parton-distribution (PDF) and Matrix-Element (ME) parameters

41

ISR Parameters Monash 13 (Default) CommentSpaceShoweralphaSvalue = 01365 = 0137 Effective alphaS(mZ) valueSpaceShoweralphaSorder = 1 = 1 Running orderSpaceShoweralphaSuseCMW = off = off Translation from MS to CMWSpaceShowersamePTasMPI = off = off ISR cutoff typeSpaceShowerpT0Ref = 20 = 20 ISR pT0 cutoffSpaceShowerecmRef = 70000 = 18000 ISR pT0 reference ECM scaleSpaceShowerecmPow = 00 = 00 ISR pT0 scaling powerSpaceShowerrapidityOrder = on = on Approx coherence via y-orderingSpaceShowerphiPolAsym = on = on Azimuth asymmetries from gluon polSpaceShowerphiIntAsym = on = on Azimuth asymmetries from interferenceTimeShowerdampenBeamRecoil = on = on Recoil dampening in final-initial dipolesBeamRemnantsprimordialKTsoft = 09 = 05 Primordial kT for soft procsBeamRemnantsprimordialKThard = 18 = 20 Primordial kT for hard procsBeamRemnantshalfScaleForKT = 15 = 10 Primordial kT softhard boundaryBeamRemnantshalfMassForKT = 10 = 10 Primordial kT softhard mass boundary

Table 6 Initial-state radiation (ISR) and primordial-kT parameters

MPI Parameters Monash 13 (Default) CommentMultipartonInteractionspT0Ref = 228 = 2085 MPI pT0 IR regularization scaleMultipartonInteractionsecmRef = 70000 = 18000 MPI pT0 reference ECM scaleMultipartonInteractionsecmPow = 0215 = 019 MPI pT0 scaling powerMultipartonInteractionsbProfile = 3 = 3 Transverse matter overlap profileMultipartonInteractionsexpPow = 185 = 20 Shape parameterBeamRemnantsreconnectRange = 18 = 15 Colour ReconnectionsSigmaTotalzeroAXB = on = on Carried over from 4CSigmaDiffractivedampen = on = on Carried over from 4CSigmaDiffractivemaxXB = 650 = 650 Carried over from 4CSigmaDiffractivemaxAX = 650 = 650 Carried over from 4CSigmaDiffractivemaxXX = 650 = 650 Carried over from 4CDiffractionlargeMassSuppress = 40 = 20 High-mass diffraction suppression power

Table 7 Multi-Parton-Interaction (MPI) Colour-Reconnection (CR) and Diffractive parameters

42

B Additional Plots

B1 LEP Event-Shape Distributions

To keep the main body of the paper as uncluttered as possible we collect various plots of event-shapedistributions in figs 28 and 29 separated into light-flavour and b-tagged events on the left and rightrespectively

The experimental results come from the L3 experiment [26] However since the data points areonly available with 3-digit precision some of the least populated bins contain artifacts like uncertain-ties being reported as exactly zero etc Thus we have been forced to make the following modificationsto the data set

The statistical uncertainty was reported as zero for the last two bins of light-flavour Thrust as wellas for the last bin of the C D and BT parameters Uncertainties lt 10minus3 were derived using anapproximate statistical scaling based on the contents and uncertainties of the other bins Likewise thesystematical uncertainty for the last bin of Thrust was given as zero which we have replaced by theupper limit 5times 10minus4 The last bin of BT quoted a measured y value of zero removed in this study

For the heavy-flavour tagged event shapes more significant rounding issues were present Thusseveral of the first and last bins of each distribution either quoted zero (statistical andor systematic)uncertainties or ones with only a single digit of precision (such as 0001 for which the rounding errorcould be up to sim 50) We have interpreted all such values conservatively inserting by hand a fourthdigit on the uncertainties as large as could be consistent with rounding

B2 Additional Particle Spectra

In addition to the K and Λ spectra shown in the main body of the paper (sections 22 and 35) wehere include for reference the x spectra of φ mesons protons and Ξ baryons at LEP in figs 30 and 31the pT spectrum of Klowast mesons and the rapidity and pT spectra of φ mesons at LHC in fig 32 (withabsolute normalizations to the number of inelastic events) and the rapidity spectrum of Ξ baryons atLHC in fig 33

The transverse-momentum spectra of Klowast and φ mesons in fig 32 exhibit the same qualitativebehaviour as that of the KS mesons (fig 23) namely an excess at very soft momenta below sim 500MeV and a depletion at slightly higher momenta between 1 and 2 GeV As discussed in section 35we did not find a way to remove these undesirable features in the Monash 2013 tune suggesting thatthis is an issue that further theoretical modeling will be needed to resolve

The rapidity spectrum of Ξ baryons fig 33 shows that although the Monash tune does producemore Ξ baryons overall (as expected also from the relative increase of Ξ production at LEP cf fig 5)there is still a significant deficit of Ξ baryons at the LHC almost a factor 2 compared with the dataThis is qualitatively similar to the situation for Λ baryons (fig 24) discussed in section 35 Sincenew physics mechanisms may be required to ldquoexplainrdquo the missing baryons we conclude that furthermeasurements and better precision on both the Λ and Ξ sectors (in addition to any other baryonsthat may be accessible) would be highly interesting More explicit recommendations can be found insections 35 and 5

43

0 01 02 03 04

d(1

-T)

σ d

σ1

-310

-210

-110

1

10

2101-Thrust (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn03

01plusmn04

02plusmn05

V I

N C

I A

R O

O T

1-T (udsc)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

d(1

-T)

σ dσ

1

-310

-210

-110

1

10

2101-T (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn13

02plusmn12

02plusmn14

V I

N C

I A

R O

O T

1-T (b)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210

310C Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn03

00plusmn04

01plusmn04

V I

N C

I A

R O

O T

C0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210 C parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn17

01plusmn24

01plusmn27

V I

N C

I A

R O

O T

C (b)0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn06

01plusmn06

V I

N C

I A

R O

O T

D0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn24

02plusmn21

02plusmn26

V I

N C

I A

R O

O T

D (b)0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

Figure 28 Hadronic Z decays atradics = 912 GeV The T C and D event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

44

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn02

01plusmn03

01plusmn04

V I

N C

I A

R O

O T

WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn05

01plusmn12

01plusmn17

V I

N C

I A

R O

O T

(b)WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn02

00plusmn02

01plusmn03

V I

N C

I A

R O

O T

TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

04plusmn24

08plusmn49

08plusmn55

V I

N C

I A

R O

O T

(b)TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

Figure 29 Hadronic Z decays atradics = 912 GeV The BW and BT event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

45

0 02 04 06 08 1

dx

φgt

dn

φ1

ltn

-210

-110

1

10 )φx(

Pythia 8183Data from ALEPH_1996_S3486095d40-x01-y01

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn37

02plusmn53

03plusmn62

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

0608

112141618

Figure 30 Hadronic Z decays atradics = 912 GeV φ meson x spectrum

-5 -4 -3 -2 -1 0

dx

pgt

dn

p1

ltn

-410

-310

-210

-110

1

10

210) (Combined)px(p+

Pythia 8183Data from Zeit Phys C66 (1995) 355 PhysRev D59 (1998) 052001

ALEPH+SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn08

00plusmn09

00plusmn08

V I

N C

I A

R O

O T

px-5 -4 -3 -2 -1 0

The

ory

Dat

a

06

08

1

12

14

0 02 04

dx

Ξgt

dn

Ξ1

ltn

-110

1

10

)plusmnΞx(

Pythia 8183Data from Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn11

02plusmn13

02plusmn14

V I

N C

I A

R O

O T

Ex0 02 04

The

ory

Dat

a

06

08

1

12

14

Figure 31 Hadronic Z decays atradics = 912 GeV pplusmn and Ξplusmn x spectra

46

0 2 4 6

Td

pK

d

nIN

EL

1N

-510

-410

-310

-210

-110

(INEL |y|lt05)T

p0K

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn35

01plusmn26

01plusmn29

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 2 4 6

Td

pφ

dn

INE

L1

N-510

-410

-310

-210

-110

gt04)T

(INEL |y|lt05 pT

pφ

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn88

03plusmn84

04plusmn173

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

)dy

[mb]

-K

+K

rarrφ(σd

0

05

1

15

2 Rapidity (INEL ATLAS cuts)φ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn14

01plusmn19

01plusmn34

V I

N C

I A

R O

O T

pp 7000 GeV

|y|0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

06 08 1 12

[mb

GeV

]φ

T)

dp-

K+

Krarrφ(

σd

0

05

1

15

2

25 (INEL ATLAS cuts)

T pφ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn21

01plusmn30

02plusmn53

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p06 08 1 12

The

ory

Dat

a

06

08

1

12

14

Figure 32 pp collisions at 7 TeV Top row Klowast and φ pperp spectra compared with ALICE data [142]Bottom row φ rapidity and pperp spectrum compared with ATLAS data [143] The ATLAS cuts areφrarr K+Kminus pperpφ isin [05 12] GeV |y(φ)| lt 08 pperpK gt 023 GeV |pK | lt 08 GeV

47

0 05 1 15 2

dygt

Ξ lt

dnN

SD

1N

0

001

002

003

004)d|y|gt (NSD)Ξltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn89

01plusmn129

01plusmn192

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

0

05

1

15

2

Figure 33 pp collisions at 7 TeV Ξminus rapidity spectrum compared with CMS data [99]

48

B3 Energy Scaling of σ2rarr2(pTmin) vs σinel from 200 GeV to 100 TeV

In fig 34 we show the LO QCD 2rarr 2 cross section integrated above pTmin as a function of pTminin pp collisions at 4 different CM energies complementing and expanding on the 8-TeV CM energyshown in the main body of the paper We compare two different αs and PDF choices correspondingto those made in tunes Monash 13 (blue filled dots) and 4C (red open squares) respectively As areference for the total inelastic cross section at each energy we base ourselves on the best-fit curvein the TOTEM cross-section measurement paper [72] which in turn represents a fit produced by theCOMPETE collaboration [144] Uncertainties are rough conservative estimates based on the plot inthe TOTEM paper but they are in any case too small to significantly affect conclusions about the scaleat which the partonic cross section saturates the hadronic one

We observe that the pTmin value for which the LO QCD 2 rarr 2 partonic cross section formallybecomes equal to the total inelastic cross section (strongly suggesting that every event has at leastone such mini-jet pair) rises from values around 1 ndash 2 GeV at energies

radics lt 1 TeV to 5 GeV atradic

s = 13 TeV and finally 10 GeV atradics = 100 TeV

49

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

FSR Parameters Monash 13 (Default) CommentTimeShoweralphaSvalue = 01365 = 01383 Effective alphaS(mZ) valueTimeShoweralphaSorder = 1 = 1 Running orderTimeShoweralphaSuseCMW = off = off Translation from MS to CMWTimeShowerpTmin = 050 = 040 Cutoff for QCD radiationTimeShowerpTminChgQ = 050 = 040 Cutoff for QED radiationTimeShowerphiPolAsym = on = on Asymmetric azimuth distributions

Table 3 Final-state radiation (FSR) parameters

HAD Parameters Monash 13 (Default) Comment String breaks pT and z distributionsStringPTsigma = 0335 = 0304 Soft pT in string breaks (in GeV)StringPTenhancedFraction = 001 = 001 Fraction of breakups with enhanced pTStringPTenhancedWidth = 20 = 20 Enhancement factorStringZaLund = 068 = 03 Lund FF a (hard fragmentation supp)StringZbLund = 098 = 08 Lund FF b (soft fragmentation supp)StringZaExtraSquark = 00 = 00 Extra a when picking up an s quarkStringZaExtraDiquark = 097 = 050 Extra a when picking up a diquarkStringZrFactC = 132 = 100 Lund-Bowler c-quark parameterStringZrFactB = 0855 = 067 Lund-Bowler b-quark parameter Flavour composition mesonsStringFlavProbStoUD = 0217 = 019 Strangeness-to-UD ratioStringFlavmesonUDvector = 05 = 062 Light-flavour vector suppressionStringFlavmesonSvector = 055 = 0725 Strange vector suppressionStringFlavmesonCvector = 088 = 106 Charm vector suppressionStringFlavmesonBvector = 22 = 30 Bottom vector suppressionStringFlavetaSup = 060 = 063 Suppression of eta mesonsStringFlavetaPrimeSup = 012 = 012 Suppression of etarsquo mesons Flavour composition baryonsStringFlavprobQQtoQ = 0081 = 009 Diquark rate (for baryon production)StringFlavprobSQtoQQ = 0915 = 1000 Strange-diquark suppressionStringFlavprobQQ1toQQ0 = 00275 = 0027 Vector diquark suppressionStringFlavdecupletSup = 10 = 10 Spin-32 baryon suppressionStringFlavsuppressLeadingB = off = off Optional leading-baryon suppressionStringFlavpopcornSpair = 09 = 05 StringFlavpopcornSmeson = 05 = 05

Table 4 String-breaking parameters

PDF and ME Parameters Monash 13 (Default) CommentPDFpSet = 13 = 8 PDF set for the protonSigmaProcessalphaSvalue = 0130 0135 alphaS(MZ) for matrix elementsMultiPartonInteractionsalphaSvalue = 0130 0135 alphaS(MZ) for MPI

Table 5 Parton-distribution (PDF) and Matrix-Element (ME) parameters

41

ISR Parameters Monash 13 (Default) CommentSpaceShoweralphaSvalue = 01365 = 0137 Effective alphaS(mZ) valueSpaceShoweralphaSorder = 1 = 1 Running orderSpaceShoweralphaSuseCMW = off = off Translation from MS to CMWSpaceShowersamePTasMPI = off = off ISR cutoff typeSpaceShowerpT0Ref = 20 = 20 ISR pT0 cutoffSpaceShowerecmRef = 70000 = 18000 ISR pT0 reference ECM scaleSpaceShowerecmPow = 00 = 00 ISR pT0 scaling powerSpaceShowerrapidityOrder = on = on Approx coherence via y-orderingSpaceShowerphiPolAsym = on = on Azimuth asymmetries from gluon polSpaceShowerphiIntAsym = on = on Azimuth asymmetries from interferenceTimeShowerdampenBeamRecoil = on = on Recoil dampening in final-initial dipolesBeamRemnantsprimordialKTsoft = 09 = 05 Primordial kT for soft procsBeamRemnantsprimordialKThard = 18 = 20 Primordial kT for hard procsBeamRemnantshalfScaleForKT = 15 = 10 Primordial kT softhard boundaryBeamRemnantshalfMassForKT = 10 = 10 Primordial kT softhard mass boundary

Table 6 Initial-state radiation (ISR) and primordial-kT parameters

MPI Parameters Monash 13 (Default) CommentMultipartonInteractionspT0Ref = 228 = 2085 MPI pT0 IR regularization scaleMultipartonInteractionsecmRef = 70000 = 18000 MPI pT0 reference ECM scaleMultipartonInteractionsecmPow = 0215 = 019 MPI pT0 scaling powerMultipartonInteractionsbProfile = 3 = 3 Transverse matter overlap profileMultipartonInteractionsexpPow = 185 = 20 Shape parameterBeamRemnantsreconnectRange = 18 = 15 Colour ReconnectionsSigmaTotalzeroAXB = on = on Carried over from 4CSigmaDiffractivedampen = on = on Carried over from 4CSigmaDiffractivemaxXB = 650 = 650 Carried over from 4CSigmaDiffractivemaxAX = 650 = 650 Carried over from 4CSigmaDiffractivemaxXX = 650 = 650 Carried over from 4CDiffractionlargeMassSuppress = 40 = 20 High-mass diffraction suppression power

Table 7 Multi-Parton-Interaction (MPI) Colour-Reconnection (CR) and Diffractive parameters

42

B Additional Plots

B1 LEP Event-Shape Distributions

To keep the main body of the paper as uncluttered as possible we collect various plots of event-shapedistributions in figs 28 and 29 separated into light-flavour and b-tagged events on the left and rightrespectively

The experimental results come from the L3 experiment [26] However since the data points areonly available with 3-digit precision some of the least populated bins contain artifacts like uncertain-ties being reported as exactly zero etc Thus we have been forced to make the following modificationsto the data set

The statistical uncertainty was reported as zero for the last two bins of light-flavour Thrust as wellas for the last bin of the C D and BT parameters Uncertainties lt 10minus3 were derived using anapproximate statistical scaling based on the contents and uncertainties of the other bins Likewise thesystematical uncertainty for the last bin of Thrust was given as zero which we have replaced by theupper limit 5times 10minus4 The last bin of BT quoted a measured y value of zero removed in this study

For the heavy-flavour tagged event shapes more significant rounding issues were present Thusseveral of the first and last bins of each distribution either quoted zero (statistical andor systematic)uncertainties or ones with only a single digit of precision (such as 0001 for which the rounding errorcould be up to sim 50) We have interpreted all such values conservatively inserting by hand a fourthdigit on the uncertainties as large as could be consistent with rounding

B2 Additional Particle Spectra

In addition to the K and Λ spectra shown in the main body of the paper (sections 22 and 35) wehere include for reference the x spectra of φ mesons protons and Ξ baryons at LEP in figs 30 and 31the pT spectrum of Klowast mesons and the rapidity and pT spectra of φ mesons at LHC in fig 32 (withabsolute normalizations to the number of inelastic events) and the rapidity spectrum of Ξ baryons atLHC in fig 33

The transverse-momentum spectra of Klowast and φ mesons in fig 32 exhibit the same qualitativebehaviour as that of the KS mesons (fig 23) namely an excess at very soft momenta below sim 500MeV and a depletion at slightly higher momenta between 1 and 2 GeV As discussed in section 35we did not find a way to remove these undesirable features in the Monash 2013 tune suggesting thatthis is an issue that further theoretical modeling will be needed to resolve

The rapidity spectrum of Ξ baryons fig 33 shows that although the Monash tune does producemore Ξ baryons overall (as expected also from the relative increase of Ξ production at LEP cf fig 5)there is still a significant deficit of Ξ baryons at the LHC almost a factor 2 compared with the dataThis is qualitatively similar to the situation for Λ baryons (fig 24) discussed in section 35 Sincenew physics mechanisms may be required to ldquoexplainrdquo the missing baryons we conclude that furthermeasurements and better precision on both the Λ and Ξ sectors (in addition to any other baryonsthat may be accessible) would be highly interesting More explicit recommendations can be found insections 35 and 5

43

0 01 02 03 04

d(1

-T)

σ d

σ1

-310

-210

-110

1

10

2101-Thrust (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn03

01plusmn04

02plusmn05

V I

N C

I A

R O

O T

1-T (udsc)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

d(1

-T)

σ dσ

1

-310

-210

-110

1

10

2101-T (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn13

02plusmn12

02plusmn14

V I

N C

I A

R O

O T

1-T (b)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210

310C Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn03

00plusmn04

01plusmn04

V I

N C

I A

R O

O T

C0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210 C parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn17

01plusmn24

01plusmn27

V I

N C

I A

R O

O T

C (b)0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn06

01plusmn06

V I

N C

I A

R O

O T

D0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn24

02plusmn21

02plusmn26

V I

N C

I A

R O

O T

D (b)0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

Figure 28 Hadronic Z decays atradics = 912 GeV The T C and D event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

44

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn02

01plusmn03

01plusmn04

V I

N C

I A

R O

O T

WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn05

01plusmn12

01plusmn17

V I

N C

I A

R O

O T

(b)WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn02

00plusmn02

01plusmn03

V I

N C

I A

R O

O T

TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

04plusmn24

08plusmn49

08plusmn55

V I

N C

I A

R O

O T

(b)TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

Figure 29 Hadronic Z decays atradics = 912 GeV The BW and BT event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

45

0 02 04 06 08 1

dx

φgt

dn

φ1

ltn

-210

-110

1

10 )φx(

Pythia 8183Data from ALEPH_1996_S3486095d40-x01-y01

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn37

02plusmn53

03plusmn62

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

0608

112141618

Figure 30 Hadronic Z decays atradics = 912 GeV φ meson x spectrum

-5 -4 -3 -2 -1 0

dx

pgt

dn

p1

ltn

-410

-310

-210

-110

1

10

210) (Combined)px(p+

Pythia 8183Data from Zeit Phys C66 (1995) 355 PhysRev D59 (1998) 052001

ALEPH+SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn08

00plusmn09

00plusmn08

V I

N C

I A

R O

O T

px-5 -4 -3 -2 -1 0

The

ory

Dat

a

06

08

1

12

14

0 02 04

dx

Ξgt

dn

Ξ1

ltn

-110

1

10

)plusmnΞx(

Pythia 8183Data from Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn11

02plusmn13

02plusmn14

V I

N C

I A

R O

O T

Ex0 02 04

The

ory

Dat

a

06

08

1

12

14

Figure 31 Hadronic Z decays atradics = 912 GeV pplusmn and Ξplusmn x spectra

46

0 2 4 6

Td

pK

d

nIN

EL

1N

-510

-410

-310

-210

-110

(INEL |y|lt05)T

p0K

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn35

01plusmn26

01plusmn29

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 2 4 6

Td

pφ

dn

INE

L1

N-510

-410

-310

-210

-110

gt04)T

(INEL |y|lt05 pT

pφ

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn88

03plusmn84

04plusmn173

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

)dy

[mb]

-K

+K

rarrφ(σd

0

05

1

15

2 Rapidity (INEL ATLAS cuts)φ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn14

01plusmn19

01plusmn34

V I

N C

I A

R O

O T

pp 7000 GeV

|y|0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

06 08 1 12

[mb

GeV

]φ

T)

dp-

K+

Krarrφ(

σd

0

05

1

15

2

25 (INEL ATLAS cuts)

T pφ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn21

01plusmn30

02plusmn53

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p06 08 1 12

The

ory

Dat

a

06

08

1

12

14

Figure 32 pp collisions at 7 TeV Top row Klowast and φ pperp spectra compared with ALICE data [142]Bottom row φ rapidity and pperp spectrum compared with ATLAS data [143] The ATLAS cuts areφrarr K+Kminus pperpφ isin [05 12] GeV |y(φ)| lt 08 pperpK gt 023 GeV |pK | lt 08 GeV

47

0 05 1 15 2

dygt

Ξ lt

dnN

SD

1N

0

001

002

003

004)d|y|gt (NSD)Ξltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn89

01plusmn129

01plusmn192

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

0

05

1

15

2

Figure 33 pp collisions at 7 TeV Ξminus rapidity spectrum compared with CMS data [99]

48

B3 Energy Scaling of σ2rarr2(pTmin) vs σinel from 200 GeV to 100 TeV

In fig 34 we show the LO QCD 2rarr 2 cross section integrated above pTmin as a function of pTminin pp collisions at 4 different CM energies complementing and expanding on the 8-TeV CM energyshown in the main body of the paper We compare two different αs and PDF choices correspondingto those made in tunes Monash 13 (blue filled dots) and 4C (red open squares) respectively As areference for the total inelastic cross section at each energy we base ourselves on the best-fit curvein the TOTEM cross-section measurement paper [72] which in turn represents a fit produced by theCOMPETE collaboration [144] Uncertainties are rough conservative estimates based on the plot inthe TOTEM paper but they are in any case too small to significantly affect conclusions about the scaleat which the partonic cross section saturates the hadronic one

We observe that the pTmin value for which the LO QCD 2 rarr 2 partonic cross section formallybecomes equal to the total inelastic cross section (strongly suggesting that every event has at leastone such mini-jet pair) rises from values around 1 ndash 2 GeV at energies

radics lt 1 TeV to 5 GeV atradic

s = 13 TeV and finally 10 GeV atradics = 100 TeV

49

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

ISR Parameters Monash 13 (Default) CommentSpaceShoweralphaSvalue = 01365 = 0137 Effective alphaS(mZ) valueSpaceShoweralphaSorder = 1 = 1 Running orderSpaceShoweralphaSuseCMW = off = off Translation from MS to CMWSpaceShowersamePTasMPI = off = off ISR cutoff typeSpaceShowerpT0Ref = 20 = 20 ISR pT0 cutoffSpaceShowerecmRef = 70000 = 18000 ISR pT0 reference ECM scaleSpaceShowerecmPow = 00 = 00 ISR pT0 scaling powerSpaceShowerrapidityOrder = on = on Approx coherence via y-orderingSpaceShowerphiPolAsym = on = on Azimuth asymmetries from gluon polSpaceShowerphiIntAsym = on = on Azimuth asymmetries from interferenceTimeShowerdampenBeamRecoil = on = on Recoil dampening in final-initial dipolesBeamRemnantsprimordialKTsoft = 09 = 05 Primordial kT for soft procsBeamRemnantsprimordialKThard = 18 = 20 Primordial kT for hard procsBeamRemnantshalfScaleForKT = 15 = 10 Primordial kT softhard boundaryBeamRemnantshalfMassForKT = 10 = 10 Primordial kT softhard mass boundary

Table 6 Initial-state radiation (ISR) and primordial-kT parameters

MPI Parameters Monash 13 (Default) CommentMultipartonInteractionspT0Ref = 228 = 2085 MPI pT0 IR regularization scaleMultipartonInteractionsecmRef = 70000 = 18000 MPI pT0 reference ECM scaleMultipartonInteractionsecmPow = 0215 = 019 MPI pT0 scaling powerMultipartonInteractionsbProfile = 3 = 3 Transverse matter overlap profileMultipartonInteractionsexpPow = 185 = 20 Shape parameterBeamRemnantsreconnectRange = 18 = 15 Colour ReconnectionsSigmaTotalzeroAXB = on = on Carried over from 4CSigmaDiffractivedampen = on = on Carried over from 4CSigmaDiffractivemaxXB = 650 = 650 Carried over from 4CSigmaDiffractivemaxAX = 650 = 650 Carried over from 4CSigmaDiffractivemaxXX = 650 = 650 Carried over from 4CDiffractionlargeMassSuppress = 40 = 20 High-mass diffraction suppression power

Table 7 Multi-Parton-Interaction (MPI) Colour-Reconnection (CR) and Diffractive parameters

42

B Additional Plots

B1 LEP Event-Shape Distributions

To keep the main body of the paper as uncluttered as possible we collect various plots of event-shapedistributions in figs 28 and 29 separated into light-flavour and b-tagged events on the left and rightrespectively

The experimental results come from the L3 experiment [26] However since the data points areonly available with 3-digit precision some of the least populated bins contain artifacts like uncertain-ties being reported as exactly zero etc Thus we have been forced to make the following modificationsto the data set

The statistical uncertainty was reported as zero for the last two bins of light-flavour Thrust as wellas for the last bin of the C D and BT parameters Uncertainties lt 10minus3 were derived using anapproximate statistical scaling based on the contents and uncertainties of the other bins Likewise thesystematical uncertainty for the last bin of Thrust was given as zero which we have replaced by theupper limit 5times 10minus4 The last bin of BT quoted a measured y value of zero removed in this study

For the heavy-flavour tagged event shapes more significant rounding issues were present Thusseveral of the first and last bins of each distribution either quoted zero (statistical andor systematic)uncertainties or ones with only a single digit of precision (such as 0001 for which the rounding errorcould be up to sim 50) We have interpreted all such values conservatively inserting by hand a fourthdigit on the uncertainties as large as could be consistent with rounding

B2 Additional Particle Spectra

In addition to the K and Λ spectra shown in the main body of the paper (sections 22 and 35) wehere include for reference the x spectra of φ mesons protons and Ξ baryons at LEP in figs 30 and 31the pT spectrum of Klowast mesons and the rapidity and pT spectra of φ mesons at LHC in fig 32 (withabsolute normalizations to the number of inelastic events) and the rapidity spectrum of Ξ baryons atLHC in fig 33

The transverse-momentum spectra of Klowast and φ mesons in fig 32 exhibit the same qualitativebehaviour as that of the KS mesons (fig 23) namely an excess at very soft momenta below sim 500MeV and a depletion at slightly higher momenta between 1 and 2 GeV As discussed in section 35we did not find a way to remove these undesirable features in the Monash 2013 tune suggesting thatthis is an issue that further theoretical modeling will be needed to resolve

The rapidity spectrum of Ξ baryons fig 33 shows that although the Monash tune does producemore Ξ baryons overall (as expected also from the relative increase of Ξ production at LEP cf fig 5)there is still a significant deficit of Ξ baryons at the LHC almost a factor 2 compared with the dataThis is qualitatively similar to the situation for Λ baryons (fig 24) discussed in section 35 Sincenew physics mechanisms may be required to ldquoexplainrdquo the missing baryons we conclude that furthermeasurements and better precision on both the Λ and Ξ sectors (in addition to any other baryonsthat may be accessible) would be highly interesting More explicit recommendations can be found insections 35 and 5

43

0 01 02 03 04

d(1

-T)

σ d

σ1

-310

-210

-110

1

10

2101-Thrust (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn03

01plusmn04

02plusmn05

V I

N C

I A

R O

O T

1-T (udsc)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

d(1

-T)

σ dσ

1

-310

-210

-110

1

10

2101-T (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn13

02plusmn12

02plusmn14

V I

N C

I A

R O

O T

1-T (b)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210

310C Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn03

00plusmn04

01plusmn04

V I

N C

I A

R O

O T

C0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210 C parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn17

01plusmn24

01plusmn27

V I

N C

I A

R O

O T

C (b)0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn06

01plusmn06

V I

N C

I A

R O

O T

D0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn24

02plusmn21

02plusmn26

V I

N C

I A

R O

O T

D (b)0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

Figure 28 Hadronic Z decays atradics = 912 GeV The T C and D event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

44

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn02

01plusmn03

01plusmn04

V I

N C

I A

R O

O T

WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn05

01plusmn12

01plusmn17

V I

N C

I A

R O

O T

(b)WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn02

00plusmn02

01plusmn03

V I

N C

I A

R O

O T

TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

04plusmn24

08plusmn49

08plusmn55

V I

N C

I A

R O

O T

(b)TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

Figure 29 Hadronic Z decays atradics = 912 GeV The BW and BT event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

45

0 02 04 06 08 1

dx

φgt

dn

φ1

ltn

-210

-110

1

10 )φx(

Pythia 8183Data from ALEPH_1996_S3486095d40-x01-y01

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn37

02plusmn53

03plusmn62

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

0608

112141618

Figure 30 Hadronic Z decays atradics = 912 GeV φ meson x spectrum

-5 -4 -3 -2 -1 0

dx

pgt

dn

p1

ltn

-410

-310

-210

-110

1

10

210) (Combined)px(p+

Pythia 8183Data from Zeit Phys C66 (1995) 355 PhysRev D59 (1998) 052001

ALEPH+SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn08

00plusmn09

00plusmn08

V I

N C

I A

R O

O T

px-5 -4 -3 -2 -1 0

The

ory

Dat

a

06

08

1

12

14

0 02 04

dx

Ξgt

dn

Ξ1

ltn

-110

1

10

)plusmnΞx(

Pythia 8183Data from Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn11

02plusmn13

02plusmn14

V I

N C

I A

R O

O T

Ex0 02 04

The

ory

Dat

a

06

08

1

12

14

Figure 31 Hadronic Z decays atradics = 912 GeV pplusmn and Ξplusmn x spectra

46

0 2 4 6

Td

pK

d

nIN

EL

1N

-510

-410

-310

-210

-110

(INEL |y|lt05)T

p0K

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn35

01plusmn26

01plusmn29

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 2 4 6

Td

pφ

dn

INE

L1

N-510

-410

-310

-210

-110

gt04)T

(INEL |y|lt05 pT

pφ

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn88

03plusmn84

04plusmn173

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

)dy

[mb]

-K

+K

rarrφ(σd

0

05

1

15

2 Rapidity (INEL ATLAS cuts)φ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn14

01plusmn19

01plusmn34

V I

N C

I A

R O

O T

pp 7000 GeV

|y|0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

06 08 1 12

[mb

GeV

]φ

T)

dp-

K+

Krarrφ(

σd

0

05

1

15

2

25 (INEL ATLAS cuts)

T pφ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn21

01plusmn30

02plusmn53

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p06 08 1 12

The

ory

Dat

a

06

08

1

12

14

Figure 32 pp collisions at 7 TeV Top row Klowast and φ pperp spectra compared with ALICE data [142]Bottom row φ rapidity and pperp spectrum compared with ATLAS data [143] The ATLAS cuts areφrarr K+Kminus pperpφ isin [05 12] GeV |y(φ)| lt 08 pperpK gt 023 GeV |pK | lt 08 GeV

47

0 05 1 15 2

dygt

Ξ lt

dnN

SD

1N

0

001

002

003

004)d|y|gt (NSD)Ξltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn89

01plusmn129

01plusmn192

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

0

05

1

15

2

Figure 33 pp collisions at 7 TeV Ξminus rapidity spectrum compared with CMS data [99]

48

B3 Energy Scaling of σ2rarr2(pTmin) vs σinel from 200 GeV to 100 TeV

In fig 34 we show the LO QCD 2rarr 2 cross section integrated above pTmin as a function of pTminin pp collisions at 4 different CM energies complementing and expanding on the 8-TeV CM energyshown in the main body of the paper We compare two different αs and PDF choices correspondingto those made in tunes Monash 13 (blue filled dots) and 4C (red open squares) respectively As areference for the total inelastic cross section at each energy we base ourselves on the best-fit curvein the TOTEM cross-section measurement paper [72] which in turn represents a fit produced by theCOMPETE collaboration [144] Uncertainties are rough conservative estimates based on the plot inthe TOTEM paper but they are in any case too small to significantly affect conclusions about the scaleat which the partonic cross section saturates the hadronic one

We observe that the pTmin value for which the LO QCD 2 rarr 2 partonic cross section formallybecomes equal to the total inelastic cross section (strongly suggesting that every event has at leastone such mini-jet pair) rises from values around 1 ndash 2 GeV at energies

radics lt 1 TeV to 5 GeV atradic

s = 13 TeV and finally 10 GeV atradics = 100 TeV

49

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

B Additional Plots

B1 LEP Event-Shape Distributions

To keep the main body of the paper as uncluttered as possible we collect various plots of event-shapedistributions in figs 28 and 29 separated into light-flavour and b-tagged events on the left and rightrespectively

The experimental results come from the L3 experiment [26] However since the data points areonly available with 3-digit precision some of the least populated bins contain artifacts like uncertain-ties being reported as exactly zero etc Thus we have been forced to make the following modificationsto the data set

The statistical uncertainty was reported as zero for the last two bins of light-flavour Thrust as wellas for the last bin of the C D and BT parameters Uncertainties lt 10minus3 were derived using anapproximate statistical scaling based on the contents and uncertainties of the other bins Likewise thesystematical uncertainty for the last bin of Thrust was given as zero which we have replaced by theupper limit 5times 10minus4 The last bin of BT quoted a measured y value of zero removed in this study

For the heavy-flavour tagged event shapes more significant rounding issues were present Thusseveral of the first and last bins of each distribution either quoted zero (statistical andor systematic)uncertainties or ones with only a single digit of precision (such as 0001 for which the rounding errorcould be up to sim 50) We have interpreted all such values conservatively inserting by hand a fourthdigit on the uncertainties as large as could be consistent with rounding

B2 Additional Particle Spectra

In addition to the K and Λ spectra shown in the main body of the paper (sections 22 and 35) wehere include for reference the x spectra of φ mesons protons and Ξ baryons at LEP in figs 30 and 31the pT spectrum of Klowast mesons and the rapidity and pT spectra of φ mesons at LHC in fig 32 (withabsolute normalizations to the number of inelastic events) and the rapidity spectrum of Ξ baryons atLHC in fig 33

The transverse-momentum spectra of Klowast and φ mesons in fig 32 exhibit the same qualitativebehaviour as that of the KS mesons (fig 23) namely an excess at very soft momenta below sim 500MeV and a depletion at slightly higher momenta between 1 and 2 GeV As discussed in section 35we did not find a way to remove these undesirable features in the Monash 2013 tune suggesting thatthis is an issue that further theoretical modeling will be needed to resolve

The rapidity spectrum of Ξ baryons fig 33 shows that although the Monash tune does producemore Ξ baryons overall (as expected also from the relative increase of Ξ production at LEP cf fig 5)there is still a significant deficit of Ξ baryons at the LHC almost a factor 2 compared with the dataThis is qualitatively similar to the situation for Λ baryons (fig 24) discussed in section 35 Sincenew physics mechanisms may be required to ldquoexplainrdquo the missing baryons we conclude that furthermeasurements and better precision on both the Λ and Ξ sectors (in addition to any other baryonsthat may be accessible) would be highly interesting More explicit recommendations can be found insections 35 and 5

43

0 01 02 03 04

d(1

-T)

σ d

σ1

-310

-210

-110

1

10

2101-Thrust (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn03

01plusmn04

02plusmn05

V I

N C

I A

R O

O T

1-T (udsc)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

d(1

-T)

σ dσ

1

-310

-210

-110

1

10

2101-T (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn13

02plusmn12

02plusmn14

V I

N C

I A

R O

O T

1-T (b)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210

310C Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn03

00plusmn04

01plusmn04

V I

N C

I A

R O

O T

C0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210 C parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn17

01plusmn24

01plusmn27

V I

N C

I A

R O

O T

C (b)0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn06

01plusmn06

V I

N C

I A

R O

O T

D0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn24

02plusmn21

02plusmn26

V I

N C

I A

R O

O T

D (b)0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

Figure 28 Hadronic Z decays atradics = 912 GeV The T C and D event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

44

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn02

01plusmn03

01plusmn04

V I

N C

I A

R O

O T

WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn05

01plusmn12

01plusmn17

V I

N C

I A

R O

O T

(b)WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn02

00plusmn02

01plusmn03

V I

N C

I A

R O

O T

TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

04plusmn24

08plusmn49

08plusmn55

V I

N C

I A

R O

O T

(b)TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

Figure 29 Hadronic Z decays atradics = 912 GeV The BW and BT event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

45

0 02 04 06 08 1

dx

φgt

dn

φ1

ltn

-210

-110

1

10 )φx(

Pythia 8183Data from ALEPH_1996_S3486095d40-x01-y01

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn37

02plusmn53

03plusmn62

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

0608

112141618

Figure 30 Hadronic Z decays atradics = 912 GeV φ meson x spectrum

-5 -4 -3 -2 -1 0

dx

pgt

dn

p1

ltn

-410

-310

-210

-110

1

10

210) (Combined)px(p+

Pythia 8183Data from Zeit Phys C66 (1995) 355 PhysRev D59 (1998) 052001

ALEPH+SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn08

00plusmn09

00plusmn08

V I

N C

I A

R O

O T

px-5 -4 -3 -2 -1 0

The

ory

Dat

a

06

08

1

12

14

0 02 04

dx

Ξgt

dn

Ξ1

ltn

-110

1

10

)plusmnΞx(

Pythia 8183Data from Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn11

02plusmn13

02plusmn14

V I

N C

I A

R O

O T

Ex0 02 04

The

ory

Dat

a

06

08

1

12

14

Figure 31 Hadronic Z decays atradics = 912 GeV pplusmn and Ξplusmn x spectra

46

0 2 4 6

Td

pK

d

nIN

EL

1N

-510

-410

-310

-210

-110

(INEL |y|lt05)T

p0K

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn35

01plusmn26

01plusmn29

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 2 4 6

Td

pφ

dn

INE

L1

N-510

-410

-310

-210

-110

gt04)T

(INEL |y|lt05 pT

pφ

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn88

03plusmn84

04plusmn173

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

)dy

[mb]

-K

+K

rarrφ(σd

0

05

1

15

2 Rapidity (INEL ATLAS cuts)φ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn14

01plusmn19

01plusmn34

V I

N C

I A

R O

O T

pp 7000 GeV

|y|0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

06 08 1 12

[mb

GeV

]φ

T)

dp-

K+

Krarrφ(

σd

0

05

1

15

2

25 (INEL ATLAS cuts)

T pφ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn21

01plusmn30

02plusmn53

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p06 08 1 12

The

ory

Dat

a

06

08

1

12

14

Figure 32 pp collisions at 7 TeV Top row Klowast and φ pperp spectra compared with ALICE data [142]Bottom row φ rapidity and pperp spectrum compared with ATLAS data [143] The ATLAS cuts areφrarr K+Kminus pperpφ isin [05 12] GeV |y(φ)| lt 08 pperpK gt 023 GeV |pK | lt 08 GeV

47

0 05 1 15 2

dygt

Ξ lt

dnN

SD

1N

0

001

002

003

004)d|y|gt (NSD)Ξltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn89

01plusmn129

01plusmn192

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

0

05

1

15

2

Figure 33 pp collisions at 7 TeV Ξminus rapidity spectrum compared with CMS data [99]

48

B3 Energy Scaling of σ2rarr2(pTmin) vs σinel from 200 GeV to 100 TeV

In fig 34 we show the LO QCD 2rarr 2 cross section integrated above pTmin as a function of pTminin pp collisions at 4 different CM energies complementing and expanding on the 8-TeV CM energyshown in the main body of the paper We compare two different αs and PDF choices correspondingto those made in tunes Monash 13 (blue filled dots) and 4C (red open squares) respectively As areference for the total inelastic cross section at each energy we base ourselves on the best-fit curvein the TOTEM cross-section measurement paper [72] which in turn represents a fit produced by theCOMPETE collaboration [144] Uncertainties are rough conservative estimates based on the plot inthe TOTEM paper but they are in any case too small to significantly affect conclusions about the scaleat which the partonic cross section saturates the hadronic one

We observe that the pTmin value for which the LO QCD 2 rarr 2 partonic cross section formallybecomes equal to the total inelastic cross section (strongly suggesting that every event has at leastone such mini-jet pair) rises from values around 1 ndash 2 GeV at energies

radics lt 1 TeV to 5 GeV atradic

s = 13 TeV and finally 10 GeV atradics = 100 TeV

49

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

0 01 02 03 04

d(1

-T)

σ d

σ1

-310

-210

-110

1

10

2101-Thrust (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn03

01plusmn04

02plusmn05

V I

N C

I A

R O

O T

1-T (udsc)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

d(1

-T)

σ dσ

1

-310

-210

-110

1

10

2101-T (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn13

02plusmn12

02plusmn14

V I

N C

I A

R O

O T

1-T (b)0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210

310C Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn03

00plusmn04

01plusmn04

V I

N C

I A

R O

O T

C0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08 1

dC

σ d

σ1

-310

-210

-110

1

10

210 C parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn17

01plusmn24

01plusmn27

V I

N C

I A

R O

O T

C (b)0 02 04 06 08 1

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D Parameter (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn06

01plusmn06

01plusmn06

V I

N C

I A

R O

O T

D0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

dD

σ d

σ1

-310

-210

-110

1

10

210D parameter (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn24

02plusmn21

02plusmn26

V I

N C

I A

R O

O T

D (b)0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

Figure 28 Hadronic Z decays atradics = 912 GeV The T C and D event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

44

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn02

01plusmn03

01plusmn04

V I

N C

I A

R O

O T

WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn05

01plusmn12

01plusmn17

V I

N C

I A

R O

O T

(b)WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn02

00plusmn02

01plusmn03

V I

N C

I A

R O

O T

TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

04plusmn24

08plusmn49

08plusmn55

V I

N C

I A

R O

O T

(b)TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

Figure 29 Hadronic Z decays atradics = 912 GeV The BW and BT event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

45

0 02 04 06 08 1

dx

φgt

dn

φ1

ltn

-210

-110

1

10 )φx(

Pythia 8183Data from ALEPH_1996_S3486095d40-x01-y01

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn37

02plusmn53

03plusmn62

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

0608

112141618

Figure 30 Hadronic Z decays atradics = 912 GeV φ meson x spectrum

-5 -4 -3 -2 -1 0

dx

pgt

dn

p1

ltn

-410

-310

-210

-110

1

10

210) (Combined)px(p+

Pythia 8183Data from Zeit Phys C66 (1995) 355 PhysRev D59 (1998) 052001

ALEPH+SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn08

00plusmn09

00plusmn08

V I

N C

I A

R O

O T

px-5 -4 -3 -2 -1 0

The

ory

Dat

a

06

08

1

12

14

0 02 04

dx

Ξgt

dn

Ξ1

ltn

-110

1

10

)plusmnΞx(

Pythia 8183Data from Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn11

02plusmn13

02plusmn14

V I

N C

I A

R O

O T

Ex0 02 04

The

ory

Dat

a

06

08

1

12

14

Figure 31 Hadronic Z decays atradics = 912 GeV pplusmn and Ξplusmn x spectra

46

0 2 4 6

Td

pK

d

nIN

EL

1N

-510

-410

-310

-210

-110

(INEL |y|lt05)T

p0K

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn35

01plusmn26

01plusmn29

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 2 4 6

Td

pφ

dn

INE

L1

N-510

-410

-310

-210

-110

gt04)T

(INEL |y|lt05 pT

pφ

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn88

03plusmn84

04plusmn173

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

)dy

[mb]

-K

+K

rarrφ(σd

0

05

1

15

2 Rapidity (INEL ATLAS cuts)φ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn14

01plusmn19

01plusmn34

V I

N C

I A

R O

O T

pp 7000 GeV

|y|0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

06 08 1 12

[mb

GeV

]φ

T)

dp-

K+

Krarrφ(

σd

0

05

1

15

2

25 (INEL ATLAS cuts)

T pφ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn21

01plusmn30

02plusmn53

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p06 08 1 12

The

ory

Dat

a

06

08

1

12

14

Figure 32 pp collisions at 7 TeV Top row Klowast and φ pperp spectra compared with ALICE data [142]Bottom row φ rapidity and pperp spectrum compared with ATLAS data [143] The ATLAS cuts areφrarr K+Kminus pperpφ isin [05 12] GeV |y(φ)| lt 08 pperpK gt 023 GeV |pK | lt 08 GeV

47

0 05 1 15 2

dygt

Ξ lt

dnN

SD

1N

0

001

002

003

004)d|y|gt (NSD)Ξltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn89

01plusmn129

01plusmn192

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

0

05

1

15

2

Figure 33 pp collisions at 7 TeV Ξminus rapidity spectrum compared with CMS data [99]

48

B3 Energy Scaling of σ2rarr2(pTmin) vs σinel from 200 GeV to 100 TeV

In fig 34 we show the LO QCD 2rarr 2 cross section integrated above pTmin as a function of pTminin pp collisions at 4 different CM energies complementing and expanding on the 8-TeV CM energyshown in the main body of the paper We compare two different αs and PDF choices correspondingto those made in tunes Monash 13 (blue filled dots) and 4C (red open squares) respectively As areference for the total inelastic cross section at each energy we base ourselves on the best-fit curvein the TOTEM cross-section measurement paper [72] which in turn represents a fit produced by theCOMPETE collaboration [144] Uncertainties are rough conservative estimates based on the plot inthe TOTEM paper but they are in any case too small to significantly affect conclusions about the scaleat which the partonic cross section saturates the hadronic one

We observe that the pTmin value for which the LO QCD 2 rarr 2 partonic cross section formallybecomes equal to the total inelastic cross section (strongly suggesting that every event has at leastone such mini-jet pair) rises from values around 1 ndash 2 GeV at energies

radics lt 1 TeV to 5 GeV atradic

s = 13 TeV and finally 10 GeV atradics = 100 TeV

49

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

01plusmn02

01plusmn03

01plusmn04

V I

N C

I A

R O

O T

WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03

Wd

Bσ

dσ

1

-310

-210

-110

1

10

210

310Wide Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn05

01plusmn12

01plusmn17

V I

N C

I A

R O

O T

(b)WB0 01 02 03

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (udsc)

Pythia 8183Data from PhysRept 399 (2004) 71

L3 PY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn02

00plusmn02

01plusmn03

V I

N C

I A

R O

O T

TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

0 01 02 03 04

Td

Bσ

dσ

1

-310

-210

-110

1

10

210

310Total Jet Broadening (b)

Pythia 8181Data from PhysRept 399 (2004) 71

L3 PY8 (Monash 13)PY8 (Default)PY8 (Fischer)

binsN2

5χ

04plusmn24

08plusmn49

08plusmn55

V I

N C

I A

R O

O T

(b)TB0 01 02 03 04

The

ory

Dat

a

06

08

1

12

14

Figure 29 Hadronic Z decays atradics = 912 GeV The BW and BT event-shape parameters as

measured by L3 [26] for light-flavour (left) and b-tagged (right) events respectively

45

0 02 04 06 08 1

dx

φgt

dn

φ1

ltn

-210

-110

1

10 )φx(

Pythia 8183Data from ALEPH_1996_S3486095d40-x01-y01

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn37

02plusmn53

03plusmn62

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

0608

112141618

Figure 30 Hadronic Z decays atradics = 912 GeV φ meson x spectrum

-5 -4 -3 -2 -1 0

dx

pgt

dn

p1

ltn

-410

-310

-210

-110

1

10

210) (Combined)px(p+

Pythia 8183Data from Zeit Phys C66 (1995) 355 PhysRev D59 (1998) 052001

ALEPH+SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn08

00plusmn09

00plusmn08

V I

N C

I A

R O

O T

px-5 -4 -3 -2 -1 0

The

ory

Dat

a

06

08

1

12

14

0 02 04

dx

Ξgt

dn

Ξ1

ltn

-110

1

10

)plusmnΞx(

Pythia 8183Data from Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn11

02plusmn13

02plusmn14

V I

N C

I A

R O

O T

Ex0 02 04

The

ory

Dat

a

06

08

1

12

14

Figure 31 Hadronic Z decays atradics = 912 GeV pplusmn and Ξplusmn x spectra

46

0 2 4 6

Td

pK

d

nIN

EL

1N

-510

-410

-310

-210

-110

(INEL |y|lt05)T

p0K

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn35

01plusmn26

01plusmn29

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 2 4 6

Td

pφ

dn

INE

L1

N-510

-410

-310

-210

-110

gt04)T

(INEL |y|lt05 pT

pφ

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn88

03plusmn84

04plusmn173

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

)dy

[mb]

-K

+K

rarrφ(σd

0

05

1

15

2 Rapidity (INEL ATLAS cuts)φ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn14

01plusmn19

01plusmn34

V I

N C

I A

R O

O T

pp 7000 GeV

|y|0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

06 08 1 12

[mb

GeV

]φ

T)

dp-

K+

Krarrφ(

σd

0

05

1

15

2

25 (INEL ATLAS cuts)

T pφ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn21

01plusmn30

02plusmn53

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p06 08 1 12

The

ory

Dat

a

06

08

1

12

14

Figure 32 pp collisions at 7 TeV Top row Klowast and φ pperp spectra compared with ALICE data [142]Bottom row φ rapidity and pperp spectrum compared with ATLAS data [143] The ATLAS cuts areφrarr K+Kminus pperpφ isin [05 12] GeV |y(φ)| lt 08 pperpK gt 023 GeV |pK | lt 08 GeV

47

0 05 1 15 2

dygt

Ξ lt

dnN

SD

1N

0

001

002

003

004)d|y|gt (NSD)Ξltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn89

01plusmn129

01plusmn192

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

0

05

1

15

2

Figure 33 pp collisions at 7 TeV Ξminus rapidity spectrum compared with CMS data [99]

48

B3 Energy Scaling of σ2rarr2(pTmin) vs σinel from 200 GeV to 100 TeV

In fig 34 we show the LO QCD 2rarr 2 cross section integrated above pTmin as a function of pTminin pp collisions at 4 different CM energies complementing and expanding on the 8-TeV CM energyshown in the main body of the paper We compare two different αs and PDF choices correspondingto those made in tunes Monash 13 (blue filled dots) and 4C (red open squares) respectively As areference for the total inelastic cross section at each energy we base ourselves on the best-fit curvein the TOTEM cross-section measurement paper [72] which in turn represents a fit produced by theCOMPETE collaboration [144] Uncertainties are rough conservative estimates based on the plot inthe TOTEM paper but they are in any case too small to significantly affect conclusions about the scaleat which the partonic cross section saturates the hadronic one

We observe that the pTmin value for which the LO QCD 2 rarr 2 partonic cross section formallybecomes equal to the total inelastic cross section (strongly suggesting that every event has at leastone such mini-jet pair) rises from values around 1 ndash 2 GeV at energies

radics lt 1 TeV to 5 GeV atradic

s = 13 TeV and finally 10 GeV atradics = 100 TeV

49

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

0 02 04 06 08 1

dx

φgt

dn

φ1

ltn

-210

-110

1

10 )φx(

Pythia 8183Data from ALEPH_1996_S3486095d40-x01-y01

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn37

02plusmn53

03plusmn62

V I

N C

I A

R O

O T

px0 02 04 06 08 1

The

ory

Dat

a

0608

112141618

Figure 30 Hadronic Z decays atradics = 912 GeV φ meson x spectrum

-5 -4 -3 -2 -1 0

dx

pgt

dn

p1

ltn

-410

-310

-210

-110

1

10

210) (Combined)px(p+

Pythia 8183Data from Zeit Phys C66 (1995) 355 PhysRev D59 (1998) 052001

ALEPH+SLDPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

00plusmn08

00plusmn09

00plusmn08

V I

N C

I A

R O

O T

px-5 -4 -3 -2 -1 0

The

ory

Dat

a

06

08

1

12

14

0 02 04

dx

Ξgt

dn

Ξ1

ltn

-110

1

10

)plusmnΞx(

Pythia 8183Data from Phys Rep 294 (1998) 1

ALEPHPY8 (Monash)PY8 (Default)PY8 (Fischer)

binsN2

5χ

02plusmn11

02plusmn13

02plusmn14

V I

N C

I A

R O

O T

Ex0 02 04

The

ory

Dat

a

06

08

1

12

14

Figure 31 Hadronic Z decays atradics = 912 GeV pplusmn and Ξplusmn x spectra

46

0 2 4 6

Td

pK

d

nIN

EL

1N

-510

-410

-310

-210

-110

(INEL |y|lt05)T

p0K

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn35

01plusmn26

01plusmn29

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 2 4 6

Td

pφ

dn

INE

L1

N-510

-410

-310

-210

-110

gt04)T

(INEL |y|lt05 pT

pφ

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn88

03plusmn84

04plusmn173

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

)dy

[mb]

-K

+K

rarrφ(σd

0

05

1

15

2 Rapidity (INEL ATLAS cuts)φ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn14

01plusmn19

01plusmn34

V I

N C

I A

R O

O T

pp 7000 GeV

|y|0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

06 08 1 12

[mb

GeV

]φ

T)

dp-

K+

Krarrφ(

σd

0

05

1

15

2

25 (INEL ATLAS cuts)

T pφ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn21

01plusmn30

02plusmn53

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p06 08 1 12

The

ory

Dat

a

06

08

1

12

14

Figure 32 pp collisions at 7 TeV Top row Klowast and φ pperp spectra compared with ALICE data [142]Bottom row φ rapidity and pperp spectrum compared with ATLAS data [143] The ATLAS cuts areφrarr K+Kminus pperpφ isin [05 12] GeV |y(φ)| lt 08 pperpK gt 023 GeV |pK | lt 08 GeV

47

0 05 1 15 2

dygt

Ξ lt

dnN

SD

1N

0

001

002

003

004)d|y|gt (NSD)Ξltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn89

01plusmn129

01plusmn192

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

0

05

1

15

2

Figure 33 pp collisions at 7 TeV Ξminus rapidity spectrum compared with CMS data [99]

48

B3 Energy Scaling of σ2rarr2(pTmin) vs σinel from 200 GeV to 100 TeV

In fig 34 we show the LO QCD 2rarr 2 cross section integrated above pTmin as a function of pTminin pp collisions at 4 different CM energies complementing and expanding on the 8-TeV CM energyshown in the main body of the paper We compare two different αs and PDF choices correspondingto those made in tunes Monash 13 (blue filled dots) and 4C (red open squares) respectively As areference for the total inelastic cross section at each energy we base ourselves on the best-fit curvein the TOTEM cross-section measurement paper [72] which in turn represents a fit produced by theCOMPETE collaboration [144] Uncertainties are rough conservative estimates based on the plot inthe TOTEM paper but they are in any case too small to significantly affect conclusions about the scaleat which the partonic cross section saturates the hadronic one

We observe that the pTmin value for which the LO QCD 2 rarr 2 partonic cross section formallybecomes equal to the total inelastic cross section (strongly suggesting that every event has at leastone such mini-jet pair) rises from values around 1 ndash 2 GeV at energies

radics lt 1 TeV to 5 GeV atradic

s = 13 TeV and finally 10 GeV atradics = 100 TeV

49

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

0 2 4 6

Td

pK

d

nIN

EL

1N

-510

-410

-310

-210

-110

(INEL |y|lt05)T

p0K

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn35

01plusmn26

01plusmn29

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 2 4 6

Td

pφ

dn

INE

L1

N-510

-410

-310

-210

-110

gt04)T

(INEL |y|lt05 pT

pφ

Pythia 8185Data from EurPhysJ C72 (2012) 2183

ALICEPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

03plusmn88

03plusmn84

04plusmn173

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p0 2 4 6

The

ory

Dat

a

06

08

1

12

14

0 02 04 06 08

)dy

[mb]

-K

+K

rarrφ(σd

0

05

1

15

2 Rapidity (INEL ATLAS cuts)φ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn14

01plusmn19

01plusmn34

V I

N C

I A

R O

O T

pp 7000 GeV

|y|0 02 04 06 08

The

ory

Dat

a

06

08

1

12

14

06 08 1 12

[mb

GeV

]φ

T)

dp-

K+

Krarrφ(

σd

0

05

1

15

2

25 (INEL ATLAS cuts)

T pφ

Pythia 8185Data from arXiv14026162

ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn21

01plusmn30

02plusmn53

V I

N C

I A

R O

O T

pp 7000 GeV

[GeV]T

p06 08 1 12

The

ory

Dat

a

06

08

1

12

14

Figure 32 pp collisions at 7 TeV Top row Klowast and φ pperp spectra compared with ALICE data [142]Bottom row φ rapidity and pperp spectrum compared with ATLAS data [143] The ATLAS cuts areφrarr K+Kminus pperpφ isin [05 12] GeV |y(φ)| lt 08 pperpK gt 023 GeV |pK | lt 08 GeV

47

0 05 1 15 2

dygt

Ξ lt

dnN

SD

1N

0

001

002

003

004)d|y|gt (NSD)Ξltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn89

01plusmn129

01plusmn192

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

0

05

1

15

2

Figure 33 pp collisions at 7 TeV Ξminus rapidity spectrum compared with CMS data [99]

48

B3 Energy Scaling of σ2rarr2(pTmin) vs σinel from 200 GeV to 100 TeV

In fig 34 we show the LO QCD 2rarr 2 cross section integrated above pTmin as a function of pTminin pp collisions at 4 different CM energies complementing and expanding on the 8-TeV CM energyshown in the main body of the paper We compare two different αs and PDF choices correspondingto those made in tunes Monash 13 (blue filled dots) and 4C (red open squares) respectively As areference for the total inelastic cross section at each energy we base ourselves on the best-fit curvein the TOTEM cross-section measurement paper [72] which in turn represents a fit produced by theCOMPETE collaboration [144] Uncertainties are rough conservative estimates based on the plot inthe TOTEM paper but they are in any case too small to significantly affect conclusions about the scaleat which the partonic cross section saturates the hadronic one

We observe that the pTmin value for which the LO QCD 2 rarr 2 partonic cross section formallybecomes equal to the total inelastic cross section (strongly suggesting that every event has at leastone such mini-jet pair) rises from values around 1 ndash 2 GeV at energies

radics lt 1 TeV to 5 GeV atradic

s = 13 TeV and finally 10 GeV atradics = 100 TeV

49

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

0 05 1 15 2

dygt

Ξ lt

dnN

SD

1N

0

001

002

003

004)d|y|gt (NSD)Ξltdn(

Pythia 8185Data from JHEP 1105 (2011) 064

CMSPY8 (Monash 13)PY8 (4C)PY8 (2C)

binsN2

5χ

01plusmn89

01plusmn129

01plusmn192

V I

N C

I A

R O

O T

pp 7000 GeV

y0 05 1 15 2

The

ory

Dat

a

0

05

1

15

2

Figure 33 pp collisions at 7 TeV Ξminus rapidity spectrum compared with CMS data [99]

48

B3 Energy Scaling of σ2rarr2(pTmin) vs σinel from 200 GeV to 100 TeV

In fig 34 we show the LO QCD 2rarr 2 cross section integrated above pTmin as a function of pTminin pp collisions at 4 different CM energies complementing and expanding on the 8-TeV CM energyshown in the main body of the paper We compare two different αs and PDF choices correspondingto those made in tunes Monash 13 (blue filled dots) and 4C (red open squares) respectively As areference for the total inelastic cross section at each energy we base ourselves on the best-fit curvein the TOTEM cross-section measurement paper [72] which in turn represents a fit produced by theCOMPETE collaboration [144] Uncertainties are rough conservative estimates based on the plot inthe TOTEM paper but they are in any case too small to significantly affect conclusions about the scaleat which the partonic cross section saturates the hadronic one

We observe that the pTmin value for which the LO QCD 2 rarr 2 partonic cross section formallybecomes equal to the total inelastic cross section (strongly suggesting that every event has at leastone such mini-jet pair) rises from values around 1 ndash 2 GeV at energies

radics lt 1 TeV to 5 GeV atradic

s = 13 TeV and finally 10 GeV atradics = 100 TeV

49

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

B3 Energy Scaling of σ2rarr2(pTmin) vs σinel from 200 GeV to 100 TeV

In fig 34 we show the LO QCD 2rarr 2 cross section integrated above pTmin as a function of pTminin pp collisions at 4 different CM energies complementing and expanding on the 8-TeV CM energyshown in the main body of the paper We compare two different αs and PDF choices correspondingto those made in tunes Monash 13 (blue filled dots) and 4C (red open squares) respectively As areference for the total inelastic cross section at each energy we base ourselves on the best-fit curvein the TOTEM cross-section measurement paper [72] which in turn represents a fit produced by theCOMPETE collaboration [144] Uncertainties are rough conservative estimates based on the plot inthe TOTEM paper but they are in any case too small to significantly affect conclusions about the scaleat which the partonic cross section saturates the hadronic one

We observe that the pTmin value for which the LO QCD 2 rarr 2 partonic cross section formallybecomes equal to the total inelastic cross section (strongly suggesting that every event has at leastone such mini-jet pair) rises from values around 1 ndash 2 GeV at energies

radics lt 1 TeV to 5 GeV atradic

s = 13 TeV and finally 10 GeV atradics = 100 TeV

49

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

02 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-210

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

09 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

-110

1

10

210

310

410

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

13 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

0 5 10 15 20

Inte

grat

ed c

ross

sec

tion

[mb]

1

10

210

310

410

510

Tmin) vs p

Tmin pge

T(p2rarr2σ

Pythia 8183

INELσTOTEM

=0130 NNPDF23LOsα=0135 CTEQ6L1sα

V I

N C

I A

R O

O T

100 TeV pp

Tminp

0 5 10 15 20

Rat

io

0

05

1

15

Figure 34 pp collisions at 4 different CM energies Integrated QCD 2rarr 2 cross section above pTminas a function of pTmin Top Left 200 GeV Top Right 900 GeV Bottom Left 13 TeV Bottom Right100 TeV

50

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

References[1] A Buckley and M Whalley ldquoHepData reloaded reinventing the HEP data archive rdquo 10060517

httphepdatacedaracuk

[2] A Buckley J Butterworth L Lonnblad D Grellscheid H Hoeth et al ldquoRivet user manualrdquoComputPhysCommun 184 (2013) 2803ndash2819 10030694

[3] T Sjostrand ldquoColour reconnection and its effects on precise measurements at the LHCrdquo 13108073

[4] T Sjostrand ldquoChallenges for QCD theory some personal reflectionsrdquo PhysScripta T158 (2013)014002 13096747

[5] J M Katzy ldquoQCD Monte-Carlo model tunes for the LHCrdquo ProgPartNuclPhys 73 (2013) 141ndash187

[6] T Sjostrand S Mrenna and P Z Skands ldquoPYTHIA 64 Physics and Manualrdquo JHEP 0605 (2006) 026hep-ph0603175

[7] T Sjostrand S Mrenna and P Z Skands ldquoA Brief Introduction to PYTHIA 81rdquoComputPhysCommun 178 (2008) 852ndash867 07103820

[8] P Z Skands ldquoTuning Monte Carlo Generators The Perugia Tunesrdquo PhysRev D82 (2010) 07401810053457

[9] R Corke and T Sjostrand ldquoInterleaved Parton Showers and Tuning Prospectsrdquo JHEP 1103 (2011) 03210111759

[10] ATLAS Collaboration ldquoCharged particle multiplicities in p p interactions atradics = 09 and 7 TeV in a

diffractive limited phase-space measured with the ATLAS detector at the LHC and new PYTHIA6tunerdquo ATLAS-CONF-2010-031 ATLAS-COM-CONF-2010-031

[11] ATLAS Collaboration ldquoNew ATLAS event generator tunes to 2010 datardquoATL-PHYS-PUB-2011-008 ATL-COM-PHYS-2011-329

[12] ATLAS Collaboration ldquoATLAS tunes of PYTHIA 6 and Pythia 8 for MC11rdquoATL-PHYS-PUB-2011-009 ATL-COM-PHYS-2011-744

[13] ATLAS Collaboration ldquoSummary of ATLAS Pythia 8 tunesrdquo ATL-PHYS-PUB-2012-003ATL-COM-PHYS-2012-738

[14] R Field ldquoThe underlying event in hadronic collisionsrdquo AnnRevNuclPartSci 62 (2012) 453ndash483

[15] J Alcaraz Maestre et al ldquoThe SM and NLO Multileg and SM MC Working Groups SummaryReportrdquo 12036803

[16] N Firdous and G Rudolph ldquoTuning of PYTHIA6 to Minimum Bias Datardquo EPJ Web Conf 60 (2013)20056

[17] A Buckley H Hoeth H Lacker H Schulz and J E von Seggern ldquoSystematic event generator tuningfor the LHCrdquo EurPhysJ C65 (2010) 331ndash357 09072973

[18] The NNPDF Collaboration Collaboration R D Ball et al ldquoUnbiased global determination of partondistributions and their uncertainties at NNLO and at LOrdquo NuclPhys B855 (2012) 153ndash22111072652

[19] NNPDF Collaboration R D Ball et al ldquoParton distributions with QED correctionsrdquo NuclPhys B877(2013) no 2 290ndash320 13080598

[20] S Carrazza S Forte and J Rojo ldquoParton Distributions and Event Generatorsrdquo 13115887

[21] B Cooper J Katzy M Mangano A Messina L Mijovic et al ldquoImportance of a consistent choice ofalpha(s) in the matching of AlpGen and Pythiardquo EurPhysJ C72 (2012) 2078 11095295

51

[22] R Field C Group and D Wilson ldquoThe Energy Dependence of Min-Bias and the Underlying Event atCDFrdquo CDF Note 10874 2012

[23] R Field ldquoThe tevatron energy scan Findings amp surprisesrdquo 2013 Published in the proceedings of theInternational Symposium on Multiparticle Dynamics September 17 2013 Chicago Illinois

[24] W Giele D Kosower and P Skands ldquoHigher-Order Corrections to Timelike Jetsrdquo PhysRev D84(2011) 054003 11022126

[25] A Karneyeu L Mijovic S Prestel and P Skands ldquoMCPLOTS a particle physics resource based onvolunteer computingrdquo 13063436 httpmcplotscernch

[26] L3 Collaboration P Achard et al ldquoStudies of hadronic event structure in e+eminus annihilation from30-GeV to 209-GeV with the L3 detectorrdquo PhysRept 399 (2004) 71ndash174 hep-ex0406049

[27] T Sjostrand and P Z Skands ldquoTransverse-momentum-ordered showers and interleaved multipleinteractionsrdquo EurPhysJ C39 (2005) 129ndash154 hep-ph0408302

[28] S Catani B R Webber and G Marchesini ldquoQCD coherent branching and semiinclusive processes atlarge xrdquo Nucl Phys B349 (1991) 635ndash654

[29] L Hartgring E Laenen and P Skands ldquoAntenna Showers with One-Loop Matrix Elementsrdquo JHEP1310 (2013) 127 13034974

[30] N Fischer S Gieseke S Platzer and P Skands ldquoRevisiting Radiation Patterns in e+eminus Collisionsrdquo14023186

[31] G Gustafson ldquoDual Description of a Confined Color Fieldrdquo PhysLett B175 (1986) 453

[32] B Andersson G Gustafson and T Sjostrand ldquoA Three-Dimensional Model for Quark and GluonJetsrdquo ZPhys C6 (1980) 235

[33] B Andersson The Lund model Camb Monogr Part Phys Nucl Phys Cosm 1997

[34] A Buckley J Butterworth S Gieseke D Grellscheid S Hoche et al ldquoGeneral-purpose eventgenerators for LHC physicsrdquo PhysRept 504 (2011) 145ndash233 11012599

[35] B Webber ldquoA QCD Model for Jet Fragmentation Including Soft Gluon Interferencerdquo NuclPhys B238(1984) 492

[36] B Andersson G Gustafson and T Sjostrand ldquoA Model for Baryon Production in Quark and GluonJetsrdquo NuclPhys B197 (1982) 45

[37] P Skands ldquoIntroduction to QCDrdquo 12072389 Lectures given at TASI 2012

[38] ALEPH Collaboration R Barate et al ldquoStudies of quantum chromodynamics with the ALEPHdetectorrdquo PhysRept 294 (1998) 1ndash165

[39] Particle Data Group Collaboration J Beringer et al ldquoReview of Particle Physics (RPP)rdquo PhysRevD86 (2012) 010001

[40] OPAL Collaboration K Ackerstaff et al ldquoProduction of f(0)(980) f(2)(1270) and phi(1020) inhadronic Z0 decayrdquo EurPhysJ C4 (1998) 19ndash28 hep-ex9802013

[41] DELPHI Collaboration P Abreu et al ldquoMeasurement of inclusive K0 (892) Phi (1020) and K(2)0(1430) production in hadronic Z decaysrdquo ZPhys C73 (1996) 61ndash72

[42] SLD Collaboration K Abe et al ldquoProduction of pi+ K+ K0 K0 phi p and Lambda0 in hadronic Z0decaysrdquo PhysRev D59 (1999) 052001 hep-ex9805029

[43] OPAL Collaboration G Alexander et al ldquoStrange baryon production in hadronic Z0 decaysrdquo ZPhysC73 (1997) 569

[44] L3 Collaboration M Acciarri et al ldquoInclusive Σ+ and Σ0 production in hadronic Z decaysrdquoPhysLett B479 (2000) 79ndash88 hep-ex0002066

52

[45] DELPHI Collaboration P Abreu et al ldquoInclusive Σminus and Λ(1520) production in hadronic Z decaysrdquoPhysLett B475 (2000) 429ndash447 hep-ex0103020

[46] OPAL Collaboration G Alexander et al ldquoDelta++ production in hadronic Z0 decaysrdquo PhysLettB358 (1995) 162ndash172

[47] DELPHI Collaboration P Abreu et al ldquoMeasurement of Delta++ (1232) production in hadronic Zdecaysrdquo PhysLett B361 (1995) 207ndash220

[48] DELPHI Collaboration P Abreu et al ldquoStrange baryon production in Z hadronic decaysrdquo ZPhysC67 (1995) 543ndash554

[49] DELPHI Collaboration W Adam et al ldquoProduction of SIGMA0 and OMEGA- in Z decaysrdquo ZPhysC70 (1996) 371ndash382

[50] MARK-II Collaboration G Abrams C Adolphsen D Averill J Ballam B C Barish et alldquoMeasurements of Charged Particle Inclusive Distributions in Hadronic Decays of the Z BosonrdquoPhysRevLett 64 (1990) 1334

[51] DELPHI Collaboration P Abreu et al ldquopi+- K+- p and anti-p production in Z0rarr q anti-q Z0rarr banti-b Z0rarr u anti-u d anti-d s anti-srdquo EurPhysJ C5 (1998) 585ndash620

[52] OPAL Collaboration K Ackerstaff et al ldquoMeasurements of flavor dependent fragmentation functionsin Z0rarr q anti-q eventsrdquo EurPhysJ C7 (1999) 369ndash381 hep-ex9807004

[53] L3 Collaboration B Adeva et al ldquoStudies of hadronic event structure and comparisons with QCDmodels at the Z0 resonancerdquo ZPhys C55 (1992) 39ndash62

[54] ALEPH Collaboration D Buskulic et al ldquoProduction of charmed mesons in Z decaysrdquo ZPhys C62(1994) 1ndash14

[55] ALEPH Collaboration R Barate et al ldquoStudy of charm production in Z decaysrdquo EurPhysJ C16(2000) 597ndash611 hep-ex9909032

[56] OPAL Collaboration G Abbiendi et al ldquoMeasurement of the production rate of charm quark pairsfrom gluons in hadronic Z0 decaysrdquo EurPhysJ C13 (2000) 1ndash13 hep-ex9908001

[57] D Miller and M H Seymour ldquoSecondary heavy quark pair production in e+ e- annihilationrdquoPhysLett B435 (1998) 213ndash220 hep-ph9805414

[58] O Biebel P Nason and B Webber ldquoJet fragmentation in e+e- annihilationrdquo hep-ph0109282

[59] ALEPH Collaboration R Barate et al ldquoA Measurement of the gluon splitting rate into b anti-b pairsin hadronic Z decaysrdquo PhysLett B434 (1998) 437ndash450

[60] DELPHI Collaboration P Abreu et al ldquoMeasurement of the multiplicity of gluons splitting to bottomquark pairs in hadronic Z0 decaysrdquo PhysLett B405 (1997) 202ndash214

[61] SLD Collaboration K Abe et al ldquoMeasurement of the probability for gluon splitting into b anti-b inZ0 decaysrdquo hep-ex9908028

[62] M G Bowler ldquoe+eminus production of heavy quarks in the string modelrdquo Z Phys C11 (1981) 169

[63] DELPHI Collaboration J Abdallah et al ldquoA study of the b-quark fragmentation function with theDELPHI detector at LEP I and an averaged distribution obtained at the Z Polerdquo EurPhysJ C71 (2011)1557 11024748

[64] SLD Collaboration K Abe et al ldquoMeasurement of the b quark fragmentation function in Z0 decaysrdquoPhysRev D65 (2002) 092006 hep-ex0202031

[65] ATLAS Collaboration G Aad et al ldquoMeasurement of Dlowast+minus meson production in jets from ppcollisions at sqrt(s) = 7 TeV with the ATLAS detectorrdquo PhysRev D85 (2012) 052005 11124432

53

[66] M Bahr S Gieseke M Gigg D Grellscheid K Hamilton et al ldquoHerwig++ Physics and ManualrdquoEurPhysJ C58 (2008) 639ndash707 08030883

[67] T Gleisberg S Hoche F Krauss M Schonherr S Schumann et al ldquoEvent generation with SHERPA11rdquo JHEP 0902 (2009) 007 08114622

[68] G Altarelli S Forte and G Ridolfi ldquoOn positivity of parton distributionsrdquo Nucl Phys B534 (1998)277ndash296 hep-ph9806345

[69] A Sherstnev and R S Thorne ldquoParton Distributions for LO Generatorsrdquo Eur Phys J C55 (2008)553ndash575 07112473

[70] H-L Lai et al ldquoParton Distributions for Event Generatorsrdquo JHEP 04 (2010) 035 09104183

[71] V Bertone S Carrazza and J Rojo ldquoAPFEL A PDF Evolution Library with QED correctionsrdquo13101394

[72] TOTEM Collaboration G Antchev et al ldquoLuminosity-Independent Measurement of theProton-Proton Total Cross Section at

radics = 8 TeVrdquo PhysRevLett 111 (2013) no 1 012001

[73] A Donnachie and P Landshoff ldquoTotal cross-sectionsrdquo PhysLett B296 (1992) 227ndash232hep-ph9209205

[74] G A Schuler and T Sjostrand ldquoTowards a complete description of high-energy photoproductionrdquoNuclPhys B407 (1993) 539ndash605

[75] A Donnachie and P Landshoff ldquopp and pp total cross sections and elastic scatteringrdquo PhysLett B727(2013) 500ndash505 13091292

[76] T Sjostrand and P Z Skands ldquoMultiple interactions and the structure of beam remnantsrdquo JHEP 0403(2004) 053 hep-ph0402078

[77] M Bahr J M Butterworth and M H Seymour ldquoThe Underlying Event and the Total Cross Sectionfrom Tevatron to the LHCrdquo JHEP 0901 (2009) 065 08062949

[78] G Gustafson and U Pettersson ldquoDipole Formulation of QCD Cascadesrdquo NuclPhys B306 (1988) 746

[79] W T Giele D A Kosower and P Z Skands ldquoA simple shower and matching algorithmrdquo PhysRevD78 (2008) 014026 07073652

[80] M Ritzmann D Kosower and P Skands ldquoAntenna Showers with Hadronic Initial Statesrdquo PhysLettB718 (2013) 1345ndash1350 12106345

[81] ATLAS Collaboration G Aad et al ldquoMeasurement of the transverse momentum distribution ofZgamma bosons in proton-proton collisions at

radics = 7 TeV with the ATLAS detectorrdquo PhysLett

B705 (2011) 415ndash434 11072381

[82] A Buckley G Hesketh F Siegert P Skands M Vesterinen and T Wyatt ldquoEffect of QED FSR onmeasurements of Zγlowast and W leptonic final states at hadron collidersrdquo in Tools and Monte CarloWorking Group Summary Report Les Houches France 2009 arXiv10031643

[83] CDF Collaboration T Affolder et al ldquoThe transverse momentum and total cross section of e+eminus pairsin the Z boson region from pp collisions at

radics = 18 TeVrdquo PhysRevLett 84 (2000) 845ndash850

hep-ex0001021

[84] G Miu and T Sjostrand ldquoW production in an improved parton shower approachrdquo PhysLett B449(1999) 313ndash320 hep-ph9812455

[85] S Frixione P Nason and C Oleari ldquoMatching NLO QCD computations with Parton Showersimulations the POWHEG methodrdquo JHEP 0711 (2007) 070 07092092

[86] K Hamilton P Nason C Oleari and G Zanderighi ldquoMerging HWZ + 0 and 1 jet at NLO with nomerging scale a path to parton shower + NNLO matchingrdquo JHEP 1305 (2013) 082 12124504

54

[87] T Sjostrand and M van Zijl ldquoA Multiple Interaction Model for the Event Structure in HadronCollisionsrdquo PhysRev D36 (1987) 2019

[88] CMS Collaboration V Khachatryan et al ldquoObservation of Long-Range Near-Side AngularCorrelations in Proton-Proton Collisions at the LHCrdquo JHEP 1009 (2010) 091 10094122

[89] R Corke and T Sjostrand ldquoMultiparton Interactions and Rescatteringrdquo JHEP 1001 (2010) 03509111909

[90] A Ortiz P Christiansen E Cuautle I Maldonado and G Paic ldquoColor reconnection and flow-likepatterns in pp collisionsrdquo PhysRevLett 111 (2013) 042001 13036326

[91] ATLAS Collaboration G Aad et al ldquoCharged-particle multiplicities in pp interactions measured withthe ATLAS detector at the LHCrdquo New JPhys 13 (2011) 053033 10125104

[92] CMS Collaboration V Khachatryan et al ldquoTransverse-momentum and pseudorapidity distributions ofcharged hadrons in pp collisions at

radics = 7 TeVrdquo PhysRevLett 105 (2010) 022002 10053299

[93] CMS Collaboration S Chatrchyan et al ldquoMeasurement of energy flow at large pseudorapidities in ppcollisions at

radics = 09 and 7 TeVrdquo JHEP 1111 (2011) 148 11100211

[94] TOTEM Collaboration G Antchev et al ldquoMeasurement of the forward charged particlepseudorapidity density in pp collisions at

radics = 7 TeV with the TOTEM experimentrdquo EurophysLett 98

(2012) 31002 12054105

[95] P Z Skands and D Wicke ldquoNon-perturbative QCD effects and the top mass at the TevatronrdquoEurPhysJ C52 (2007) 133ndash140 hep-ph0703081

[96] CDF Collaboration T Aaltonen et al ldquoMeasurement of Particle Production and Inclusive DifferentialCross Sections in p anti-p Collisions at s(12) = 196-TeVrdquo PhysRev D79 (2009) 11200509041098

[97] H Schulz and P Skands ldquoEnergy Scaling of Minimum-Bias Tunesrdquo EurPhysJ C71 (2011) 164411033649

[98] ATLAS Collaboration G Aad et al ldquoMeasurement of underlying event characteristics using chargedparticles in pp collisions at

radics = 900GeV and 7 TeV with the ATLAS detectorrdquo PhysRev D83 (2011)

112001 10120791

[99] CMS Collaboration V Khachatryan et al ldquoStrange Particle Production in pp Collisions atradics = 09

and 7 TeVrdquo JHEP 1105 (2011) 064 11024282

[100] TASSO Collaboration W Braunschweig et al ldquoCharged Multiplicity Distributions and Correlations ine+ e- Annihilation at PETRA Energiesrdquo ZPhys C45 (1989) 193

[101] M Derrick K Gan P Kooijman J Loos B Musgrave et al ldquoStudy of Quark Fragmentation in e+ e-Annihilation at 29-GeV Charged Particle Multiplicity and Single Particle Rapidity DistributionsrdquoPhysRev D34 (1986) 3304

[102] TOPAZ Collaboration K Nakabayashi et al ldquoCharged particle multiplicities of quark and gluon jetsin e+ e- annihilation at TRISTANrdquo PhysLett B413 (1997) 447ndash452

[103] ALEPH Collaboration D Buskulic et al ldquoStudies of QCD in e+ e-rarr hadrons at E(cm) = 130-GeVand 136-GeVrdquo ZPhys C73 (1997) 409ndash420

[104] OPAL Collaboration G Alexander et al ldquoQCD studies with e+ e- annihilation data at 130-GeV and136-GeVrdquo ZPhys C72 (1996) 191ndash206

[105] DELPHI Collaboration P Abreu et al ldquoCharged particle multiplicity in e+ e-rarr q anti-q events at161-GeV and 172-GeV and from the decay of the W bosonrdquo PhysLett B416 (1998) 233ndash246

[106] OPAL Collaboration K Ackerstaff et al ldquoQCD studies with e+ e- annihilation data at 161-GeVrdquoZPhys C75 (1997) 193ndash207

55

[107] OPAL Collaboration G Abbiendi et al ldquoQCD studies with e+ e- annihilation data at 172-GeV -189-GeVrdquo EurPhysJ C16 (2000) 185ndash210 hep-ex0002012

[108] DELPHI Collaboration P Abreu et al ldquoCharged and identified particles in the hadronic decay of Wbosons and in e+ e-rarr q anti-q from 130-GeV to 200-GeVrdquo EurPhysJ C18 (2000) 203ndash228hep-ex0103031

[109] CMS Collaboration V Khachatryan et al ldquoTransverse momentum and pseudorapidity distributions ofcharged hadrons in pp collisions at

radic(s) = 09 and 236 TeVrdquo JHEP 1002 (2010) 041 10020621

[110] UA5 Collaboration G Alner et al ldquoScaling of Pseudorapidity Distributions at cm Energies Up to09-TeVrdquo ZPhys C33 (1986) 1ndash6

[111] UA5 Collaboration R Ansorge et al ldquoCharged Particle Multiplicity Distributions at 200-GeV and900-GeV Center-Of-Mass Energyrdquo ZPhys C43 (1989) 357

[112] D Bourilkov R C Group and M R Whalley ldquoLHAPDF PDF use from the Tevatron to the LHCrdquohep-ph0605240

[113] P Skands B Webber and J Winter ldquoQCD Coherence and the Top Quark Asymmetryrdquo JHEP 1207(2012) 151 12051466

[114] J Winter P Z Skands and B R Webber ldquoMonte Carlo event generators and the top quarkforwardndashbackward asymmetryrdquo EPJ Web Conf 49 (2013) 17001 13023164

[115] P Richardson and D Winn ldquoInvestigation of Monte Carlo Uncertainties on Higgs Boson searchesusing Jet Substructurerdquo EurPhysJ C72 (2012) 2178 12070380

[116] S Navin ldquoDiffraction in Pythiardquo 10053894

[117] R Ciesielski and K Goulianos ldquoMBR Monte Carlo Simulation in PYTHIA8rdquo PoS ICHEP2012(2013) 301 12051446

[118] UA5 Collaboration R Ansorge et al ldquoCharged Particle Correlations in PP Collisions at cm Energiesof 200-GeV 546-GeV and 900-GeVrdquo ZPhys C37 (1988) 191ndash213

[119] K Wraight and P Skands ldquoForward-Backward Correlations and Event Shapes as probes ofMinimum-Bias Event Propertiesrdquo EurPhysJ C71 (2011) 1628 11015215

[120] C Soslashgaard Measurement of Forward-Backward Charged Particle Correlations with ALICE PhDthesis Copenhagen University 2012

[121] E Sicking Multiplicity Dependence of Two-Particle Angular Correlations in Proton-Proton CollisionsMeasured with ALICE at the LHC PhD thesis Munster University 2012 CERN-THESIS-2012-210

[122] ALICE Collaboration G Feofilov et al ldquoForward-backward multiplicity correlations in pp collisionsin ALICE at 09 276 and 7 TeVrdquo PoS Baldin-ISHEPP-XXI (2012) 075

[123] ALICE Collaboration B Abelev et al ldquoMultiplicity dependence of two-particle azimuthalcorrelations in pp collisions at the LHCrdquo JHEP 1309 (2013) 049 13071249

[124] D Lange ldquoThe EvtGen particle decay simulation packagerdquo NuclInstrumMeth A462 (2001) 152ndash155

[125] R Corke and T Sjostrand ldquoImproved Parton Showers at Large Transverse Momentardquo EurPhysJ C69(2010) 1ndash18 10032384

[126] S Hoche F Krauss and M Schonherr ldquoUncertainties in MEPSNLO calculations of h+jetsrdquo14017971

[127] M L Mangano M Moretti F Piccinini R Pittau and A D Polosa ldquoALPGEN a generator for hardmultiparton processes in hadronic collisionsrdquo JHEP 0307 (2003) 001 hep-ph0206293

[128] J Alwall M Herquet F Maltoni O Mattelaer and T Stelzer ldquoMadGraph 5 Going Beyondrdquo JHEP1106 (2011) 128 11060522

56

[129] V Hirschi R Frederix S Frixione M V Garzelli F Maltoni et al ldquoAutomation of one-loop QCDcorrectionsrdquo JHEP 1105 (2011) 044 11030621

[130] S Alioli P Nason C Oleari and E Re ldquoA general framework for implementing NLO calculations inshower Monte Carlo programs the POWHEG BOXrdquo JHEP 1006 (2010) 043 10022581

[131] J Alwall A Ballestrero P Bartalini S Belov E Boos et al ldquoA Standard format for Les Houchesevent filesrdquo ComputPhysCommun 176 (2007) 300ndash304 hep-ph0609017

[132] S Catani F Krauss R Kuhn and B R Webber ldquoQCD Matrix Elements + Parton Showersrdquo JHEP 11(2001) 063 hep-ph0109231

[133] L Lonnblad ldquoCorrecting the color dipole cascade model with fixed order matrix elementsrdquo JHEP 0205(2002) 046 hep-ph0112284

[134] N Lavesson and L Lonnblad ldquoW+jets matrix elements and the dipole cascaderdquo JHEP 0507 (2005)054 hep-ph0503293

[135] M L Mangano M Moretti F Piccinini and M Treccani ldquoMatching matrix elements and showerevolution for top-quark production in hadronic collisionsrdquo JHEP 0701 (2007) 013hep-ph0611129

[136] S Mrenna and P Richardson ldquoMatching matrix elements and parton showers with HERWIG andPYTHIArdquo JHEP 0405 (2004) 040 hep-ph0312274

[137] L Lonnblad and S Prestel ldquoUnitarising Matrix Element + Parton Shower mergingrdquo JHEP 1302 (2013)094 12114827

[138] N Lavesson and L Lonnblad ldquoExtending CKKW-merging to One-Loop Matrix Elementsrdquo JHEP 0812(2008) 070 08112912

[139] L Lonnblad and S Prestel ldquoMerging Multi-leg NLO Matrix Elements with Parton Showersrdquo JHEP1303 (2013) 166 12117278

[140] T Pierog I Karpenko J Katzy E Yatsenko and K Werner ldquoEPOS LHC test of collectivehadronization with LHC datardquo 13060121

[141] T Sjostrand and P Z Skands ldquoBaryon number violation and string topologiesrdquo NuclPhys B659(2003) 243 hep-ph0212264

[142] ALICE Collaboration B Abelev et al ldquoProduction of Klowast(892)0 and φ(1020) in pp collisions atradics = 7 TeVrdquo EurPhysJ C72 (2012) 2183 12085717

[143] ATLAS Collaboration G Aad et al ldquoThe differential production cross section of the φ(1020) mesoninradics = 7 TeV pp collisions measured with the ATLAS Detectorrdquo 14026162

[144] COMPETE Collaboration J Cudell et al ldquoBenchmarks for the forward observables at RHIC theTevatron Run II and the LHCrdquo PhysRevLett 89 (2002) 201801 hep-ph0206172

57