high-energy-physics event generation with pythiawahl/d0/analysis/wwz/pythiav61manual2001.pdf ·...

Computer Physics Communications 135 (2001) 238–259www.elsevier.nl/locate/cpc

High-energy-physics event generation with PYTHIA 6.1

Torbjörn Sjöstranda,∗, Patrik Edénb, Christer Friberga, Leif Lönnblada, Gabriela Miua,Stephen Mrennac, Emanuel Norrbina

a Department of Theoretical Physics, Lund University, Sölvegatan 14A, S-223 62 Lund, Swedenb NORDITA, Blegdamsvej 17, DK-2100 Copenhagen, Denmark

c Physics Department, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA

Received 3 October 2000

Abstract

PYTHIA version 6 represents a merger of the PYTHIA 5, JETSET 7 and SPYTHIA programs, with many improvements. Itcan be used to generate high-energy-physics ‘events’, i.e. sets of outgoing particles produced in the interactions between twoincoming particles. The objective is to provide as accurate as possible a representation of event properties in a wide range ofreactions. The underlying physics is not understood well enough to give an exact description; the programs therefore contain acombination of analytical results and various models. The emphasis in this article is on new aspects, but a few words of generalintroduction are included. Further documentation is available on the web. 2001 Elsevier Science B.V. All rights reserved.

PACS:13.60.-r; 13.65.+i; 13.85.-t; 12.15.-y; 12.38.-t; 12.60.-i

Keywords:Event generators; Multiparticle production

NEW VERSION SUMMARY

Title of program: PYTHIA

Version number:6.154

Catalogue identifier:ADNN

Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADNN

References to most recent previous versions:Computer PhysicsCommunications 82 (1994) 74 and Computer Physics Communi-cations 101 (1997) 232, respectively

Catalogue identifiers of most recent previous versions:ACTU

Authors of most recent previous versions:T. Sjöstrand andS. Mrenna, respectively

Does the new version supersede the previous versions?:yes

Computers for which the new program is designed and others onwhich it has been tested:

Computer: DELL Precision 210 and any other machine with a For-tran 77 compiler

Installation: Lund University

* Corresponding author.E-mail address:[email protected] (T. Sjöstrand).

0010-4655/01/$ – see front matter 2001 Elsevier Science B.V. All rights reserved.PII: S0010-4655(00)00236-8

T. Sjöstrand et al. / Computer Physics Communications 135 (2001) 238–259 239

Operating system under which the new program has been tested:Red Hat Linux 6.2

Programming language used:Fortran 77; is also fully compatiblewith Fortran 90, i.e. does not make use of any obsolescent featuresof the Fortran 90 standard

Memory required to execute with typical data:about 800 kwords

No. of bits in word:32 (double precision real uses two words)

No. of processors used:1

Has the code been vectorized or parallelized?:no

No. of bytes in distributed program, including test data, etc.:379 336

Distribution format: gzip file

Keywords: QCD, standard model, beyond standard model, hardscattering, e+e− annihilation, leptoproduction, photoproduction,hadronic processes, high-p⊥ scattering, prompt photons, gaugebosons, Higgs physics, parton distribution functions, jet production,parton showers, fragmentation, hadronization, beam remnants, mul-tiple interactions, particle decays, event measures

Nature of physical problemHigh-energy collisions between elementary particles normally giverise to complex final states, with large multiplicities of hadrons, lep-tons, neutrinos and photons. The relation between these final statesand the underlying physics description is not a simple one, for twomain reasons. Firstly, we do not even in principle have a completeunderstanding of the physics. Secondly, any analytical approach ismade intractable by the large multiplicities.

Method of solutionComplete events are generated by Monte Carlo methods. The com-plexity is mastered by a subdivision of the full problem into a setof simpler separate tasks. All main aspects of the events are sim-ulated, such as hard-process selection, initial- and final-state radia-tion, beam remnants, fragmentation, decays, and so on. Thereforeevents should be directly comparable with experimentally observ-able ones. The programs can be used to extract physics from com-parisons with existing data, or to study physics at future experi-ments.

Restrictions on the complexity of the problemDepends on the problem studied.

Typical running time10–1000 events per second, depending on process studied.

Unusual features of the program:none

LONG WRITE-UP

1. Introduction

The PYTHIA and JETSET programs [1] are fre-quently used for event generation in high-energyphysics. The emphasis is on multiparticle productionin collisions between elementary particles. This in par-ticular means hard interactions in e+e−, pp and ep col-liders, although also other applications are envisaged.The programs can be used both to compare with ex-isting data, for physics studies or detector corrections,and to explore possibilities at present or future exper-iments. The programs are intended to generate com-plete events, in as much detail as experimentally ob-servable ones, within the bounds of our current under-standing of the underlying physics. The quantum me-chanical variability between events in nature is here re-placed by Monte Carlo methods, to obtain ‘correctly’both the average behaviour and the amount of fluctu-ations. Many of the components of the programs rep-

resent original research, in the sense that models havebeen developed and implemented for a number of as-pects not covered by standard theory.

Although originally conceived separately, thePYTHIA [2] and JETSET [3] programs today areso often used together that they have here beenjoined under the PYTHIA header. To this has beenadded the code of SPYTHIA [4], an extension ofPYTHIA that also covers the generation of supersym-metric processes. The current article is not intendedto give a complete survey of all the program ele-ments or all the physics — we refer to the long man-ual and further documentation on the PYTHIA webpagehttp://www.thep.lu.se/∼torbjorn/Pythia.html for this. Instead the objective is togive a survey of new features since the latest offi-cial publications, with some minimal amount of back-ground material to tie the story together. Many of theadvances are related to physics studies, which are fur-

240 T. Sjöstrand et al. / Computer Physics Communications 135 (2001) 238–259

ther described in separate articles. Others are of a moretechnical nature, or have been of too limited a scope toresult in individual publications (so far).

Some of the main topics are:• An improved simulation of supersymmetric

physics, with several new processes.• Many new processes of beyond-the-standard-model

physics, in areas such as technicolor and doubly-charged Higgses.

• An expanded description of QCD processes invirtual-photon interactions, combined with a newmachinery for the flux of virtual photons from lep-tons.

• Initial-state parton showers are matched to the next-to-leading order matrix elements for gauge bosonproduction.

• Final-state parton showers are matched to a num-ber of different first-order matrix elements for gluonemission, including full mass dependence.

• The hadronization description of low-mass stringshas been improved, with consequences especiallyfor heavy-flavour production.

• An alternative baryon production model has beenintroduced.

• Colour rearrangement is included as a new option,and several alternative Bose–Einstein descriptionsare added.

Many further examples will be given. In the process,the total size of the program code has almost doubledin the six years since the previous main publication.

The report is subdivided so that the physics newsare highlighted in Section 2 and the programming ones(plus a few more physics ones) in Section 3. Section 4contains some concluding remarks and an outlook.

2. Physics news

For the description of a typical high-energy event,an event generator should contain a simulation of sev-eral physics aspects. If we try to follow the evolutionof an event in some semblance of a time order, onemay arrange these aspects as follows:(1) Initially two beam particles are coming in to-

wards each other. Normally each particle is char-acterized by a set of parton distributions, whichdefines the partonic substructure in terms offlavour composition and energy sharing.

(2) One shower initiator parton from each beamstarts off a sequence of branchings, such as q→qg, which build up an initial-state shower.

(3) One incoming parton from each of the two show-ers enters the hard process, where then a numberof outgoing partons are produced, usually two. Itis the nature of this process that determines themain characteristics of the event.

(4) The hard process may produce a set of short-lived resonances, like the Z0/W± gauge bosons,whose decay to normal partons has to be consid-ered in close association with the hard processitself.

(5) The outgoing partons may branch as well, tobuild up final-state showers.

(6) In addition to the hard process considered above,further semihard interactions may occur betweenthe other partons of two incoming hadrons.

(7) When a shower initiator is taken out of a beamparticle, a beam remnant is left behind. This rem-nant may have an internal structure, and a netcolour charge that relates it to the rest of the finalstate.

(8) The QCD confinement mechanism ensures thatthe outgoing quarks and gluons are not ob-servable, but instead fragment to colour neutralhadrons.

(9) Normally the fragmentation mechanism can beseen as occurring in a set of separate colour sin-glet subsystems, but interconnection effects suchas colour rearrangement or Bose–Einstein maycomplicate the picture.

(10) Many of the produced hadrons are unstable anddecay further.

In the following subsections, we will survey up-dates of the above aspects, not in the same order asgiven here, but rather in the order in which they appearin the program execution, i.e. starting with the hardprocess.

2.1. Physics subprocesses

2.1.1. Process classificationsPYTHIA contains a rich selection of physics sce-

narios, with well above 200 different subprocesses,see Tables 1, 2 and 3. The process number space hastended to become a bit busy, so processes are not al-ways numbered logically. Some processes are closely


related variants of the same basic process (e.g., theproduction of a neutralino pair in processes 216–225),others are alternative formulations (e.g., Z0Z0 → h0

has to be convoluted with the flux of Z0’s aroundfermions, and thus is an approximation to fi fj →fi fjh0; when the latter was implemented the formerwas still kept). A process may also have hidden fur-ther layers of processes (e.g., H± can be produced intop decays, whichever way top is produced).

One classification of the subprocesses is accordingto the physics scenario. The following major groupsmay be distinguished:• Hard QCD processes, i.e. leading to jet production.• Soft QCD processes, such as diffractive and elastic

scattering, and minimum-bias events. Hidden in thisclass is also process 96, which is used internally forthe merging of soft and hard physics, and for thegeneration of multiple interactions.

• Heavy-flavour production, both open and hidden(i.e. as bound states like the J/ψ). Hadronizationof open heavy flavour will be discussed in Sec-tion 2.4.1. Some new processes have been addedfor closed heavy flavour, but we remind that datahere are yet not fully understood, and have givenrise to models extending on the more conventionalPYTHIA treatment [5].

• W/Z production. A first-order process such asfi fj → gW± is now quite accurately modeled bythe initial-state shower acting on fi fj → W±, seeSection 2.2.1, but the former can still be useful fora dedicated study of the high-p⊥ tail.

• Prompt-photon production.• Photon-induced processes, including Deep Inelastic

Scattering. A completely new machinery forγ ∗pand γ ∗γ ∗ physics has been constructed here, seeSection 2.1.3.

• Standard model Higgs production, where the Higgsis reasonably light and narrow, and can thereforestill be considered as a resonance.

• Gauge boson scattering processes, such asWLWL → WLWL (L = longitudinal), when thestandard model Higgs is so heavy and broad thatresonant and non-resonant contributions have to beconsidered together.

• Non-standard Higgs particle production, within theframework of a two-Higgs-doublet scenario withthree neutral (h0, H0 and A0) and two charged(H±) Higgs states. Normally associated with SUSY

(see below), but does not have to be. The Higgspair production processes were previously hiddenin process 141, but are now included explicitly.

• Production of new gauge bosons, such as a Z′, W′and R (a horizontal boson, coupling between gener-ations).

• Technicolor production, as an alternative scenarioto the standard picture of electroweak symmetrybreaking by a fundamental Higgs. Processes 149,191, 192 and 193 may be considered obsolete, sincethe other processes now include the decays to theallowed final states of theρ0

tc/ω0tc/ρ

±tc bosons, also

including interferences withγ /Z0/W±. The defaultscenario is based on [6].

• Compositeness is a possibility not only in the Higgssector, but may also apply to fermions, e.g., givingd∗ and u∗ production. At energies below the thresh-old for new particle production, contact interactionsmay still modify the standard behaviour; this is im-plemented not only for processes 165 and 166, butalso for 11, 12 and 20.

• Left–right symmetric models give rise to doublycharged Higgs states, in fact one set belonging tothe left and one to the right SU(2) gauge group. De-cays involve right-handed W’s and neutrinos. Theexisting scenario is based on [7].

• Leptoquark (LQ) production is encountered in somebeyond-the-standard-model scenarios.

• Supersymmetry (SUSY) is probably the favouritescenario for physics beyond the standard model.A rich set of processes are allowed, even if oneobeys R-parity conservation. The supersymmet-ric machinery and process selection is inheritedfrom SPYTHIA [4], however with many improve-ments in the event generation chain. Relative tothe SPYTHIA process repertoire, the main new ad-ditions is sbottom production, where a classifica-tion by mass eigenstates is necessary and manyFeynman graphs are related to the possibility tohave incoming b quarks. Many different SUSY

scenarios have been proposed, and the programis flexible enough to allow input from severalof these, in addition to the ones provided inter-nally.

Obviously the list is far from exhaustive; it is a majorproblem to keep up to date with all the new physicsscenarios and signals that are proposed and have tobe studied. One example of another physics area that


Table 1Subprocesses, Part 1: Standard model, according to the subprocess numbering of PYTHIA . ‘f’ denotes a fermion (quark orlepton), ‘Q’ a heavy quark and ‘F’ a heavy fermion

No. subprocess No. subprocess No. subprocess

Hard QCD processes:

11 fi fj → fi fj

12 fi fi → fk fk

13 fi fi → gg

28 fig→ fig

53 gg→ fk fk

68 gg→ gg

Soft QCD processes:

91 elastic scattering

92 single diffraction (XB)

93 single diffraction (AX)

94 double diffraction

95 low-p⊥ production

Open heavy flavour:

(also fourth generation)

81 fi fi → QkQk

82 gg→ QkQk

83 qi fj → Qk fl

84 gγ → QkQk

85 γ γ → FkFk

Closed heavy flavour:

86 gg→ J/ψg

87 gg→ χ0cg

88 gg→ χ1cg

89 gg→ χ2cg

104 gg→ χ0c

105 gg→ χ2c

106 gg→ J/ψγ

107 gγ → J/ψg

108 γ γ → J/ψγ

W/Z production:

1 fi fi → γ ∗/Z0

2 fi fj → W±

22 fi fi → Z0Z0

23 fi fj → Z0W±

25 fi fi → W+W−

15 fi fi → gZ0

16 fi fj → gW±

30 fig→ fiZ0

31 fig→ fkW±

19 fi fi → γZ0

20 fi fj → γW±

35 fi γ → fiZ0

36 fi γ → fkW±

69 γ γ → W+W−

70 γW± → Z0W±

Prompt photons:

14 fi fi → gγ

18 fi fi → γ γ

29 fig→ fi γ

114 gg→ γ γ

115 gg→ gγ

Deep inelastic scatt.:

10 fi fj → fi fj

99 γ ∗fi → fi

Photon-induced:

33 fi γ → fig

34 fi γ → fi γ

54 gγ → fk fk

58 γ γ → fk fk

131 fi γ ∗T → fig

132 fi γ∗L → fig

133 fi γ ∗T → fi γ

134 fi γ ∗L → fi γ

135 gγ ∗T → fi fi

136 gγ ∗L → fi fi

137 γ ∗T γ ∗

T → fi fi

138 γ ∗T γ ∗

L → fi fi

139 γ ∗L γ ∗

T → fi fi

140 γ ∗L γ ∗

L → fi fi

80 qi γ → qkπ±

Light SM Higgs:

3 fi fi → h0

24 fi fi → Z0h0

26 fi fj → W±h0

102 gg→ h0

103 γ γ → h0

110 fi fi → γh0

121 gg→ QkQkh0

122 qiqi → QkQkh0

123 fi fj → fi fjh0

124 fi fj → fk flh0

Heavy SM Higgs:

5 Z0Z0 → h0

8 W+W− → h0

71 Z0LZ0

L → Z0LZ0

L

72 Z0LZ0

L → W+L W−

L

73 Z0LW±

L → Z0LW±

L

76 W+L W−

L → Z0LZ0

L

77 W±L W±

L → W±L W±

L

has attracted much attention recently is the possibil-ity of extra dimensions on ‘macroscopic’ scales. Also,a general-purpose program can not be optimized forall kinds of processes. If a generator for some kind

of partonic configurations is already available, outsideof PYTHIA , there exists the possibility to feed this infor subsequent treatment of showers and hadroniza-tion.


Table 2Subprocesses, Part 2: Beyond the standard model non-SUSY, with notation as above


BSM neutral Higgses:

151 fi fi → H0

152 gg→ H0

153 γ γ → H0

171 fi fi → Z0H0

172 fi fj → W±H0

173 fi fj → fi fj H0

174 fi fj → fk flH0

181 gg→ QkQkH0

182 qiqi → QkQkH0

156 fi fi → A0

157 gg→ A0

158 γ γ → A0

176 fi fi → Z0A0

177 fi fj → W±A0

178 fi fj → fi fj A0

179 fi fj → fk flA0

186 gg→ QkQkA0

187 qiqi → QkQkA0

Charged Higgs:

143 fi fj → H+

161 fig→ fkH+

Higgs pairs:

297 fi fj → H±h0

298 fi fj → H±H0

299 fi fi → A0h0

300 fi fi → A0H0

301 fi fi → H+H−

New gauge bosons:

141 fi fi → γ/Z0/Z′0

142 fi fj → W′+

144 fi fj → R

Technicolor:

149 gg→ ηtc

191 fi fi → ρ0tc

192 fi fj → ρ+tc

193 fi fi → ω0tc

194 fi fi → fk fk

195 fi fj → fk fl

361 fi fi → W+L W−

L

362 fi fi → W±L π∓

tc

363 fi fi → π+tcπ

−tc

364 fi fi → γπ0tc

365 fi fi → γπ ′0tc

366 fi fi → Z0π0tc

367 fi fi → Z0π ′0tc

368 fi fi → W±π∓tc

370 fi fj → W±L Z0

L

371 fi fj → W±L π0

tc

372 fi fj → π±tc Z0

L

373 fi fj → π±tc π0

tc

374 fi fj → γπ±tc

375 fi fj → Z0π±tc

376 fi fj → W±π0tc

377 fi fj → W±π ′0tc

Compositeness:

146 eγ → e∗

147 dg→ d∗

148 ug→ u∗

167 qiqj → d∗qk

168 qiqj → u∗qk

169 qiqi → e±e∗∓

165 fi fi (→ γ ∗/Z0) → fk fk

166 fi fj (→ W±) → fk fl

Doubly-charged Higgs:

341 �i�j → H±±L

342 �i�j → H±±R

343 �±iγ → H±±

L e∓

344 �±iγ → H±±

R e∓

345 �±iγ → H±±

L µ∓

346 �±iγ → H±±

R µ∓

347 �±iγ → H±±

L τ∓

348 �±iγ → H±±

R τ∓

349 fi fi → H++L H−−

L

350 fi fi → H++R H−−

R

351 fi fj → fk flH±±L

352 fi fj → fk flH±±R

Leptoquarks:

145 qi �j → LQ

162 qg→ �LQ

163 gg→ LQLQ

164 qiqi → LQLQ

2.1.2. Parton distributionsFor cross section calculations, the hard partonic

cross section has to be convoluted with the parton dis-tributions of the incoming beam particles. The currentdefault is GRV 94L for protons [8] and SaS 1D forreal and virtual photons [9]. Some further parameter-izations are available in PYTHIA , such as the recent

CTEQ 5 proton ones [10], and a much richer reper-toire if the PDFLIB library [11] is linked.

2.1.3. Photon physicsSince before, a model for the interactions of real

photons is available, i.e. forγp andγ γ events [12].This has now been improved and extended also to in-


Table 3Subprocesses, Part 3: SUSY, with notation as above. A trailing+ on a final state indicates that the charge-conjugated oneis included as well


SUSY:

201 fi fi → eL e∗L

202 fi fi → eRe∗R

203 fi fi → eL e∗R+

204 fi fi → µLµ∗L

205 fi fi → µRµ∗R

206 fi fi → µLµ∗R+

207 fi fi → τ1τ∗1

208 fi fi → τ2τ∗2

209 fi fi → τ1τ∗2 +

210 fi fj → �L ν∗�+

211 fi fj → τ1ν∗τ +

212 fi fj → τ2ντ∗+

213 fi fi → ν�ν�∗

214 fi fi → ντ ν∗τ

216 fi fi → χ1χ1

217 fi fi → χ2χ2

218 fi fi → χ3χ3

219 fi fi → χ4χ4

220 fi fi → χ1χ2

221 fi fi → χ1χ3

222 fi fi → χ1χ4

223 fi fi → χ2χ3

224 fi fi → χ2χ4

225 fi fi → χ3χ4

226 fi fi → χ±1 χ∓

1

227 fi fi → χ±2 χ∓

2

228 fi fi → χ±1 χ∓

2

229 fi fj → χ1χ±1

230 fi fj → χ2χ±1

231 fi fj → χ3χ±1

232 fi fj → χ4χ±1

233 fi fj → χ1χ±2

234 fi fj → χ2χ±2

235 fi fj → χ3χ±2

236 fi fj → χ4χ±2

237 fi fi → gχ1

238 fi fi → gχ2

239 fi fi → gχ3

240 fi fi → gχ4

241 fi fj → gχ±1

242 fi fj → gχ±2

243 fi fi → gg

244 gg→ gg

246 fig→ qiL χ1

247 fig→ qiRχ1

248 fig→ qiL χ2

249 fig→ qiRχ2

250 fig→ qiL χ3

251 fig→ qiRχ3

252 fig→ qiL χ4

253 fig→ qiRχ4

254 fig→ qj L χ±1

256 fig→ qj L χ±2

258 fig→ qiL g

259 fig→ qiRg

261 fi fi → t1t∗1262 fi fi → t2t∗2

263 fi fi → t1t∗2+264 gg→ t1t∗1265 gg→ t2t∗2271 fi fj → qiLqj L

272 fi fj → qiRqj R

273 fi fj → qiLqj R+274 fi fj → qiLq∗

j L

275 fi fj → qiRq∗j R

276 fi fj → qiLq∗j R+

277 fi fi → qj Lq∗j L

278 fi fi → qj Rq∗j R

279 gg→ qiL q∗i L

280 gg→ qiRq∗i R

281 bqi → b1qiL

282 bqi → b2qiR

283 bqi → b1qiR + b2qiL

284 bqi → b1q∗i L

285 bqi → b2q∗i R

286 bqi → b1q∗i R + b2q∗

i L

287 qiqi → b1b∗1

288 qiqi → b2b∗2

289 gg→ b1b∗1

290 gg→ b2b∗2

291 bb→ b1b1

292 bb→ b2b2

293 bb→ b1b2

294 bg→ b1g

295 bg→ b2g

296 bb→ b1b∗2+

clude virtual photons, i.e.γ ∗p andγ ∗γ ∗ events [13].It is especially geared towards the transition regionof rather small photon virtualitiesQ2 � 10 GeV2,where the physics picture is rather complex, while it

may be overkill for largeQ2, where the picture againsimplifies.

Photon interactions are complicated since the pho-ton wave function contains so many components, each


with its own interactions. To first approximation, itmay be subdivided into a direct and a resolved part.(In higher orders, the two parts can mix, so one hasto provide sensible physical separations between thetwo.) In the former the photon acts as a pointlike parti-cle, while in the latter it fluctuates into hadronic states.These fluctuations are ofO(αem), and so correspond toa small fraction of the photon wave function, but thisis compensated by the bigger cross sections allowedin strong-interaction processes. For real photons there-fore the resolved processes dominate the total crosssection, while the pointlike ones take over for virtualphotons.

The fluctuationsγ → qq(→ γ ) can be character-ized by the transverse momentumk⊥ of the quarks,or alternatively by some mass scalem 2k⊥, with aspectrum of fluctuations∝ dk2⊥/k2⊥. The low-k⊥ partcannot be calculated perturbatively, but is instead para-meterized by experimentally determined couplings tothe lowest-lying vector mesons,V = ρ0, ω0, φ0 andJ/ψ , an ansatz called VMD for Vector Meson Dom-inance. Parton distributions are defined with a unitmomentum sum rule within a fluctuation [9], givingrise to total hadronic cross sections, jet activity, mul-tiple interactions and beam remnants as in hadronicinteractions. States at largerk⊥ are called GVMD orGeneralized VMD, and their contributions to the par-ton distribution of the photon are called anomalous.Given a dividing linek0 0.5 GeV to VMD states,the parton distributions are perturbatively calculable.The total cross section of a state is not, however, sincethis involves aspects of soft physics and eikonalizationof jet rates. Therefore an ansatz is chosen where thetotal cross section scales likek2

V /k2⊥, where the ad-justable parameterkV ≈ mρ/2 for light quarks. Thespectrum of states is taken to extend over a rangek0 < k⊥ < k1, wherek1 is identified with thep⊥min(s)

defined in Eq. (6) below. There is some arbitrariness inthat choice, and for jet rate calculations also contribu-tions to the parton distributions from above this regionare included.

If the photon is virtual, it has a reduced probabil-ity to fluctuate into a vector meson state, and this statehas a reduced interaction probability. This can be mod-eled by a traditional dipole factor(m2

V /(m2V + Q2))2

for a photon of virtualityQ2, wheremV → 2k⊥ for a

GVMD state. Putting it all together, the cross sectionof the GVMD sector then scales likek2

1∫

k20

dk2⊥k2⊥

k2V

k2⊥

(4k2⊥

4k2⊥ + Q2

)2

. (1)

A real direct photon in aγp collision can interactwith the parton content of the proton:γq → qg andγg → qq. Thep⊥ in this collision is taken to exceedk1, in order to avoid double-counting with the interac-tions of the GVMD states. For a virtual photon the DIS(deeply inelastic scattering) processγ ∗q → q is alsopossible, but by gauge invariance its cross section mustvanish in the limitQ2 → 0. At largeQ2, the directprocesses can instead be considered as theO(αs) cor-rection to the lowest-order DIS process. The DISγ ∗pcross section is here proportional to the structure func-tion F2(x,Q

2) with the Bjorkenx = Q2/(Q2 + W2).Since normal parton distribution parameterizations arefrozen below someQ0 scale and therefore do notobey the gauge invariance condition, an ad hoc fac-tor (Q2/(Q2 +m2

ρ))2 is introduced for the conversion

from the parameterizedF2(x,Q2) = ∑

e2q q(x,Q2) to

a σγ ∗pDIS . In order to avoid double-counting between

DIS and direct events, we decide to introduce a re-quirementp⊥ > max(k1,Q) on direct events. In theremaining DIS ones, thusp⊥ < Q. The DIS rateshould be reduced accordingly, by a Sudakov formfactor giving the probability not to have an interac-tion above scaleQ, which can be approximated by

exp(−σγ ∗pdirect/σ

γ ∗pDIS ).

Note that theQ2 dependence of the DIS and directprocesses is implemented in the matrix element ex-pressions. This is different from VMD/GVMD, wheredipole factors are used to reduce the assumed flux ofpartons inside a virtual photon relative to those of areal one, but the matrix elements contain no parton vir-tuality dependence.

After some further minor corrections for double-counting, we arrive at a picture of hadronicγ ∗p eventsas being composed of four main components: VMD,GVMD, direct and DIS. Most of these in their turnhave a complicated internal structure, as we have seen.The γ ∗γ ∗ collision between two inequivalent pho-tons contains 13 components: four when the VMDand GVMD states interact with each other (‘double-resolved’), eight with a direct or DIS photon inter-


action on a VMD or GVMD state on either side(‘single-resolved’, including the traditional DIS), andone where two direct photons interact by the processγ ∗γ ∗ → qq (‘direct’, not to be confused with the di-rect process ofγ ∗p).

Several further aspects can be added to the abovemachinery. The impact of resolved longitudinal pho-tons is unknown, except that it has to vanish in thelimit Q2 → 0, and can be approximated by someQ2-dependent enhancement of the normal transverseone. For a complete description of ep events or e+e−two-photon ones, a convolution with thex- andQ2-dependent flux of virtual photons inside an electron isalso now provided.

2.1.4. SupersymmetryPYTHIA simulates the Minimal Supersymmetric

Standard Model (MSSM), based on an effective La-grangian of softly-broken SUSY with parameters de-fined at the weak scale, which is typically betweenmZand 1 TeV. The MSSM particle spectrum is minimal inthe sense that it includes only the partners of all Stan-dard Model particles (presently without massive neu-trinos), a two-Higgs doublet — one Higgs Hu couplingonly to up-type fermions and one Hd coupling only todown-type fermions — and partners, and the gravitino.Once the parameters of the softly-broken SUSY La-grangian are specified, the interactions are fixed, andthe sparticle masses can be calculated [14].

The masses of the scalar partners to fermions,sfermions, depend on soft scalar masses, trilinear cou-plings, the Higgsino massµ, and tanβ , the ratioof Higgs vacuum expectation values〈Hu〉/〈Hd〉. Themasses of the fermion partners to the gauge and Higgsbosons, the neutralinos and charginos, depend on softgaugino masses,µ, and tanβ . Finally, the propertiesof the Higgs scalar sector is calculated from the inputpseudoscalar Higgs boson massmA, tanβ , µ, trilinearcouplings and the sparticle properties in an effectivepotential approach [15]. Of course, these calculationsalso depend on SM parameters (mt,mZ, αs, etc.). Anymodifications to these quantities from virtual MSSMeffects are not taken into account. In principle, thesparticle masses also acquire loop corrections that de-pend on all MSSM masses.

R-parity conservation is assumed (at least on thetime and distance scale of a typical collider experi-ment), and only lowest order, sparticle pair produc-

tion processes are included. Only those processes withe+e−, µ+µ−, or quark and gluon initial states are sim-ulated. Likewise, only R-parity conserving decays areallowed, so that one sparticle is stable, either the light-est neutralino, the gravitino, or a sneutrino. SUSY de-cays of the top quark are included, but all other SMparticle decays are unaltered.

Various improvements to the simulation are be-ing implemented in stages. Some of these can havea significant impact on the collider phenomenology.Among these are: the generalization to complex-valued soft SUSY-breaking parameters in the neu-tralino and chargino sector; the same in the Higgs sec-tor, which removes the possibility of CP-even or CP-odd labels; the calculation of neutralino and charginodecay rates which are accurate for large tanβ ; andmatrix element weighting of particle distributions inthree-body decays.

2.1.5. Strong dynamics in electroweak symmetrybreaking

The simulation of strong dynamics associated withelectroweak symmetry breaking in PYTHIA is basedon an effective Lagrangian for the lightest resonancesof a technicolor (TC)-like model. In TC, the break-ing of a chiral symmetry in a new, strongly inter-acting gauge theory generates the Goldstone bosonsnecessary for electroweak symmetry breaking. Boundstates of technifermions provide a QCD-like spectrumof technipions (πtc), technirhos (ρtc), techniomegas(ωtc), etc. The mass hierarchies, however, are unlikeQCD because of the behavior of the gauge couplingsin realistic models of extended TC (ETC). The diffi-culties of ETC in explaining the top quark mass whilesuppressing FCNC’s is circumvented by the additionof topcolor interactions, which provide the bulk ofmt.

In ETC models, hard mass contributions to tech-nipion masses make decays likeρtc → πtcπtc kine-matically inaccessible. Instead, decays likeρew

tc →πew

tc WL, for example, dominate, where ew denotesconstituent technifermions with only electroweakquantum numbers and WL is a longitudinal W bosons.As a result, the ew technirho and techniomega tend tohave small total widths.

Effective couplings are derived in the valence tech-nifermion approximation, and the techniparticle de-cays can be calculated directly [6]. Technirhos andtechniomegas are produced through kinematic mixing


with gauge bosons, leading to final states containingStandard Model particles and/or pseudo-Goldstonebosons (technipions).

As an additional wrinkle, SUc(3) non-singlet statesare included along with the coloron of topcolor as-sisted technicolor. In this case, colored technirhos (andthe coloron) can have substantial total widths and en-hanced couplings to bottom and top quarks.

2.2. QCD radiation

The matrix-element (ME) and parton-shower (PS)approaches to higher-order QCD corrections both havetheir advantages and disadvantages. The former offersa systematic expansion in orders ofαs, and a pow-erful machinery to handle multi-parton configurationson the Born level, but loop calculations are tough andlead to messy cancellations at small resolution scales.Resummed matrix elements may circumvent the latterproblem for specific quantities, but then do not pro-vide exclusive accompanying events. Parton showersare based on an improved leading-log (almost next-to-leading-log) approximation, and so cannot be accu-rate for well separated partons, but they offer a simple,process-independent machinery that gives a smoothblending of event classes (by Sudakov form factors)and a sensible match to hadronization. It is thereforenatural to try to combine these descriptions, so thatME results are recovered for widely separated partonswhile the PS sets the sub-jet structure.

For final-state showers in Z0 → qq, where q isassumed essentially massless, such solutions are thestandard since long [16], e.g., by letting the showerslightly overpopulate the qqg phase space and then us-ing a Monte Carlo veto technique to reduce down tothe ME level.

2.2.1. Initial-state showersA similar technique is now available for the descrip-

tion of initial-state radiation in the production of a sin-gle colour-singlet resonance, such asγ ∗/Z0/W± [17].The basic idea is to map the kinematics between the PSand ME descriptions, and to find a correction factorthat can be applied to hard emissions in the shower soas to bring agreement with the matrix-element expres-sion. The PYTHIA shower kinematics definitions arebased onQ2 as the spacelike virtuality of the partonproduced in a branching andz as the factor by which

the s of the scattering subsystem is reduced by thebranching. Some simple algebra then shows that thetwo qq′ → gW± emission rates disagree by a factor

Rqq′→gW(s, t ) = (dσ /dt )ME

(dσ /dt )PS= t2 + u2 + 2m2

Ws

s2 + m4W

,

(2)

which is always between 1/2 and 1. The shower cantherefore be improved in two ways, relative to the olddescription. Firstly, the maximum virtuality of emis-sions is raised fromQ2

max ≈ m2W to Q2

max = s, i.e. theshower is allowed to populate the full phase space.Secondly, the emission rate for the final (which nor-mally also is the hardest) q→ qg emission on eachside is corrected by the factorR(s, t ) above, so asto bring agreement with the matrix-element rate inthe hard-emission region. In the backwards evolutionshower algorithm [18], this is the first branching con-sidered.

The other possibleO(αs) graph is qg→ q′W±,where the corresponding correction factor is

Rqg→q′W(s, t ) = (dσ /dt )ME

(dσ /dt )PS= s2 + u2 + 2m2

Wt

(s − m2W)2 + m4

W

,

(3)

which lies between 1 and 3. A probable reason forthe lower shower rate here is that the shower doesnot explicitly simulate thes-channel graph qg→q∗ → q′W. The g→ qq branching therefore has to bepreweighted by a factor of 3 in the shower, but other-wise the method works the same as above. Obviously,the shower will mix the two alternative branchings,and the correction factor for a final branching is basedon the current type.

The reweighting procedure prompts some otherchanges in the shower. In particular,u < 0 translatesinto a constraint on the phase space of allowed branch-ings, not previously implemented.

Our published comparisons with data on thep⊥Wspectrum show quite a good agreement with this im-proved simulation [17]. A worry was that an unexpect-edly large primordialk⊥, around 4 GeV, was requiredto match the data in the low-p⊥W region. However,at that time we had not realized that the data were notfully unsmeared. The required primordialk⊥ thereforedrops by about a factor of two [19].

The method can also be used for initial-state photonemission, e.g., in the process e+e− → γ ∗/Z0. There


the old defaultQ2max = m2

Z allowed no emission atlargep⊥, p⊥ � mZ at LEP2. This is now correctedby the increasedQ2

max= s, and using theR of Eq. (2)with mW → mZ.

The above method does not address the issue ofnext-to-leading order corrections to the total W crosssection, which instead can be studied with more so-phisticated matching procedures [20]. Also extensionsto other processes can be considered in the future.

There are also some other changes to the initial stateradiation algorithm:• The cut on minimum gluon energy emitted in a

branching is modified by an extra factor roughlycorresponding to the 1/γ factor for the boost to thehard subprocess frame. Earlier, when a subsystemwas strongly boosted, the minimum energy require-ment became quite stringent on the low-energy in-coming side, and could cut out much radiation.

• The angular-ordering requirement is now based onorderingp⊥/p rather thanp⊥/pL, i.e. replacingtanθ by sinθ . Earlier the starting value(tanθ)max=10 could actually be violated by some bona fideemissions for strongly boosted subsystems.

• TheQ2 value of the backwards evolution of a heavyquark like c in a proton beam is by force kept abovem2

c, so as to ensure that the branching g→ cc is not‘forgotten’ by evolvingQ2 belowQ2

0. Thereby thepossibility of having a c in the beam remnant properis eliminated [21]. The procedure is not forced fora photon beam, where charm occurs as part of thevalence flavour content.

• For incomingµ± (or τ±) beams the kinematicalvariables are better selected to represent the differ-ences in lepton mass, and the lepton-inside-leptonparton distributions are properly defined.

2.2.2. Final-state showersThe traditional final-state shower algorithm in

PYTHIA [16] is based on an evolution inQ2 = m2,i.e. potential branchings are considered in order ofdecreasing mass. A branchinga → bc is then char-acterized bym2

a and z = Eb/Ea . For the processγ ∗/Z0 → qq, the first gluon emission off both q andq are corrected to the first-order matrix elements forγ ∗/Z0 → qqg. (Theαs and the Sudakov form fac-tor are omitted from the comparison, since the showerprocedure here attempts to include higher-order effectsabsent in the first-order matrix elements.)

This matching is well-defined for massless quarks,and was originally used unchanged for massive ones.A first attempt to include massive matrix elementsdid not compensate for mass effects in the showerkinematics, and therefore came to exaggerate the sup-pression of radiation off heavy quarks [22]. Now theshower has been modified to solve this issue, and alsoimproved and extended to cover better a host of differ-ent reactions [23].

The starting point is the calculation of processesa → bc anda → bcg, where the ratio

WME(x1, x2) = 1

σ(a → bc)

dσ(a → bcg)

dx1 dx2(4)

gives the process-dependent differential gluon-emission rate. Here the phase space variables arex1 = 2Eb/ma and x2 = 2Ec/ma , expressed in therest frame of partona. Using the standard modeland the minimal supersymmetric extension thereof astemplates, a wide selection of colour and spin struc-tures have been addressed, exemplified by Z0 → qq,t → bW+, H0 → qq, t→ bH+, Z0 → qq, q → q′W+,H0 → qq, q → q′H+, χ → qq, q → qχ , t → tχ , g →qq, q → qg, and t→ tg. The mass ratiosr1 = mb/ma

and r2 = mc/ma have been kept as free parameters.When allowed, processes have been calculated for anarbitrary mixture of “parities”, i.e. without or witha γ5 factor, like in the vector/axial vector structure ofγ ∗/Z0. All the matrix elements are encoded in the newfunction PYMAEL(NI,X1,X2,R1,R2,ALPHA),whereNI distinguishes the matrix elements andAL-PHA is related to theγ5 admixture.

In order to match to the singularity structure of themassive matrix elements, the evolution variableQ2 ischanged fromm2 to m2 − m2

on-shell, i.e. 1/Q2 is thepropagator of a massive particle. Furthermore, thez

variable of a branching needs to be redefined, which isachieved by reducing the three-momenta of the daugh-ters in the rest frame of the mother. For the showerhistoryb → bg this gives a differential probability

WPS,1(x1, x2) = αs

2πCF

dQ2

Q2

2 dz

1− z

1

dx1 dx2

= αs

2πCF

2

x3 (1+ r22 − r2

1 − x2), (5)

where the numerator 1+ z2 of the splitting kernel forq → qg has been replaced by a 2 in the shower algo-rithm. For a process with only one radiating parton in


the final state, such as t→ bW+, the ratioWME/WPS,1gives the acceptance probability for an emission inthe shower. The singularity structure exactly agreesbetween ME and PS, giving a well-behaved ratio al-ways below unity. If bothb andc can radiate, there isa second possible shower history that has to be con-sidered. The matrix element is here split in two parts,one arbitrarily associated withb → bg branchings andthe other withc → cg ones. A convenient choice isWME,1 = WME(1 + r2

1 − r22 − x1)/x3 and WME,2 =

WME(1+ r22 − r2

1 − x2)/x3, which again gives match-ing singularity structures inWME,i/WPS,i and thus awell-behaved Monte Carlo procedure.

Also subsequent emissions of gluons off the pri-mary particles are corrected toWME. To this end, areduced-energy system is constructed, which retainsthe kinematics of the branching under considerationbut omits the gluons already emitted, so that an ef-fective three-body shower state can be mapped to an(x1, x2, r1, r2) set of variables. For light quarks thisprocedure is almost equivalent with the original oneof using the simple universal splitting kernels after thefirst branching. For heavy quarks it offers an improvedmodelling of mass effects also in the collinear region.

Some further changes have been introduced, a fewminor as default and some more significant ones asnon-default options [23]. This includes the descriptionof coherence effects andαs arguments, in general andmore specifically for secondary heavy flavour produc-tion by gluon splittings.

Further issues remain to be addressed, e.g., radia-tion off particles with non-negligible width. In gen-eral, however, the new shower should allow an im-proved description of gluon radiation in many differentprocesses.

2.3. Beam remnants and multiple interactions

2.3.1. Beam remnantsIn a hadron–hadron collision, the initial-state radi-

ation algorithm reconstructs one shower initiator ineach beam, by backwards evolution from the hard scat-tering. This initiator only takes some fraction of the to-tal beam energy, leaving behind a beam remnant thattakes the rest. Since the initiator is coloured, so is theremnant. It is therefore colour-connected to the hardinteraction, and forms part of the same fragmentingsystem. Often the remnant can be complicated, e.g., a

g initiator would leave behind a uud proton-remnantsystem in a colour octet state, which can convenientlybe subdivided into a colour triplet quark and a colourantitriplet diquark, each of which are colour-connectedto the hard interaction. The energy sharing betweenthese two remnant objects, and their relative transversemomentum, introduces additional nonperturbative de-grees of freedom. Some of the default values have re-cently been updated [21].

One would expect an ep event to have only onebeam remnant, and an e+e− event none. This is not al-ways correct, e.g., aγ γ → qq interaction in an e+e−event would leave behind the e+ and e− as beam rem-nants. The photons may in their turn leave behind rem-nants.

It is customary to assign a primordial transverse mo-mentum to the shower initiator, to take into accountthe motion of quarks inside the original hadron, basi-cally as required by the uncertainty principle. A num-ber of the order of〈k⊥〉 ≈ mp/3 ≈ 300 MeV couldtherefore be expected. However, in hadronic collisionsmuch higher numbers than that are often required todescribe data, typically of the order of 1 GeV [19,24]if a Gaussian parameterization is used. (This numberis now the default.) Thus, an interpretation as a purelynonperturbative motion inside a hadron is difficult tomaintain.

Instead a likely culprit is the initial-state shower al-gorithm. This is set up to cover the region of hardemissions, but may miss out on some of the softeractivity, which inherently borders on nonperturbativephysics. By default, the shower does not evolve downto scales belowQ0 = 1 GeV. Any shortfall in showeractivity around or below this cutoff then has to be com-pensated by the primordialk⊥ source, which therebylargely loses its original meaning.

2.3.2. Multiple interactionsMultiple parton–parton interactions is the concept

that, based on the composite nature of hadrons, severalparton pairs may interact in a typical hadron–hadroncollision [25]. Over the years, evidence for this mech-anism has accumulated, such as the recent direct ob-servation by CDF [26]. The occurrences with two par-ton pairs at reasonably largep⊥ just form the top ofthe iceberg, however. In the PYTHIA model, most in-teractions are at lowerp⊥, where they are not visi-ble as separate jets but only contribute to the underly-


ing event structure. As such, they are at the origin ofa number of key features, like the broad multiplicitydistributions, the significant forward–backward multi-plicity correlations, and the pedestal effect under jets.

Since the perturbative jet cross section is divergentfor p⊥ → 0, it is necessary to regularize it, e.g., by acut-off at somep⊥min scale. That such a regularizationshould occur is clear from the fact that the incominghadrons are colour singlets — unlike the coloured par-tons assumed in the divergent perturbative calculations— and that therefore the colour charges should screeneach other in thep⊥ → 0 limit. Also other dampingmechanisms are possible [27]. Fits to data typicallygivep⊥min ≈ 2 GeV, which then should be interpretedas the inverse of some colour screening length in thehadron.

One key question is the energy-dependence ofp⊥min; this may be relevant, e.g., for comparisons ofjet rates at different Tevatron energies, and even morefor any extrapolation to LHC energies. The problemactually is more pressing now than at the time of theoriginal study [25], since nowadays parton distribu-tions are known to be rising more steeply at smallx than the flatxf (x) behaviour normally assumedfor small Q2 before HERA. This translates into amore dramatic energy dependence of the multiple-interactions rate for a fixedp⊥min.

The larger number of partons also should increasethe amount of screening, however, as confirmed bytoy simulations [28]. As a simple first approximation,p⊥min is assumed to increase in the same way as thetotal cross section, i.e. with some powerε ≈ 0.08 [29]that, via reggeon phenomenology, should relate to thebehaviour of parton distributions at smallx andQ2.Thus the new default in PYTHIA is

p⊥min(s) = (1.9 GeV)

(s

1 TeV2

)0.08

. (6)

2.4. Fragmentation and decays

QCD perturbation theory, formulated in terms ofquarks and gluons, is valid at short distances. At longdistances, QCD becomes strongly interacting and per-turbation theory breaks down. In this confinementrégime, the coloured partons are transformed intocolourless hadrons, a process called either hadroniza-tion or fragmentation.

The fragmentation process has yet to be under-stood from first principles, starting from the QCD La-grangian. This has left the way clear for the develop-ment of a number of different phenomenological mod-els. PYTHIA is intimately connected with string frag-mentation, in the form of the time-honoured ‘Lundmodel’ [30]. This is the default for all applications.Improvements have been made in some areas, how-ever.

2.4.1. Low-mass stringsA hadronic event is conventionally subdivided into

sets of partons that form separate colour singlets.These sets are represented by strings, that, e.g., stretchfrom a quark end via a number of intermediate gluonsto an antiquark end. Three string mass regions may bedistinguished for the hadronization.(1) Normal string fragmentation. In the ideal situa-

tion, each string has a large invariant mass. Thenthe standard iterative fragmentation scheme [30,31] works well. In practice, this approach can beused for all strings above some cut-off mass of afew GeV.

(2) Cluster decay. If a string is produced with a smallinvariant mass, maybe only two-body final statesare kinematically accessible. The traditional it-erative Lund scheme is then not applicable. Wecall such a low-mass string a cluster, and con-sider it separately from above. In recent programversions, the modeling has now been improvedto give a smooth match on to the standard stringscheme in the high-cluster-mass limit [21].

(3) Cluster collapse. This is the extreme case of theabove situation, where the string mass is so smallthat the cluster cannot decay into two hadrons. Itis then assumed to collapse directly into a sin-gle hadron, which inherits the flavour content ofthe string endpoints. The original continuum ofstring/cluster masses is replaced by a discrete setof hadron masses. Energy and momentum thencannot be conserved inside the cluster, but mustbe exchanged with the rest of the event. This de-scription has also been improved [21].

String systems below a threshold mass are handledby the cluster machinery. In it, an attempt is first madeto produce two hadrons, by having the string break inthe middle by the production of a new qq pair, withflavours and hadron spins selected according to the


normal string rules. If the sum of the hadron massesis larger than the cluster mass, repeated attempts canbe made to find allowed hadrons; the default is twotries. If an allowed set is found, the angular distribu-tion of the decay products in the cluster rest framed ispicked isotropically near the threshold, but then grad-ually more elongated along the string direction, to pro-vide a smooth match to the string description at largermasses. This also includes a forward–backward asym-metry, so that each hadron is preferentially in the samehemisphere as the respective original quark it inher-its.

If the attempts to find two hadrons fail, one sin-gle hadron is formed from the given flavour content.The basic strategy thereafter is to exchange some min-imal amount of energy and momentum between thecollapsing cluster and other string pieces in the neigh-bourhood. The momentum transfer can be in either di-rection, depending on whether the hadron is lighter orheavier than the cluster it comes from. When lighter,the excess momentum is split off and put as an ex-tra ‘gluon’ on the nearest string piece, where ‘near-est’ is defined by a space–time history-based distancemeasure. When the hadron is heavier, momentum isinstead borrowed from the endpoints of the neareststring piece.

The free parameters of the model can be tunedto data, especially to the significant asymmetries ob-served between the production of D andD mesons inπ−p collisions, with hadrons that share some of theπ− flavour content very much favoured at largexF intheπ− fragmentation region [32]. These spectra andasymmetries are closely related to the cluster collapsemechanism, and also to other effects of the colourtopology of the event (‘beam drag’) [21]. Also otherparameters enter the description, however, such as theeffective charm mass and the beam remnant structure.

2.4.2. Baryon productionA new advanced scheme has been introduced for

baryon production with the popcorn mechanism [33],plus some minor changes to the older popcornscheme [34]. These new features currently only ap-pear as options, with the default unchanged, and canbe separated into three parts.

Firstly, an improved implementation of SU(6)weights for baryon production. This should not be re-garded as a new model, rather a more correct imple-

mentation of the old. However, in order to enable theuser to see the effects of the SU(6) weighting sepa-rately, both procedures are available as different op-tions. The main change is that, if a step q→ B + qq′is SU(6)-rejected, the new try may now instead give aq → M + q′ step (where B stands for baryon, M formeson). The old procedure leads to a slightly fasteralgorithm and a better interpretation of the input para-meter for the diquark-to-quark production rate. How-ever, the probability that a quark will produce a baryonand a antidiquark is then flavour independent, whichis not in agreement with the model. Further, for qq→M + qq′, SU(6) symmetry is included in the weightsfor qq′, while qq is kept with unit probability. The pro-cedures for qq→ B+q′ and a final joining qq+q→ Bare unchanged.

Secondly, a suppression of diquark vertices occur-ing at small proper times. This is based on a study ofthe production dynamics of the three quarks that forma baryon. The main experimental consequence is asuppression of the baryon production rate at large mo-mentum fraction. This in particular implies a smallerrate of first-rank light baryon production, while charmand bottom baryons are less affected (since the pro-duction proper time is larger for a heavy hadron thana light one of the same momentum). It thereby substi-tutes and explains the older brute-force possibility tosuppress the production of first-rank baryons.

Thirdly, a completely new flavour algorithm forbaryons and popcorn mesons, also using the small-proper-time suppression above. While the old pop-corn alternative allowed at most one meson to beproduced in between the baryon and the antibaryon,the new model allows an arbitrary number. The newflavour model makes explicit use of the popcorn sup-pression factor exp(−2m⊥M⊥/κ), wherem⊥ is thetransverse mass of the quark creating the colour fluc-tuation,M⊥ is the total invariant transverse mass ofthe popcorn meson system, andκ is the string ten-sion constant. Thus two parameters, representing themean 2m⊥/κ for light quarks and s-quarks, respec-tively, govern both diquark and popcorn meson pro-duction. A corresponding parameter is introduced forthe fragmentation of strings that contain diquarks al-ready from the beginning, i.e. baryon remnants. Thenew procedure therefore requires far fewer parametersthan the old one, and still provides a comparable qual-ity in the description of the various baryon production


rates. This was investigated in detail in [35]. (The con-cluding worry of an “improper treatment” was causedby an unfortunate misunderstanding and can be disre-garded.) Other features, such as baryon correlations,are also modified.

Several new routines have been added, and the di-quark code has been extended with information aboutthe curtain quark flavour, i.e. the qq pair that is sharedbetween the baryon and antibaryon, but this is not vis-ible externally. Some parameters are no longer used,while others have to be given modified values, as de-scribed in the long writeup.

2.4.3. Interconnection effectsThe widths of the W, Z and t are all of the order

of 2 GeV. A standard model Higgs with a mass above200 GeV, as well as many supersymmetric and otherbeyond the standard model particles would also havewidths in the multi-GeV range. Not far from threshold,the typical decay timesτ = 1/Γ ≈ 0.1 fm � τhad ≈1 fm. Thus hadronic decay systems overlap, between aresonance and the underlying event, or between pairsof resonances, so that the final state may not containindependent resonance decays.

So far, studies have mainly been performed in thecontext of W pair production at LEP2. Pragmatically,one may here distinguish three main eras for such in-terconnection:(1) Perturbative: this is suppressed for gluon energies

ω > Γ by propagator/timescale effects; thus onlysoft gluons may contribute appreciably.

(2) Nonperturbative in the hadroformation process:normally modeled by a colour rearrangement be-tween the partons produced in the two resonancedecays and in the subsequent parton showers.

(3) Nonperturbative in the purely hadronic phase: bestexemplified by Bose–Einstein effects.

The above topics are deeply related to the unsolvedproblems of strong interactions: confinement dynam-ics, 1/N2

C effects, quantum mechanical interferences,etc. Thus they offer an opportunity to study the dy-namics of unstable particles, and new ways to probeconfinement dynamics in space and time [36,37],butthey also risk to limit or even spoil precision measure-ments.

The reconnection scenarios outlined in [37] are nowavailable, plus also an option along the lines suggestedin [38]. Currently they can only be invoked in process

25, e+e− → W+W− → q1q2q3q4, which is the mostinteresting one for the foreseeable future. (Process 22,e+e− → γ ∗/Z0 γ ∗/Z0 → q1q2q3q4 can also be used,but the travel distance is calculated based only on theZ0 propagator part.) If normally the event is consid-ered as consisting of two separate colour singlets, q1q2from the W+ and q3q4 from the W−, a colour re-arrangement can give two new colour singlets q1q4and q3q2. It therefore leads to a different hadronic finalstate, although differences usually turn out to be subtleand difficult to isolate [39]. When also gluon emissionis considered, the number of potential reconnectiontopologies increases. Apart from the overall rate of re-connection, the scenarios in PYTHIA differ in the rel-ative probability assigned to each of these topologies,based on their properties in momentum space and/orspace–time. For instance, scenario I is based on ananalogy with type I superconductors, with the colourfield represented by extended flux tubes. By contrast,scenario II assumes that narrow vortex lines carry allthe topological information, like in type II supercon-ductors, even if the full energy is stored over a widerregion.

Bose–Einstein effects are simulated in a simpli-fied manner, by introducing small momentum shifts inidentical final-state mesons (primarilyπ± andπ0) soas to bring them closer to each other [40]. The shiftscan be chosen to reproduce a desired BE enhancement

shape for small relative momentumQ =√

m2ij − 4m2

i

between identical bosonsi andj . Typically the shapeis chosen as a Gaussian,f2(Q) = 1+ λexp(−Q2R2),with λ andR two free parameters. The input is onlyexactly reproduced in the limit of an isotropic and low-density initial particle distribution; since these condi-tions are not completely fulfilled in reality, there aredistortions [41], for better or worse. (The nontrivialthree-particle correlations in data are described qual-itatively, although not quantitatively.)

A major shortcoming of the algorithm is that energyis not automatically conserved, even though three-momentum is. In the original algorithm, this wassolved by a uniform rescaling of all three-momenta,with undesirable side effects, e.g., when studying BEeffects in W+W− hadronic final states. In the currentversion, several new options have been added that,based on different principles, instead shifts pairs apart.


The default one, BE32, operates on identical particles,introducing an extra factor

1+ αλexp(−Q2R2/9

){1− exp(−Q2R2/4)

}(7)

to f2(Q). Hereα is a negative number adjusted eventby event for overall energy conservation, with〈α〉 ≈−0.25. This scenario can be viewed as a simplifiedversion of a dampened oscillating correlation function,where only the first peak and dip has been retained.Further new options have also been introduced specif-ically geared towards studies of W+W− hadronicevents, e.g., to include the effects of the separated W+and W− decay vertices.

2.4.4. DecaysTwo separate decay treatments exist in PYTHIA .

One is making use of a set of tables where branchingratios and decay modes are stored, and is used, e.g.,for hadronic decays, where branching ratios normallycannot be calculated from first principles.

The other treatment is used for a set of fundamen-tal resonances in or beyond the standard model, suchas t, Z0, W±, h0, supersymmetric particles, and manymore. Characteristic here is that these resonances haveperturbatively calculable widths to each of their de-cay channels. The decay products are typically quarks,leptons, or other resonances. In decays to quarks, par-ton showers are automatically added to give a morerealistic multijet structure, and one may also allowphoton emission off leptons. If the decay products inturn are resonances, further decays are necessary. Of-ten spin information is available in resonance decaymatrix elements, leading to nonisotropic decays. Thispart has been improved in several processes, but is stillmissing in many others.

The routine used to calculate the partial and totalwidth of resonances (now expressed in GeV through-out), has been expanded for all the new particles anddecay modes introduced. Some alternative calculationschemes have also been adopted, e.g., based on a sim-ple rescaling of the on-shell widths rather than a com-plete recalculation (which may at times not be feasi-ble) based on the current mass.

The width to be used in the denominator of a res-onance propagator is only well-defined near the peak.Well away from the peak, an unfortunate choice maylead to a loss of cancellation between resonant andnonresonant diagrams. A special problem exists for

a massive standard model Higgs, where the widthΓh ∝ m3

h is so large that the choice ofs dependence ofthe width significantly influences the resonance peakshape. Following [42], the default now isΓh ∝ m2

h

√s.

3. Program news

Essentially all of the basic philosophy and frame-work remain from the previous PYTHIA and JETSET

versions, so no user familiar with these should feel atloss with PYTHIA 6.1. Most of the changes and addi-tions instead are under the surface, and are only vis-ible as new options added to the existing repertoire.However, some changes are fairly obvious, and otherless obvious ones still of general interest. These will becovered in this section, in fairly general terms. Againwe refer to the PYTHIA web page for a detailed docu-mentation.

3.1. Coding conventions

As before, the FORTRAN 77 standard is adhered to.A very few minor extensions may be used in isolatedplaces, like the 7-character names of the PDFLIB rou-tines [11], but are not known to cause problems on anycompiler in use.

An obvious consequence of the PYTHIA /JETSET

code merging is that the old JETSETroutines and com-monblocks have been renamed to begin withPY (in-stead ofLU orUL), just like the PYTHIA ones. In mostcases, the rest of the name is unchanged, but thereare a few exceptions, mainlyRLU→PYR,KLU→PYK,PLU→PYP and LUXTOT→PYXTEE. Three integerfunctions now begin withPY, namelyPYK, PYCHGEandPYCOMP, and therefore have to be declared extra.The LUDATA block data has been merged intoPY-DATA, and the test routineLUTEST into PYTEST.For rotations and boosts, thePYROBO routine now re-quires the range of affected entries to be given, likethe oldLUDBRB but unlikeLUROBO (but 0,0 as rangearguments gives back the oldLUROBO behaviour).

All real variables are now inDOUBLE PRECI-SION, which is assumed to mean 64 bits, and also realconstants have been promoted to the higher precision.This is required to ensure proper functioning at cur-rently studied energies, such as the LHC and beyond.


Table 4The current form of the main commonblock declarations

COMMON/PYJETS/N,NPAD,K(4000,5),P(4000,5),V(4000,5)COMMON/PYDAT1/MSTU(200),PARU(200),MSTJ(200),PARJ(200)COMMON/PYDAT2/KCHG(500,4),PMAS(500,4),PARF(2000),VCKM(4,4)COMMON/PYDAT3/MDCY(500,3),MDME(4000,2),BRAT(4000),KFDP(4000,5)COMMON/PYDAT4/CHAF(500,2)CHARACTER CHAF*16COMMON/PYDATR/MRPY(6),RRPY(100)COMMON/PYSUBS/MSEL,MSELPD,MSUB(500),KFIN(2,-40:40),CKIN(200)COMMON/PYPARS/MSTP(200),PARP(200),MSTI(200),PARI(200)COMMON/PYINT1/MINT(400),VINT(400)COMMON/PYINT2/ISET(500),KFPR(500,2),COEF(500,20),ICOL(40,4,2)COMMON/PYINT3/XSFX(2,-40:40),ISIG(1000,3),SIGH(1000)COMMON/PYINT4/MWID(500),WIDS(500,5)COMMON/PYINT5/NGENPD,NGEN(0:500,3),XSEC(0:500,3)COMMON/PYINT6/PROC(0:500)CHARACTER PROC*28COMMON/PYMSSM/IMSS(0:99),RMSS(0:99)COMMON/PYUPPR/NUP,KUP(20,7),NFUP,IFUP(10,2),PUP(20,5),Q2UP(0:10)COMMON/PYBINS/IHIST(4),INDX(1000),BIN(20000)

To take into account this, all routines begin with thedeclarations

C...Double precision andinteger declarations.

IMPLICIT DOUBLE PRECISION(A-H, O-Z)IMPLICIT INTEGER(I-N)INTEGER PYK,PYCHGE,PYCOMP

and users should do the same in their main programs.On a machine whereDOUBLE PRECISIONwould

give 128 bits, it may make sense to use compiler op-tions to revert to 64 bits, since the program is anywaynot constructed to make use of 128 bit precision.

The random number generator is the same as in pre-vious versions [43], but has now been expanded to op-erate with a 48 bit mantissa for the real numbers.

FORTRAN 77 makes no provision for double-precision complex numbers, but sinceCOMPLEX isused only sparingly, no problems should be expectedfrom this omission. For the technicolor processes,some variables are declaredCOMPLEX*16 in thePYSIGH routine. Should the compiler not accept this,that one declaration can be changed toCOMPLEX withsome drop in precision for the affected processes.

Several compilers report problems when an oddnumber of integers precede a double-precision vari-able in a commonblock. Therefore an extra integer has

been introduced as padding in a few instances (NPAD,MSELPD andNGENPD in Table 4).

In order to cater for the increased offering of sub-processes, some arrays in commonblocks have beenexpanded. A few, such asPYINT4, have also beenreorganized to represent improvements in the physicsmodeling. Most commonblocks and commonblockvariables are easily recognizable from previous pro-gram versions, however. The current complement isgiven in Table 4, omitting some of the less interestingones.

Since FORTRAN 77 provides no date-and-time rou-tine, PYTIME allows a system-specific routine to beinterfaced, with some commented-out examples givenin the code. This routine is only used for cosmetic im-provements of the output, however, so can be left atthe default with time 0 given.

For a program written to run PYTHIA 5 and JET-SET 7, most of the conversion required for PYTHIA 6is fairly straightforward, and can be automatized. Botha simple FORTRAN routine and a more sophisticatedPERL [44] script exists to this end. Some manualchecks and interventions may still be required.

3.2. Particle codes and data

A number of new particle codesKF have been intro-duced, or modified, see Table 5. Mostly this is based


Table 5New or modified particle codes or names

Renamed:

7 b′

8 t′

17 τ ′

18 ν′τ

25 h0

35 H0

Moved:

100443 ψ ′

100553 ϒ ′

4000001 d∗

4000002 u∗

4000011 e∗

4000012 ν∗e

Technicolor:

51 π0tc

52 π+tc

53 π ′tc

0

54 ρ0tc

55 ρ+tc

56 ω0tc

LR-symmetric:

61 H++L

62 H++R

63 W+R

64 νRe

65 νRµ

66 νRτ

SUSY:

1000001 dL

1000002 uL

1000003 sL

1000004 cL

1000005 b1

1000006 t1

1000011 eL

1000012 νeL

1000013 µL

1000014 νµL

1000015 τ1

1000016 ντL

1000021 g

1000022 χ01

1000023 χ02

1000024 χ+1

SUSY:

2000001 dR

2000002 uR

2000003 sR

2000004 cR

2000005 b2

2000006 t2

2000011 eR

2000012 νeR

2000013 µR

2000014 νµR

2000015 τ2

2000016 ντR

1000025 χ03

1000035 χ04

1000037 χ+2

1000039 G

on the PDG-agreed conventions [45,46], but some notyet standardized codes appear in the ‘empty’ range41–80. Furthermore, the fourth generation fermionsand neutral scalar Higgs states have been renamed.The two fermion spartners are labelled left and right,except in the third generation, where an expectedlarger mixing makes the two mass eigenstates a bet-ter choice of classification.

The top hadrons are gone. It is now known that topis too short-lived to form hadronic bound states, so areasonable description is instead to have the top quarksdecay before hadronization is considered. The sameis now assumed about a hypothetical fourth genera-tion. Should the need ever arise in the future to con-sider a new long-lived coloured object, an effectivedescription of a hadron as a small string with an or-dinary colour-matching flavour at the other end shouldbe sufficient. One such example would be leptoquark-hadrons [47].

Bottom hadrons are now defined individually, e.g.,the previous common decay scheme is gone in favourof individual branching ratios for each hadron. Onthe other hand, given the sketchy knowledge of many

branching ratios, the default description is still fairlystandardized.

Decay data is mainly based on the 1996 PDG edi-tion [48], but with many ‘educated guesses’ to fill inmissing information.

Since running fermion masses are used in an in-creasing number of processes, e.g., for Higgs cou-plings, a functionPYMRUN(KF,Q2) has been intro-duced to give the mass as a function ofQ2 scale.

The compressed codes,KC = PYCOMP(KF), arecompletely changed. We remind thatKF can range upto seven-digit codes, plus a sign. They therefore can-not be used to directly access information in particledata tables. TheKC codes range between 1 and 500,and give the index to the particle data arrays. EachKFcode is now one-to-one associated with aKC code; theonly ambiguity is thatKC does not distinguish antipar-ticles from particles. WhereasKF codes below 100still obeyKF = KC, the mapping of codes above 100is completely changed. It is no longer hard-coded inPYCOMP, but defined by the fourth component of theKCHG array. Therefore it can be changed or expanded


during the course of a run, either byPYUPDA calls orby direct user intervention.

3.3. New options

A large amount of new options have been added,related to almost all the physics changes above andmore, and we here only mention some of the more sig-nificant ones.

The inclusion of SUSY processes means that all theSPYTHIA PYMSSM commonblock switches and para-meters are inherited. New parameters are added alsofor other new physics scenarios, such as technicolorand doubly-charged Higgses.

The extensions to the physics of virtual photons,outlined in Section 2.1.3, has resulted in two setsof new possibilities. One is in the description of thevirtual-photon flux, where newCKIN switches hasbeen introduced, e.g., to set the range of photonx

andQ2. This is available whenPYINIT is called with’gamma/lepton’ as beam or target, to denote thatthe photon flux inside the lepton has to be consideredas a new administrative layer, also documented in theevent record. The other is the new physics machinery.Here the main switch isMSTP(14) that sets the as-sumed nature of the photon or photons, e.g., ‘a directphoton from the left collides with a VMD one from theright’. The default is the most general mixture, mean-ing 4 components forγ ∗p and 13 forγ ∗γ ∗. This is therelevant approach for studies of QCD processes. Thereis no corresponding automatic mixing machinery forother processes, so then the relevant contributing com-ponents have to be handled separately and added af-terwards. Further options are available for several ofthe components, e.g., the DIS process dampening inthe Q2 → 0 limit, the relative normalization of theGVMD spectrum, the scale choice for parton distri-butions, and the possibility to add the effects of a lon-gitudinal resolved contribution.

The matrix-element options for e+e− → γ ∗/Z0 →2, 3 or 4 partons have previously only been availablevia the LUEEVT/PYEEVT routine, that suffers fromproblems of its own in having a rather old-fashionedmachinery for QED initial-state radiation and elec-troweak parameters. Now the QCD matrix-elementdescription is accessible as an option to the shower de-fault for e+e− events generated with subprocess 1 ofthe standard PYTHIA machinery.

3.4. Interfaces

While PYTHIA contains an extensive library of sub-processes, it is far from up to all the requirements ofthe experimental community. Both further processesand a more detailed treatment of the existing ones isrequired at times. In particular, it is not uncommonwith a generator dedicated to one specific process,where also higher-order electroweak corrections, ab-sent in PYTHIA , have been included in the cross sec-tion. None of these programs are geared to handlethe QCD aspects of parton showers and hadronization,however, so it makes sense to combine the individualstrengths.

A generic facility to include external processes ex-ists since long in PYTHIA . Here one can feed in par-tonic configurations from an external generator, to-gether with some basic information on colour flow andwhich partons are allowed to radiate, and let PYTHIA

construct a complete event based on this informa-tion. For the simple configurations encountered ine+e− annihilation events, this would often be overkill,since neither the initial-state QCD radiation nor beam-remnant treatment of the generic (hadronic) collisionis present.

Based on the concepts presented in the LEP2 work-shop [46], a few simpler alternatives are therefore nowprovided for this kind of tasks:• CALL PY2FRM(IRAD,ITAU,ICOM) allows a

parton shower to develop and partons to hadronizefrom a given two-fermion starting point.IRAD setswhether quarks are allowed also to radiate photonsor not,ITAU whetherτ leptons should be decayedor not, andICOMwhether the input and output eventrecord isHEPEVT or PYJETS. An arbitrary num-ber of photons (e.g., from initial-state radiation)may also be stored with the input.

• CALL PY4FRM(ATOTSQ,A1SQ,A2SQ,ISTRAT,IRAD,ITAU,ICOM) allows partonshowers to develop and partons to hadronize froma given four-fermion starting point. The extra para-meters can be used to select between the two colourpairings allowed for a q1q2q3q4 state, according tosome different strategies when interference termsdo not allow unique probabilities to be found.

• CALL PY6FRM(P12,P13,P21,P23,P31,P32,PTOP,IRAD,ITAU,ICOM) allows parton


showers to develop and partons to hadronize from agiven six-fermion starting point. ThePij parame-ters give the relative probabilities for the six colourpairings allowed for a six-quark state, andPTOPthe probability that the event originates from a ttpair (in which case the shower handling has to bedifferent than, e.g., in a Z0W+W− event).The above routines are not set up to handle QCD

four-jet events, i.e. events of the types qqgg andqqq′q′, with q′q′ coming from a gluon branching.Such events are generated in normal parton showers,but not necessarily at the right rate (a problem thatmay be especially interesting for massive quarks likeb). Therefore one would like to start a QCD partonshower from a given four-parton configuration. Sometime ago, a machinery was developed to handle thiskind of occurences [49]. This approach has now beenadapted to the current PYTHIA version, in a somewhatmodified form. In it, an imagined shower history oftwo branchings is (re)constructed from the four-partonstate, according to relative probabilities derived in theshower language. Thereafter a normal shower is al-lowed to develop, with branchings chosen at randomexcept for these two predetermined ones. The rou-tine CALL PY4JET(PMAX,IRAD,ICOM) takes anoriginal four-parton configuration stored inHEPEVTor PYJETS and lets a shower develop as describedabove.PMAX can be used to set the maximum virtu-ality of those parts of the shower not given from theparton configuration itself, either to a fixed value or tothe lowest virtuality of the reconstructed shower.

3.5. Utilities

The clustering algorithmPYCLUS has been ex-tended also to accept the Durham distance mea-sure [50] as an alternative. This isp⊥-based, like theoriginalLUCLUS distance measure, but differs in thedetails.

TheGBOOK histogramming package was written in1979 as a lightweight substitute forHBOOK [51] beforethat program was available in FORTRAN 77. The one-dimensional histogram part now appears in the stan-dard distribution, in order to make the sample runs of-fered on the web a bit more realistic. The main routinesare:• CALL PYBOOK(ID,TITLE,NX,XL,XU) to

book a one-dimensional histogram with integer

identifier ID (in the range 1–1000), character ti-tle TITLE andNX bins stretching fromXL to XU.

• CALL PYFILL(ID,X,W) to fill histogramID atpositionX with weightW.

• CALL PYFACT(ID,F) to rescale the contents ofhistogramID by a factorF.

• CALL PYOPER(ID1,OPER,ID2,ID3,F1,F2) to perform operations on several histograms,such as adding or dividing them by each other.

• CALL PYDUMP(MDUMP,LFN,NHI,IHI) todump histogram contents to a file from which theycould be read in for plotting in another program.

• CALL PYHIST to print all histograms in a sim-ple line-printer mode, and thereafter reset histogramcontents.

A commonblock of dimension 20 000 is used to storethe histograms; this size may need to be expanded ifmany histograms are to be booked.

ThePYUPDA routine has been expanded with a newoption that allows a set of particle data to be read in,in tabular form as before, as an addition to or partialreplacement of the existing particle data.

4. Summary and outlook

We have here given a very brief survey of news inthe PYTHIA 6.1 program. A more detailed descriptionof physics and programs is available separately [52].Any serious user should turn to this publication, andto the original physics papers, for further information.

The treasure trove for information is thePYTHIA webpage,http://www.thep.lu.se/∼torbjorn/Pythia.html, where one may find thecurrent and previous subversions, with documentation,sample main programs, links to related programs, etc.

The PYTHIA program is continuously being devel-oped. We are aware of many physics shortcomings,which hopefully will be addressed in the future. It isin the nature of a program of this kind never to be fin-ished, at least as long as it is of importance for thehigh-energy physics experimental community.

The main visible change in the future is the tran-sition to C++ as the programming language forPYTHIA 7. Even if much of the physics will be carriedover unchanged, none of the existing code will sur-vive. The structure of the event record and the wholeadministrative apparatus is completely different from


the current one, in order to allow a much more gen-eral and flexible formulation of the event generationprocess. Following the formulation of a strategy doc-ument [53], a first proof-of-concept version was re-leased recently [54]. So far it only contains one reason-ably complete physics module, however, namely thatof string fragmentation. More realistic versions shouldfollow, but it will take a long time to convert all im-portant physics components from PYTHIA 6. The twoversions therefore will coexist for several years, withthe FORTRAN one used for physics ‘production’ andthe C++ one for exploration of the object-oriented ap-proach that will be standard at the LHC.

Acknowledgements

A large number of persons should be thanked fortheir contributions. Bo Andersson and Gösta Gustaf-son are the originators of the Lund model, and stronglyinfluenced the early development of the programs.Hans-Uno Bengtsson is the originator of the PYTHIA

program. Mats Bengtsson is the original author ofthe final-state parton-shower algorithm. Several piecesof code have been donated by other persons. Furthercomments on the programs have been obtained fromusers too numerous to be mentioned here, but who areall gratefully acknowledged. To write programs of thissize and complexity would be impossible without astrong user feedback.

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