aachen, november 2007 event generators 2 advanced topics peter skands cern / fermilab evolution...

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!


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


► 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


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


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



Hard Scattering

PT(hard)

Outgoing Parton

Outgoing Parton



Proton AntiProton


Proton AntiProton


“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!


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


► 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


“Toward”

“Away”


“Away-Side” Jet

Jet #1 Direction


“Toward”

“Away”


“Away-Side” Jet

Jet #3

Min-Bias0.25 per unit -

Log Scale!

Charged Particle Density Charged Particle Density Dependence Dependence


► 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.


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



30 < ET(jet#1) < 70 GeV

"Transverse" Region

Jet#1

Jet #1 Direction

“Toward”


“Away”

Jet #1 Direction

“Toward”


“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.


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



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


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


Jet #1 Direction

“Toward”


“Away”

Jet #1 Direction

“Toward”


“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


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


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





► 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


► 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


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


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


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


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+)


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


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


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” ?


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


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


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


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


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:


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


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”


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


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


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


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


•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) …


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


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


Dipole-Antenna ShowersDipole-Antenna Showers► Dipole branching and phase space



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


Gehrmann-De Ridder, Gehrmann, Glover, JHEP 09 (2005) 056

Singular parts fixed, finite terms arbitrary


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


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)



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



Soft Standard Hard

Matched Soft Standard Matched Hard

Phase Space PopulationPhase Space Population

Positive correction Negative correction


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)



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)



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)


Tree-Level Matching “NLO” Matching


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


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)

aachen, november 2007 event generators 2 advanced topics peter skands cern / fermilab evolution...

Documents

event generator statuslecture

underlying event observables

event generators

parton showers

hard core component

hard core crosssection

hard partonic scattering

beambeam remnants