Matching of Matrix Elements and Parton Showers with ...conferences.fnal.gov/loopfest6/Slides/s10/alwall.pdf · 1Fixed order calculation 2Limited number of particles 3Valid when partons

Matching withMadEvent-Pythia

Johan Alwall

Why Matching?

Matching schemes

Results

Conclusions

Matching of Matrix Elements and Parton Showerswith MadEvent and Pythia

Johan Alwall

SLAC

LoopFest ’07, Fermilab, April 18, 2007

1 / 28


Johan Alwall

Why Matching?

Matching schemes

Results

Conclusions

Outline

1 Why Matching?

2 Matching schemes

3 Results

4 Conclusions

2 / 28


Johan Alwall

Why Matching?

Matrix elementsvs. parton showers

Parton showering

Matrix elementgenerators

Matching schemes

Results

Conclusions

Why Matching? – Matrix elements vs. parton showers

Matrix elements

1 Fixed order calculation

2 Limited number of particles

3 Valid when partons are hardand well separated

4 Quantum interferencecorrect

5 Needed for multi-jetdescription

Parton showers

1 Resums large logs

2 No limit on particle multiplicity

3 Valid when partons arecollinear and/or soft

4 Partial quantum interferencethrough angular ordering

5 Needed for hadronization/detector simulation

Matrix element and Parton showers complementary approaches

Both necessary in high-precision studies of multijet processes

Need to combine them without double-counting!

3 / 28


Johan Alwall

Why Matching?


Parton showering


Matching schemes

Results

Conclusions

Parton showering

QCD strahlung from soft/collinear emission approximation

Evolves down from hard interaction scale to hadronizationscale/initial state hadron scale

Sudakov form factors gives non-branching probability between scales

∆LL(t1, t2) = exp

(−

Z t1

t2

dt′

t′

Z 1−ε(t)

ε(t)

dzαs(t)

2πbP(z)

)

t2 distribution from − d∆(t1,t2)dt2

z distribution from QCD splitting functions Pa→bc(z)

For initial state radiation (backward evolution), extra factor off (x , t2)/f (x , t1) at each splitting to account for parton content atdifferent scales

Different choice of evolution variable t in different generators

Pythia: Q2 (old), p2T (new) – Herwig E 2θ2 – Ariadne p2

T (2 → 3)

4 / 28


Johan Alwall

Why Matching?


Parton showering


Matching schemes

Results

Conclusions

Matrix element generators

Use complete matrix element

Diagrams for ud → e+νeuug by MadGraph

Get appropriate description for well separated jets (away fromcollinear region)Get interference effects/correlations correctly

Examples: MadGraph/MadEvent, Alpgen, HELAC, Sherpa5 / 28


Johan Alwall

Why Matching?

Matching schemes

CKKW matching

MLM matching

Differencesbetween CKKWand MLM

Matching schemesin MadEvent

Results

Conclusions

Matching schemes

The simple idea behind matching

Use matrix element description for well separated jets, and partonshowers for collinear jets

Phase-space cutoff to separate regions

This allows to combine different jet multiplicities from matrix elementswithout double counting with parton shower emissions

Difficulties

Get smooth transition between regions

No/small dependence from precise cutoff

No/small dependence from largest multiplicity sample

How to accomplish this

Two solutions so far:

CKKW matching

MLM matching

(Interesting newcomer: SCET M. Schwartz)

6 / 28


Johan Alwall

Why Matching?

Matching schemes

CKKW matching

MLM matching



Results

Conclusions

CKKW matching

Catani, Krauss, Kuhn, Webber [hep-ph/0109231], Krauss [hep-ph/0205283]

Imitate parton shower procedure for matrix elements

1 Choose a cutoff (jet resolution) scale dini

2 Generate multiparton event with dmin = dini andfactorization scale dini

3 Cluster event with kT algorithm to find “parton shower history”

4 Use di ' k2T in each vertex as scale for αs

5 Weight event with NLL Sudakov factor ∆(dj , dini)/∆(di , dini) foreach parton line between vertices i and j (dj can be dini)

6 Shower event, allowing only emissions with kT < dini (“vetoedshower”)

7 For highest multiplicity sample, use min(di ) of event as dini

Boost-invariant kT measure:diB = p2

T ,i

dij = min(p2T ,i , p

2T ,j)Fij

Fij = cosh(ηi − ηj)− cos(φi − φj)

7 / 28


Johan Alwall

Why Matching?

Matching schemes

CKKW matching

MLM matching



Results

Conclusions

Sudakov reweighting

Telescopic product – in theexample:

[∆q(d3, dini)]2 ∆g (d2, dini)

∆g (d1, dini)

×∆q(d1, dini)∆q(d1, dini)

Vetoed showers

Start shower for parton at scale of mothernode (cf. upper scale for Sudakovsuppression)

Veto (forbid) emissions with d > dini, butcontinue shower as if emission happened

Allow emissions below dini

8 / 28


Johan Alwall

Why Matching?

Matching schemes

CKKW matching

MLM matching



Results

Conclusions

PDF factors in the Krauss algorithm

Want to account for probability of PS configuration in ME correctionweightFor ISR process shown, get PS probability:

∆q(t, tini)2∆g (t1, tini)∆g (t2, tini)

× q(x2, tini)

q(x2, t)

q(x1/z1z2, tini)

q(x1/z1z2, t2)

× q(x1/z1z2, t2)

q(x1/z1, t1)

αs(t2)

2π

Pqq(z2)

z2

× q(x1/z1, t1)

q(x1, t)

αs(t1)

2π

Pqq(z1)

z1

t2/z

/z t1

x2

z1

x 1

tx

gives, combined with LO cross-section q(x1, t)q(x2, t)d σqq→ll :

dσDY+gg = ∆q(t, tini)2∆g (t1, tini)∆g (t2, tini)q(x ′1, tini)q(x2, tini)

× αs(t1)

2π

αs(t2)

2π

Pqq(z1)

z1

Pqq(z2)

z2d σqq→ll(s/z1z2)

Red: Correction weight Blue: PDFs Green: d σPSqq→llgg (x

′1 = x1

z1z2, x2)

9 / 28


Johan Alwall

Why Matching?

Matching schemes

CKKW matching

MLM matching



Results

Conclusions

For final-state showers (e+e−collision):Combination of NLL Sudakov factors and vetoed NLL showersguarantees independence of qini to NLL order

For initial-state showers: No proof but seems to work ok (Sherpa)

Problem in practice: No NLL shower implementation!(Sherpa uses Pythia-like showers and adapted Sudakovs)

/GeV)1log(Q-0.5 0 0.5 1 1.5 2 2.5 3

/GeV

)1

/dlo

g(Q

σ dσ

1/

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1

SHERPA

=100 GeVcutQ

/GeV)1log(Q-0.5 0 0.5 1 1.5 2 2.5 3

/GeV

)1

/dlo

g(Q

σ dσ

1/

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1

SHERPA

=30 GeVcutQ

/GeV)1log(Q-0.5 0 0.5 1 1.5 2 2.5 3

/GeV

)1

/dlo

g(Q

σ dσ

1/

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1

SHERPA

=15 GeVcutQ

Differential 0 → 1 jet rate by Sherpa in pp → Z + jets for three differentcutoffs dini, compared to averaged reference curve [hep-ph/0503280]

10 / 28


Johan Alwall

Why Matching?

Matching schemes

CKKW matching

MLM matching



Results

Conclusions

MLM matching

M.L. Mangano [2002, Alpgen home page, hep-ph/0602031]

Use parton shower to choose events

1 Generate multiparton event with cut on jet pTmin, ηmax and ∆Rmin,and factorizations scale = “central scale” (e.g. transverse mass)

2 Cluster event (according to color) and use k2T for αs scale

3 Shower event (using Pythia or Herwig) starting from fact. scale

4 Collect showered partons in cone jets with same ∆Rmin andpTcut > pTmin

5 Keep event only if each jet matched to one parton(∆R(jet, parton < 1.5∆R)

6 For highest multiplicity sample, allow extra jets with pT < ppartonTmin

Keep Discard Keep only if highestmultiplicity 11 / 28


Johan Alwall

Why Matching?

Matching schemes

CKKW matching

MLM matching



Results

Conclusions

Differences between CKKW and MLM

CKKW scheme: Assumes intimate knowledge of and modificationsto parton shower. Needs analytical form for parton shower Sudakovs.

MLM scheme: Effective Sudakov suppression directly from partonshower

However: MLM not sensitive to parton types of internal lines(remedied by pseudoshower approach, see below)

Factorization scale: In CKKW jet resolution scale, in MLM centralscale. Not clear (?) which is better.

Highest multiplicity treatment – less obvious in MLM than in CKKW

CKKW with pseudoshowers

Lonnblad [hep-ph/0112284] (ARIADNE)Mrenna, Richardsson [hep-ph/0312274]

Apply parton shower stepwize to clustered event, reject event if toohard emission

Apply vetoed parton shower as in the CKKW approach

12 / 28


Johan Alwall

Why Matching?

Matching schemes

CKKW matching

MLM matching



Results

Conclusions

Matching schemes in MadEvent

J.A. et al. [in preparation] (cf. Mrenna, Richardsson [hep-ph/0312274])

CKKW scheme (for Sherpa showers) (with S. Hoche)

MLM scheme (Pythia showers)

MLM scheme with kT jet clustering (Pythia showers)

Event rejection at parton shower level (work in progress)

Details of MadEvent kT MLM scheme

1 Generate multiparton event with jet measure cutoff dmin

2 Cluster event (according to diagrams) and use kT for αs scale

3 Shower event with Pythia starting from highest clustering scale (=factorization scale)

4 Perform jet clustering with kT algorithm with dcut > dmin

5 Match clustered jets to partons (d(jet, parton) < dcut)

6 Discard events where jets not matched

7 For highest multiplicity sample, jets matched ifd(jet, parton) < dmin(parton, parton)

13 / 28


Johan Alwall

Why Matching?

Matching schemes

Results

Results 1: W± +jets

Comparisonbetween codes

Results 2: Toppairs + jets atLHC

Results 3: Gluinopairs at LHC

Results 4: QCDjets at LHC

Conclusions

Results 1: W± + jets

Important background (especially at the Tevatron)

Only one hard scale

Mainly initial state radiation

Implemented by all matching softwares

) (GeV)3

log(Q0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

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Sum of contributions

0-jet sample

1-jet

2-jet

3-jet

4-jet scale x 0.5/2sα

) (GeV)2

log(Q0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

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Sum of contributions

0-jet sample

1-jet

2-jet

3-jet

4-jet

=10 GeVcut

Matched, Q

) (GeV)2

log(Q0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

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Differential 0 → 1, 1 → 2, 2 → 3 jet rates at parton level byMadEvent + Pythia in pp → W + jets at the Tevatron,dcut = 10 GeV (top), 30 GeV (bottom).

14 / 28


Johan Alwall

Why Matching?

Matching schemes

Results






Conclusions

(GeV)TWP0 20 40 60 80 100 120 140 160 180 200 220

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10

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scale x 0.5/2sαD0 run 1 data

(GeV)TWP0 5 10 15 20 25 30 35 40 45 50

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2-jet

3-jet4-jet

=10 GeVcut

Matched total, Q

D0 run 1 data

(GeV)TWP0 5 10 15 20 25 30 35 40 45 50

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pT of W± by MadEvent + Pythia in pp → W + jets at the Tevatron,dcut = 10 GeV (top), 30 GeV (bottom).

Note:Pure Pythia shower (without matrix element corrections) below cut.

15 / 28


Johan Alwall

Why Matching?

Matching schemes

Results






Conclusions

Comparison between codes

J.A. et al. [hep-ph/soon]Alpgen+Herwig, Ariadne, Helac+Pythia, MadEvent+Pythia, Sherpa

0

0.5

1

1.5

2

2.5

≥ 0 ≥ 1 ≥ 2 ≥ 3 ≥ 4

σ(W

+/-+

≥ N

jets

) / <

σ>

AlpgenAriadne

HelacMadEvent

Sherpa

0

0.5

1

1.5

2

2.5

3

≥ 0 ≥ 1 ≥ 2 ≥ 3 ≥ 4

σ(W

++

≥ N

jets

) / <

σ>

AlpgenAriadne

HelacMadEvent

Sherpa

Jet rates at the Tevatron (top) andLHC (bottom)

pT of the W± at the Tevatron(top) and LHC (bottom)

16 / 28


Johan Alwall

Why Matching?

Matching schemes

Results






Conclusions

W± + jets comparison plots: Jet ET for LHC

dσ/d

E⊥

1 (p

b/G

eV)

(a)Alpgen

AriadneHelac

MadEventSherpa

10-2

10-1

100

101

102

E⊥ 1 (GeV)

-2-1 0 1 2

0 50 100 150 200 250 300 350 400 450 500

dσ/d

E⊥

2 (p

b/G

eV)

(b)

10-2

10-1

100

101

102

E⊥ 2 (GeV)

-2-1 0 1 2

0 50 100 150 200 250 300 350 400

dσ/d

E⊥

3 (p

b/G

eV)

(c)

10-3

10-2

10-1

100

101

E⊥ 3 (GeV)

-2-1 0 1 2

0 50 100 150 200 250 300dσ

/dE

⊥4

(pb/

GeV

)

(d)

10-3

10-2

10-1

100

101

E⊥ 4 (GeV)

-2-1 0 1 2

0 50 100 150 200

17 / 28


Johan Alwall

Why Matching?

Matching schemes

Results






Conclusions

W± + jets comparison plots: Jet η for LHC

(1/σ

)dσ/

dη1

(a)

AlpgenAriadne

HelacMadEvent

Sherpa

0.1

0.2

η1

-0.4-0.2

0 0.2 0.4

-4 -3 -2 -1 0 1 2 3 4

(1/σ

)dσ/

dη2

(b)

0.1

0.2

η2

-0.4-0.2

0 0.2 0.4

-4 -3 -2 -1 0 1 2 3 4

(1/σ

)dσ/

dη3

(c)

0.1

0.2

η3

-0.4-0.2

0 0.2 0.4

-4 -3 -2 -1 0 1 2 3 4(1

/σ)d

σ/dη

4

(d)

0.1

0.2

η4

-0.4-0.2

0 0.2 0.4

-4 -3 -2 -1 0 1 2 3 4

18 / 28


Johan Alwall

Why Matching?

Matching schemes

Results






Conclusions

Results 2: Top pairs + jets at LHC

J.A., S. de Vissher et al. [in preparation]

One of the most important backgrounds to new physics at the LHC

pT of the tt pair – indicator of jet activity/hardness

(t,tbar)tP0 100 200 300 400 500 600

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in)

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Matched contributions

0+1+2 jets excl sample

0+1 jets excl sample

0 jets excl sample

Pythia (no matching)

Matched MadEvent+Pythiatt + jets compared to onlytt + Pythia parton showers

Matched Alpgen+Herwig –agrees well within statistics

19 / 28


Johan Alwall

Why Matching?

Matching schemes

Results






Conclusions

Differential jet rates (once again) to check smoothness over transition +independence of cut

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log(d0 0.5 1 1.5 2 2.5 3

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0-jet sample

1-jet sample

2-jet sample

3-jet sample

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0-jet sample

1-jet sample

2-jet sample

3-jet sample=25 GeVcutMatched d

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log(d0 0.5 1 1.5 2 2.5 3

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Differential 0 → 1, 1 → 2, 2 → 3 jet rates at parton level by MadEvent +Pythia in pp → tt + jets at the LHC,dcut = 25 GeV (top), 60 GeV (bottom). No top decays.

20 / 28


Johan Alwall

Why Matching?

Matching schemes

Results






Conclusions

Results 3: Gluino pairs at LHC

Work in progress using new scheme

600 GeV mass gluino pair production (SPS1a) at LHC

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Differential 0 → 1, 1 → 2, 2 → 3 jet rates at parton level by MadEvent +Pythia in pp → g g + jets at the LHC, dcut = 40 GeV, compared todefault Pythia showers (red curve). No gluino decays.

21 / 28


Johan Alwall

Why Matching?

Matching schemes

Results






Conclusions

Results 4: QCD jets at LHC

Work in progress using new scheme

Pure QCD jets – difficult since no fixed hard scale

Ptjet20 20 40 60 80 100 120 140 160 180 200 220

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2-jet sample

3-jet sample

4-jet sample

Pythia non-matched

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PRELIMINARY

PRELIMINARY

Steeply falling pT spectra – Pythia showers (red curve) seems to give OKshape description with the correct starting scale (p2

T of jets)

22 / 28


Johan Alwall

Why Matching?

Matching schemes

Results

Conclusions

Conclusions

Matrix elements and parton showers - complementary descriptions ofparton production:

ME needed to describe hard and widely separated jetsPS needed for very high multiplicities / substructure of jets /evolution to hadronization scale

For realistic description of multijet backgrounds – necessary tocombine descriptions: Matching!

Important backgrounds: Z/W± + jets, tt + jets,W +W−/ZZ/W±Z + jets, pure QCD

Also interesting to study jet structure of signal, e.g. WBF

Comparison with other codes done!

Validation with Tevatron data underway

MadGraph/MadEvent can do it – more studies underway!

Visit us – generate processes – generate events on

http://madgraph.phys.ucl.ac.be

http://madgraph.roma2.infn.it

http://madgraph.hep.uiuc.edu

23 / 28


Johan Alwall

Why Matching?

Matching schemes

Results

Conclusions

BACKUP SLIDES

24 / 28


Johan Alwall

Why Matching?

Matching schemes

Results

Conclusions

MadGraph/MadEvent

A user-driven matrix element generator and event generator

Madgraph (T.Stelzer and W.F.Long - 1994)

Matrix element generation

Identifies all Feynman diagrams and creates Fortran code for thematrix element squared (calls HELAS routines)

Handles tree-level processes with many particles in the final state

Keeps full spin correlations / interference

MadEvent (F.Maltoni and T.Stelzer - 2003)

Phase space integration and event generation

Uses the MadGraph output and diagram information

Efficient phase space integration using the techniqueSingle-Diagram-Enhanced multichannel integration

fi =|Atot|2P

i |Ai |2|Ai |2

Algorithm parallell in nature - optimal for clusters!

25 / 28


Johan Alwall

Why Matching?

Matching schemes

Results

Conclusions

More about MadGraph/MadEvent

ModelsImplemented by default: SM, SUSY, 2HDM, Higgs EFTFramework for easy implementation of new modelsSoon to come: MadRules (MG files from Lagrangian)

ToolsPythia and PGS interface for shower/hadronization and detectorsimulationMadAnalysis, ExRootAnalysisBRIDGE (Reece, Meade): Decay of particles in any MadGraph model

Complete simulation chain available: from hard scale physics todetector simulation! (MadGraph/MadEvent – Pythia – PGS)

Web-based generation or download code

Three public clusters:Belgium (http://madgraph.phys.ucl.ac.be)Italy (http://madgraph.roma2.infn.it)US (http://madgraph.hep.uiuc.edu)

26 / 28


Johan Alwall

Why Matching?

Matching schemes

Results

Conclusions

Sherpa like Pythia – New Pythia shower similar to Ariadne

27 / 28


Johan Alwall

Why Matching?

Matching schemes

Results

Conclusions

28 / 28

Documents

Matching of Matrix Elements and Parton Showers with ...conferences.fnal.gov/loopfest6/Slides/s10/alwall.pdf · 1Fixed order calculation 2Limited number of particles 3Valid when partons