Aachen, November 2007
Event Generators 2Advanced Topics
Peter Skands
CERN / Fermilab
Evolution
First day Hands-on-sessions
Peter Skands Event Generator Status 2
Master PlanMaster Plan► Lecture 1: Fundamental Topics
• Fundamentals of Generators, Parton Showers, and Hadronization
► Lecture 2: Advanced Topics
• Hadron Collisions and the Underlying Event
• Matching
► Lecture 3: Practical Topics + Open Q & A
• Overview of Event Generator Landscape
• Overview of useful parameters in PYTHIA
• Open Question-and-Answer Session
• Beer
Done!
Peter Skands Event Generator Status 3
Lecture 2: Advanced TopicsLecture 2: Advanced Topics► You are now experts on parton showers and all that
• What more do you want to know?
► The Hadron Collider Environment: the Underlying Event
• Models
• Tuning
• Early constraints from LHC
► Matching
• What’s the problem?
• When do you need matching?
• What’s the difference: PYTHIA/HERWIG, MLM, CKKW, MC@NLO, etc
The Underlying Event
Towards a complete picture of hadron collisions
Peter Skands Event Generator Status 5
► Domain of fixed order and parton shower calculations: hard partonic scattering, and bremsstrahlung associated with it.
► But hadrons are not elementary
► + QCD diverges at low pT
► multiple perturbative parton-parton collisions should occur
► Normally omitted in explicit perturbative expansions
► + Remnants from the incoming beams
► + additional (non-perturbative / collective) phenomena?• Bose-Einstein Correlations• Non-perturbative gluon exchanges / colour reconnections ?• String-string interactions / collective multi-string effects ?• Interactions with “background” vacuum / with remnants / with active
medium?
e.g. 44, 3 3, 32
Additional Sources of Particle ProductionAdditional Sources of Particle Production
Peter Skands Event Generator Status 6
From Rick Field
Elastic Scattering Single Diffraction
M
tot = ELSD DD HC
Double Diffraction
M1 M2
Proton AntiProton
“Soft” Hard Core (no hard scattering)
Proton AntiProton
PT(hard)
Outgoing Parton
Outgoing Parton
Underlying Event Underlying Event
Initial-State Radiation
Final-State Radiation
“Hard” Hard Core (hard scattering)
Hard Core
1.8 TeV: 78mb = 18mb + 9mb + (4-7)mb + (47-44)mb
The CDF “Min-Bias” trigger picks up most of the “hard
core” cross-section plus a small amount of single & double
diffraction.
The “hard core” component contains both “hard” and
“soft” collisions.
Beam-Beam Counters
3.2 < || < 5.9
CDF “Min-Bias” trigger1 charged particle in forward BBC
AND1 charged particle in backward BBC
tot = ELIN
Proton - Antiproton Collisions Proton - Antiproton Collisions at the Tevatronat the Tevatron
Peter Skands Event Generator Status 7
QCD Monte-Carlo Models:QCD Monte-Carlo Models:High Transverse Momentum JetsHigh Transverse Momentum Jets
► Start with the perturbative 2-to-2 (or sometimes 2-to-3) parton-parton scattering and add initial and final-state gluon radiation (in the leading log approximation or modified leading log approximation).
Hard Scattering
PT(hard)
Outgoing Parton
Outgoing Parton
Initial-State Radiation
Final-State Radiation
Hard Scattering
PT(hard)
Outgoing Parton
Outgoing Parton
Initial-State Radiation
Final-State Radiation
Proton AntiProton
Underlying Event Underlying Event
Proton AntiProton
Underlying Event Underlying Event
“Hard Scattering” Component
“Jet”
“Jet”
“Underlying Event”
►The “underlying event” consists of the “beam-beam remnants” and from particles arising from soft or semi-soft multiple parton interactions (MPI).
►Of course the outgoing colored partons fragment into hadron “jet” and inevitably “underlying event” observables receive contributions from initial and final-state radiation.
“Jet”
The “underlying event” is an unavoidable background to most collider observables and having good understand of it leads to
more precise collider measurements!
Peter Skands Event Generator Status 8
Jet #1 Direction
“Transverse” “Transverse”
“Toward”
“Away”
“Toward-Side” Jet
“Away-Side” Jet
► Look at charged particle correlations in the azimuthal angle relative to the leading calorimeter jet (JetClu R = 0.7, || < 2).
► Define || < 60o as “Toward”, 60o < - < 120o and 60o < < 120o as “Transverse 1” and “Transverse 2”, and || > 120o as “Away”. Each of the two “transverse” regions have area = 2x60o = 4/6. The overall “transverse” region is the sum of the two transverse regions ( = 2x120o = 4/3).
Charged Particle Correlations pT > 0.5 GeV/c || < 1
“Transverse” region is very sensitive to the “underlying event”!
Jet #1 Direction
“Toward”
“Trans 1” “Trans 2”
“Away”
-1 +1
2
0
Leading Jet
Toward Region
Transverse Region 1
Transverse Region 2
Away Region
Away Region
Look at the charged particle density in the “transverse” region!
The “Transverse” RegionsThe “Transverse” Regionsas defined by the Leading Jetas defined by the Leading Jet
Peter Skands Event Generator Status 9
► Shows the dependence of the charged particle density, dNchg/dd, for charged particles in the range pT > 0.5 GeV/c and || < 1 relative to jet#1 (rotated to 270o) for “leading jet” events 30 < ET(jet#1) < 70 GeV.
► Also shows charged particle density, dNchg/dd, for charged particles in the range pT > 0.5 GeV/c and || < 1 for “min-bias” collisions.
Leading Jet
Charged Particle Density: dN/dd
0.1
1.0
10.0
0 30 60 90 120 150 180 210 240 270 300 330 360
(degrees)
Ch
arg
ed
Pa
rtic
le D
en
sit
y
CDF Preliminarydata uncorrected
Charged Particles (||<1.0, PT>0.5 GeV/c)
30 < ET(jet#1) < 70 GeV
"Transverse" Region
Jet#1
Jet #1 Direction
“Transverse” “Transverse”
“Toward”
“Away”
“Toward-Side” Jet
“Away-Side” Jet
Jet #1 Direction
“Transverse” “Transverse”
“Toward”
“Away”
“Toward-Side” Jet
“Away-Side” Jet
Jet #3
Min-Bias0.25 per unit -
Log Scale!
Charged Particle Density Charged Particle Density Dependence Dependence
Peter Skands Event Generator Status 10
► Look at the “transverse” region as defined by the leading jet (JetClu R = 0.7, || < 2) or by the leading two jets (JetClu R = 0.7, || < 2). “Back-to-Back” events are selected to have at least two jets with Jet#1 and Jet#2 nearly “back-to-back” (12 > 150o) with almost equal transverse energies (ET(jet#2)/ET(jet#1) > 0.8) and with ET(jet#3) < 15 GeV.
Charged Particle Density: dN/dd
0.1
1.0
10.0
0 30 60 90 120 150 180 210 240 270 300 330 360
(degrees)
Ch
arg
ed
Pa
rtic
le D
en
sit
y
CDF Preliminarydata uncorrected
Charged Particles (||<1.0, PT>0.5 GeV/c)
30 < ET(jet#1) < 70 GeV
"Transverse" Region
Jet#1
Jet #1 Direction
“Toward”
“Transverse” “Transverse”
“Away”
Jet #1 Direction
“Toward”
“Transverse” “Transverse”
“Away”
Jet #2 Direction
► Shows the dependence of the charged particle density, dNchg/dd, for charged particles in the range pT > 0.5 GeV/c and || < 1 relative to jet#1 (rotated to 270o) for 30 < ET(jet#1) < 70 GeV for “Leading Jet” and “Back-to-Back” events.
Charged Particle Density: dN/dd
0.1
1.0
10.0
0 30 60 90 120 150 180 210 240 270 300 330 360
(degrees)
Ch
arg
ed
Pa
rtic
le D
en
sit
y
Back-to-Back
Leading Jet
Min-Bias
CDF Preliminarydata uncorrected
Charged Particles (||<1.0, PT>0.5 GeV/c)
30 < ET(jet#1) < 70 GeV
"Transverse" Region
Jet#1
Refer to this as a “Leading Jet” event
Refer to this as a “Back-to-Back” event
Su
bset
Charged Particle Density Charged Particle Density Dependence Dependence
Peter Skands Event Generator Status 11
Basic PhysicsBasic PhysicsSjöstrand and van Zijl (1987):
► First serious model for the underlying event
► Based on multiple perturbative QCD 22 scatterings (at successively smaller scales) multiple parton-parton interactions
► Dependence on impact parameter crucial to explain Nch distributions.
• Peripheral collisions little matter overlap few interactions. Central collisions many
• Nch Poissonian for each impact parameter convolution with impact parameter profile wider than Poissonian!
• Concrete evidence for ‘lumpiness’ in the proton!
UA5
Nch
540 GeV
T. Sjöstrand & M. van Zijl PRD36(1987)2019
Peter Skands Event Generator Status 12
Jet #1 Direction
“Toward”
“Transverse” “Transverse”
“Away”
Jet #1 Direction
“Toward”
“Transverse” “Transverse”
“Away”
Jet #2 Direction
► Shows the average charged PTsum density, dPTsum/dd, in the “transverse” region (pT > 0.5 GeV/c, || < 1) versus ET(jet#1) for “Leading Jet” and “Back-to-Back” events.
► Compares the (uncorrected) data with PYTHIA Tune A and HERWIG after CDFSIM.
“Leading Jet”
“Back-to-Back”
"AVE Transverse" PTsum Density: dPT/dd
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 50 100 150 200 250
ET(jet#1) (GeV)
"Tra
nsv
erse
" P
Tsu
m D
ensi
ty (
GeV
/c)
CDF Preliminarydata uncorrectedtheory + CDFSIM
Charged Particles (||<1.0, PT>0.5 GeV/c)
Back-to-Back
Leading Jet
PY Tune A
HW
1.96 TeV
““Transverse” PTsum DensityTransverse” PTsum Density PYTHIA Tune A vs HERWIG PYTHIA Tune A vs HERWIG
Peter Skands Event Generator Status 13
The “Underlying Event” inThe “Underlying Event” inHigh PHigh PTT Jet Production (LHC) Jet Production (LHC)
►Charged particle density in the “Transverse” region versus PT(jet#1) at 1.96 TeV for PY Tune AW and HERWIG (without MPI).
►Charged particle density in the “Transverse” region versus PT(jet#1) at 14 TeV for PY Tune AW and HERWIG (without MPI).
The “Underlying Event”
"Transverse" Charged Particle Density: dN/dd
0.0
0.2
0.4
0.6
0.8
1.0
0 50 100 150 200 250 300 350 400 450 500
PT(particle jet#1) (GeV/c)
"Tra
ns
ve
rse
" C
ha
rge
d D
en
sit
y
RDF Preliminarygenerator level
Charged Particles (||<1.0, PT>0.5 GeV/c) "Leading Jet"
PY Tune AW
1.96 TeV
HERWIG
"Transverse" Charged Particle Density: dN/dd
0.0
0.5
1.0
1.5
2.0
0 250 500 750 1000 1250 1500 1750 2000 2250 2500
PT(particle jet#1) (GeV/c)
"Tra
ns
vers
e" C
ha
rge
d D
en
sity
RDF Preliminarygenerator level
Charged Particles (||<1.0, PT>0.5 GeV/c) "Leading Jet"
PY Tune AW
CDF
LHC
HERWIG
Charged particle density versus PT(jet#1)
“Underlying event” much more active at the LHC!
Proton AntiProton
High PT Jet Production
PT(hard)
Outgoing Parton
Outgoing Parton
Underlying Event Underlying Event
Final-State Radiation
Initial-State Radiation
Peter Skands Event Generator Status 14
► Theory “predictions” for tracker occupancy (idealized 4π tracker):
► This was theory – how related to what is more realistically measured?
• Restrict to |η| < 2.5, pT > 0.5 GeV
LHC Forecasts 1LHC Forecasts 1
A bunch of models
and tunes
<Nch> ~ 80-120
Peter Skands Event Generator Status 15
► Theory “predictions” for tracker occupancy:
► Even 500 000 events will tell us a lot about which models could be right
• But not all. Interesting to go to as low pT as possible not to miss anything.
LHC Forecasts 2LHC Forecasts 2
<Nch> ~ 13-20
Peter Skands Event Generator Status 16
Under the Hood (theory)Under the Hood (theory)► How is this multiplicity built up?
Number of “colour sparks” per pp collision
<Nint> ~ 4 - 11
PS: you don’t have to believe this, but you should know that this is what you
get if you run Pythia
Peter Skands Event Generator Status 18
Underlying Event and ColourUnderlying Event and Colour► In PYTHIA (up to 6.2), some “theoretically sensible” default values for the
colour correlation parameters had been chosen
• Rick Field (CDF) noted that the default model produced too soft charged-particle spectra.
• (The same is seen at RHIC:)
• For ‘Tune A’ etc, Rick noted that <pT> increased when he increased the colour correlation parameters
• Virtually all ‘tunes’ now used by the Tevatron and LHC experiments employ these more ‘extreme’ correlations
• Tune A, and hence its more extreme colour correlations are now the default in PYTHIA
M. Heinz (STAR), nucl-ex/0606020; nucl-ex/0607033
STAR
pp @ 200GeV
Peter Skands Event Generator Status 19
The ‘Intermediate’ ModelThe ‘Intermediate’ Model► Meanwhile in Lund: Sjöstrand and PS (2003):
• Further developments on the multiple-interactions idea
• First serious attempt at constructing multi-parton densitities• If sea quark kicked out, “companion” antiquark introduced in remnant (distribution
derived from gluon PDF and gluon splitting kernel)
• If valence quark kicked out, remaining valence content reduced
• Introduction of “string junctions” to represent beam baryon number• Detailed hadronization model for junction fragmentation can address baryon
number flow separately from valence quarks
Sjöstrand & PS : Nucl.Phys.B659(2003)243, JHEP03(2004)053
Peter Skands Event Generator Status 20
The ‘New’ Model The ‘New’ Model Pythia 8 Pythia 8► Sjöstrand and PS (2005):
• ‘Interleaved’ evolution of multiple interactions and parton showers
Sjöstrand & PS : JHEP03(2004)053, EPJC39(2005)129
multipartonPDFs derivedfrom sum rules
Beam remnantsFermi motion / primordial kT
Fixed ordermatrix elements
pT-orderedparton shower(matched to MEfor W/Z/H/G + jet)
perturbative “intertwining”?
NB: Tune A still default since more thoroughly tested. To use new models, see e.g. PYTUNE (Pythia6.408+)
Peter Skands Event Generator Status 21
The Underlying EventThe Underlying Event
► Latest Developments
• Parton Showers also for the Multiple Interactions: Pythia 6.4, Pythia 8, Sherpa
• Re-interactions of partons Pythia 8
• Non-QCD multiple interactions• Double Drell-Yan Pythia 8 (e.g., W+W+ production = background)
• New interest in non-perturbative phenomena:• Reconnections / interactions of strings precision top mass, Pythia 6
► Summary
• Even in the perturbative region, there is much left to understand. Early experimental studies at LHC will be extremely influential
• The non-perturbative region is even more interesting, but also always more difficult … meaning that the experiments will be even more important to show us the way
Fixed Order Matrix Elements and Parton Shower Resummations
Peter Skands Event Generator Status 23
Fixed Order vs Parton ShowersFixed Order vs Parton Showers
ME
PS 1
PS 2
LHC - sps1a - m~600 GeV
► We saw yesterday that:
• Parton Showers include all orders, but only the singular terms
• Matrix Elements include all terms, but only up to the given order
Plehn, Rainwater, PS: PLB645(2007)217 & hep-ph/0511306
►Conventional Wisdom
•When “close” to singularities (soft jets), use parton showers
•When “far away” from singularities (hard jets), use matrix elements
►In the past, these approaches were often pursued independently
Peter Skands Event Generator Status 24
More About Fixed OrderMore About Fixed Order► What “Order” are we talking about, and of what?
• Naively, it’s the order of the coupling at which we truncate the perturbative expansion.
• However, only in Germany will you often hear “This is the distribution of zo und zo, calculated up to O(gs
n gwm) …” – more often, you will hear
words like “LO” and “NLO” ...
► Is it a number of emissions?
• “Tree-level”
► Is it a number of emssions plus loops?
• “Complete Orders”
► And what is meant by an “LO” or “NLO” event generator?
• Are all distributions calculated with an “NLO” generator now “NLO” ?
Peter Skands Event Generator Status 25
A ProblemA Problem
►The best of both worlds? We want:
• A description which accurately predicts hard additional jets
• + jet structure and the effects of multiple soft emissions
an “inclusive” sample on which we could evaluate any observable, whether it is sensitive or not to extra hard jets, or to soft radiation
Peter Skands Event Generator Status 26
A ProblemA Problem
►How to do it?
• Compute emission rates by parton showering (PS)?• Misses relevant terms for hard jets, rates only correct for strongly ordered
emissions pT1 >> pT2 >> pT3 ...
• Unknown contributions from higher logarithmic orders, subleading colors, …
• Compute emission rates with matrix elements (ME)?• Misses relevant terms for soft/collinear emissions, rates only correct for
well-separated individual partons
• Quickly becomes intractable beyond one loop and a handfull of legs
• Unknown contributions from higher fixed orders
Peter Skands Event Generator Status 27
A (Stupid) SolutionA (Stupid) Solution► Combine different starting multiplicites
inclusive sample?
► In practice – Combine
1. [X]ME + showering
2. [X + 1 jet]ME + showering
3. …
► Doesn’t work
• [X] + shower is inclusive
• [X+1] + shower is also inclusive
X inclusiveX inclusive
X+1 inclusiveX+1 inclusive
X+2 inclusiveX+2 inclusive ≠X exclusiveX exclusive
X+1 exclusiveX+1 exclusive
X+2 inclusiveX+2 inclusive
Run generator for X (+ shower)
Run generator for X+1 (+ shower)
Run generator for … (+ shower)
Combine everything into one sample
What you get
What you want
Overlapping “bins” One sample
Peter Skands Event Generator Status 28
Double CountingDouble Counting
► Double Counting:
• [X]ME + showering produces some X + jet configurations• The result is X + jet in the shower approximation
• If we now add the complete [X + jet]ME as well• the total rate of X+jet is now approximate + exact ~ double !!
• some configurations are generated twice.
• And the total inclusive cross section is also not well defined• Is it the “LO” cross section?
• Is it the “LO” cross section plus the integral over [X + jet] ?
• What about “complete orders” and KLN ?
► When going to X, X+j, X+2j, X+3j, etc, this problem gets worse
Peter Skands Event Generator Status 29
MatchingMatching
► Traditional Approach: take the showers you have, expand them to 1st order, and fix them up
• Sjöstrand (1987): Introduce re-weighting factor on first emission 1st order tree-level matrix element (ME) (+ further showering)
• Seymour (1995): + where shower is “dead”, add separate events from 1st order tree-level ME, re-weighted by “Sudakov-like factor” (+ further showering)
• Frixione & Webber (2002): Subtract 1st order expansion from 1st order tree and 1-loop ME add remainder ME correction events (+ further showering)
► Multi-leg Approaches (Tree level only):
• Catani, Krauss, Kuhn, Webber (2001): Substantial generalization of Seymour’s approach, to multiple emissions, slicing phase space into “hard” M.E. ; “soft” P.S.
• Mangano (?): pragmatic approach to slicing: after showering, match jets to partons, reject events that look “double counted”
A brief history of conceptual breakthroughs in widespread use today:
Peter Skands Event Generator Status 30
New Creations: Fall 2007New Creations: Fall 2007► Showers designed specifically for matching
• Nagy, Soper (2006): Catani-Seymour showers• Dinsdale, Ternick, Weinzierl (Sep 2007) & Schumann, Krauss (Sep 2007): implementations
• Giele, Kosower, PS (Jul 2007): Antenna showers • (incl. implementation)
► Other new showers: partially designed for matching• Sjöstrand (Oct 2007): New interleaved evolution of FSR/ISR/UE
• Official release of Pythia8 last week
• Webber et al (HERWIG++): Improved angular ordered showers
• Nagy, Soper (Jun 2007): Quantum showers subleading color, polarization (implementation in 2008?)
► New matching proposals• Nason (2004): Positive-weight variant of MC@NLO
• Frixione, Nason, Oleari (Sep 2007): Implementation: POWHEG
• Giele, Kosower, PS (Jul 2007): Antenna subtraction• VINCIA
Peter Skands Event Generator Status 31
Matching – When?Matching – When?
► Matching is not necessary if• You are only interested in an observable which only contains well separated
scales (e.g., top pair + 1 jet at 25 GeV)
► The matching in HERWIG/PYTHIA times K-factor is sufficient if
• Your reaction is one of the “matched” ones (see respective manual) and your observable at most contains 1 “hard jet”
► MC@NLO matching is relevant if
• Your reaction is one of the “matched” ones (see manual) and your observable ne at most contains 1 “hard jet”, and the total normalization is important
► Multi-leg matching (CKKW/MLM, …) is relevant if
• Your observable contains 2 or more “hard jets”
Peter Skands Event Generator Status 32
S. Catani, F. Krauss, R. Kuhn, B.R. Webber, JHEP 0111 (2001) 063
CKKW and L-CKKWCKKW and L-CKKW► The CKKW algorithm
• Divide phase space into two regions:• Use matrix elements to describe the initial distribution of all particles having a separation
larger than some minimum pT > pTcut
• Modify it by “rejections” according to the parton shower “unitarise”
• Use parton showers for pT < pTcut
1. [W]ME |pT>pTcut * Wveto(pTcut) + showeringpT<pTcut
2. [W + j]ME|pT>pTcut * Wveto(pTcut) + showeringpT<pTcut
3. …
• Wveto are there to kill the “double counting”
• = The probability that no emission happened above pTcut
• This probability is also called the Sudakov factor, or the no-emission probabilit, Δ
• SHERPA uses an analytical approximation
• Lönnblad’s ARIADNE uses ‘trial’ or ‘pseudo’ showers
► The “double counting” disappears since the events which would have caused it are exactly those which have emissions above pTcut
L. L¨onnblad, JHEP05 (2002) 046
Rejection Factors
Wveto < 1
Peter Skands Event Generator Status 33
Matched Mix of W+0,1,2,3,4 jetsMatched Mix of W+0,1,2,3,4 jets
S. Mrenna, P. Richardson, JHEP0405 (2004) 040
► Matching can also be done with AlpGen/MadGraph/… + Pythia/Herwig
Peter Skands Event Generator Status 34
ALPGENALPGEN► “MLM” matching (Mangano)
• Simpler but similar in spirit to CKKW
► First generate events the “stupid” way:
1. [W]ME + showering
2. [W + jet]ME + showering
3. …
► a set of fully showered events, with double counting. To get rid of the excess, accept/reject each event based on:
• (cone-)cluster showered event njets
• match partons from the ME to the clustered jets
• If all partons are matched, keep event. Else discard it.
► Roughly equivalent to the pseudoshower approach above
• Virtue: can be done without knowledge of the internal workings of the generator. Only the fully showered final events are needed
Peter Skands Event Generator Status 35
MC@NLOMC@NLOFrixione, Nason, Webber, JHEP 0206(2002)029 and 0308(2003)007
► MC@NLO in comparison• Superior precision for total cross section• Equivalent to tree-level matching for event shapes (differences higher order)
• Inferior to multi-jet matching for multijet topologies
• So far has been using HERWIG parton shower complicated subtractions
HERWIG++: O. Latunde-Dada, hep-ph/0708.4390
Peter Skands Event Generator Status 36
•MC@NLO: •Used to think it was impossible! •But complicated much work needed for each process •“Only” gets first jet right (rest is PS) •Hardwired to HERWIG
•CKKW & MLM: •Best approach when multiple hard jets important.•Relatively straightforward (but still time-consuming)•Retains LO normalization •Dependence on matching scale
• All constructed to use existing showers (HW or PY) hard to trace analytically•Not easy to control theoretical uncertainty on exponentiated part •How to add X+1 @ 1 loop ?
MC@
NLO
MLM
CKKW
New Methods – Why?New Methods – Why?
Much recent work
Really Advanced Topics
… (werbung) …
Peter Skands Event Generator Status 38
Towards Improved GeneratorsTowards Improved Generators► The final answer will depend on:
• The choice of evolution variable
• The splitting functions (finite terms not fixed)
• The phase space map ( dΦn+1/dΦn )
• The renormalization scheme (argument of αs)
• The infrared cutoff contour (hadronization cutoff)
► Step 1, Quantify uncertainty: vary all of these (within reasonable limits)
► Step 2, Systematically improve: Understand the importance of each and how it is canceled by
• Matching to fixed order matrix elements
• Higher logarithms, subleading color, etc, are included
► Step 3, Write a generator: Make the above explicit (while still tractable) in a Markov Chain context matched parton shower MC algorithm
Peter Skands Event Generator Status 39
Gustafson, PLB175(1986)453; Lönnblad (ARIADNE), CPC71(1992)15.Azimov, Dokshitzer, Khoze, Troyan, PLB165B(1985)147 Kosower PRD57(1998)5410; Campbell,Cullen,Glover EPJC9(1999)245
VINCIAVINCIA
► Based on Dipole-Antennae• Shower off color-connected pairs of partons
• Plug-in to PYTHIA 8.1 (C++)
► So far:
• Final-state QCD cascades (massless quarks)
• 2 different shower evolution variables:• pT-ordering (~ ARIADNE, PYTHIA 8)
• Mass-ordering (~ PYTHIA 6, SHERPA)
• For each: an infinite family of antenna functions • Laurent series in branching invariants with arbitrary finite terms
• Shower cutoff contour: independent of evolution variable IR factorization “universal”
• Several different choices for αs (evolution scale, pT, mother antenna mass, 2-loop, …)
• Phase space mappings: 2 different choices implemented • Antenna-like (ARIADNE angle) or Parton-shower-like: Emitter + longitudinal Recoiler
Dipoles (=Antennae, not CS) – a dual description of QCD
a
b
r
VIRTUAL NUMERICAL COLLIDER WITH INTERLEAVED ANTENNAE
Giele, Kosower, PS : hep-ph/0707.3652
Peter Skands Event Generator Status 40
Dipole-Antenna ShowersDipole-Antenna Showers► Dipole branching and phase space
Giele, Kosower, PS : hep-ph/0707.3652
Peter Skands Event Generator Status 41
Dipole-Antenna FunctionsDipole-Antenna Functions► Starting point: “GGG” antenna functions, e.g.,
► Generalize to arbitrary Laurent series:
Can make shower systematically “softer” or “harder”
• Will see later how this variation is explicitly canceled by matching
quantification of uncertainty
quantification of improvement by matching
yar = sar / si
si = invariant mass of i’th dipole-antenna
Giele, Kosower, PS : hep-ph/0707.3652
Gehrmann-De Ridder, Gehrmann, Glover, JHEP 09 (2005) 056
Singular parts fixed, finite terms arbitrary
Peter Skands Event Generator Status 42
Quantifying MatchingQuantifying Matching► The unknown finite terms are a major source of uncertainty
• DGLAP has some, GGG have others, ARIADNE has yet others, etc…
• They are arbitrary (and in general process-dependent)
Using αs(MZ)=0.137, μR=1/4mdipole, pThad = 0.5 GeV
Peter Skands Event Generator Status 43
MatchingMatching
Fixed Order (all orders)
Matched shower (including simultaneous tree- and 1-loop matching for any number of legs)
Tree-level “real” matching term for X+k
Loop-level “virtual+unresolved” matching term for X+k
Pure Shower (all orders)
Giele, Kosower, PS : hep-ph/0707.3652
Peter Skands Event Generator Status 44
Tree-level matching to X+1Tree-level matching to X+11. Expand parton shower to 1st order (real radiation term)
2. Matrix Element (Tree-level X+1 ; above thad)
Matching Term:
variations in finite terms (or dead regions) in Ai canceled (at this order)
• (If A too hard, correction can become negative negative weights)
Inverse phase space map ~ clustering
Giele, Kosower, PS : hep-ph/0707.3652
Peter Skands Event Generator Status 45
Soft Standard Hard
Matched Soft Standard Matched Hard
Phase Space PopulationPhase Space Population
Positive correction Negative correction
Peter Skands Event Generator Status 46
Quantifying MatchingQuantifying Matching► The unknown finite terms are a major source of uncertainty
• DGLAP has some, GGG have others, ARIADNE has yet others, etc…
• They are arbitrary (and in general process-dependent)
Using αs(MZ)=0.137, μR=1/4mdipole, pThad = 0.5 GeV
Peter Skands Event Generator Status 47
1-loop matching to X1-loop matching to X► NLO “virtual term” from parton shower (= expanded Sudakov: exp=1 - … )
► Matrix Elements (unresolved real plus genuine virtual)
► Matching condition same as before (almost):
► You can choose anything for Ai (different subtraction schemes) as long as you use the same one for the shower
Tree-level matching just corresponds to using zero• (This time, too small A correction negative)
Giele, Kosower, PS : hep-ph/0707.3652
Peter Skands Event Generator Status 48
Note about “NLO” matchingNote about “NLO” matching► Shower off virtual matching term uncanceled O(α2) contribution
to 3-jet observables (only canceled by 1-loop 3-parton matching)
► While normalization is improved, shapes are not (shape still LO)
Using αs(MZ)=0.137, μR=1/4mdipole, pThad = 0.5 GeV
Tree-Level Matching “NLO” Matching
Peter Skands Event Generator Status 49
What to do next?What to do next?► Go further with tree-level matching
• Demonstrate it beyond first order (include H,Z 4 partons)
• Automated tree-level matching (w. Rikkert Frederix (MadGraph) + …?)
► Go further with one-loop matching
• Demonstrate it beyond first order (include 1-loop H,Z 3 partons)• Should start to see cancellation of ordering variable and renormalization scale
• Should start to see stabilization of shapes as well as normalizations
► Extend the formalism to the initial state
► Extend to massive particles
• Massive antenna functions, phase space, and evolution
The Generator Outlook
Peter Skands Event Generator Status 51
The Generator OutlookThe Generator Outlook► Generators in state of continuous development:
► Better & more user-friendly general-purpose matrix element calculators+integrators
► Improved parton showers and improved matching to matrix elements
► Improved models for underlying events / minimum bias
► Upgrades of hadronization and decays
► Moving to C++
► Data needed to constrain models & rule out crazy ideas• New methods could QCD become a precision science?
► Important for virtually all other measurements + can shed light on fundamental & interesting aspects of QCD (e.g. string interactions)