matching of matrix elements and parton showers with...
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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
Matching withMadEvent-Pythia
Johan Alwall
Why Matching?
Matching schemes
Results
Conclusions
Outline
1 Why Matching?
2 Matching schemes
3 Results
4 Conclusions
2 / 28
Matching withMadEvent-Pythia
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
Matching withMadEvent-Pythia
Johan Alwall
Why Matching?
Matrix elementsvs. parton showers
Parton showering
Matrix elementgenerators
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
Matching withMadEvent-Pythia
Johan Alwall
Why Matching?
Matrix elementsvs. parton showers
Parton showering
Matrix elementgenerators
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
Matching withMadEvent-Pythia
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
Matching withMadEvent-Pythia
Johan Alwall
Why Matching?
Matching schemes
CKKW matching
MLM matching
Differencesbetween CKKWand MLM
Matching schemesin MadEvent
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
Matching withMadEvent-Pythia
Johan Alwall
Why Matching?
Matching schemes
CKKW matching
MLM matching
Differencesbetween CKKWand MLM
Matching schemesin MadEvent
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
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Matching withMadEvent-Pythia
Johan Alwall
Why Matching?
Matching schemes
CKKW matching
MLM matching
Differencesbetween CKKWand MLM
Matching schemesin MadEvent
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)
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Matching withMadEvent-Pythia
Johan Alwall
Why Matching?
Matching schemes
CKKW matching
MLM matching
Differencesbetween CKKWand MLM
Matching schemesin MadEvent
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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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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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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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
Matching withMadEvent-Pythia
Johan Alwall
Why Matching?
Matching schemes
CKKW matching
MLM matching
Differencesbetween CKKWand MLM
Matching schemesin MadEvent
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
Matching withMadEvent-Pythia
Johan Alwall
Why Matching?
Matching schemes
CKKW matching
MLM matching
Differencesbetween CKKWand MLM
Matching schemesin MadEvent
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
Matching withMadEvent-Pythia
Johan Alwall
Why Matching?
Matching schemes
CKKW matching
MLM matching
Differencesbetween CKKWand MLM
Matching schemesin MadEvent
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)
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Matching withMadEvent-Pythia
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
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Sum of contributions
0-jet sample
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4-jet scale x 0.5/2sα
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Sum of contributions
0-jet sample
1-jet
2-jet
3-jet
4-jet
=10 GeVcut
Matched, Q
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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
Matching withMadEvent-Pythia
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
(GeV)TWP0 20 40 60 80 100 120 140 160 180 200 220
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scale x 0.5/2sαD0 run 1 data
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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
Matching withMadEvent-Pythia
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
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
Matching withMadEvent-Pythia
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
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
Matching withMadEvent-Pythia
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
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
Matching withMadEvent-Pythia
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 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
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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
Matching withMadEvent-Pythia
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
Differential jet rates (once again) to check smoothness over transition +independence of cut
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0-jet sample
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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
Matching withMadEvent-Pythia
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 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
Matching withMadEvent-Pythia
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 4: QCD jets at LHC
Work in progress using new scheme
Pure QCD jets – difficult since no fixed hard scale
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2-jet sample
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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
Matching withMadEvent-Pythia
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
Matching withMadEvent-Pythia
Johan Alwall
Why Matching?
Matching schemes
Results
Conclusions
BACKUP SLIDES
24 / 28
Matching withMadEvent-Pythia
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
Matching withMadEvent-Pythia
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
Matching withMadEvent-Pythia
Johan Alwall
Why Matching?
Matching schemes
Results
Conclusions
Sherpa like Pythia – New Pythia shower similar to Ariadne
27 / 28
Matching withMadEvent-Pythia
Johan Alwall
Why Matching?
Matching schemes
Results
Conclusions
28 / 28
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