MatchingME+Pythia
Johan Alwall
Jet matching –ME vs. PS
Jet matchingschemes
Matching inMadGraph /MadEvent
Conclusions
Matching of W +jets in
MadEvent and Pythia
Johan Alwall
SLAC
Berkeley workshop on Boson + jets productionMarch 27, 2008
1 / 19
MatchingME+Pythia
Johan Alwall
Jet matching –ME vs. PS
Jet matchingschemes
Matching inMadGraph /MadEvent
Conclusions
Outline
1 Jet matching – ME vs. PS
2 Jet matching schemes
3 Matching in MadGraph / MadEvent
4 Conclusions
2 / 19
MatchingME+Pythia
Johan Alwall
Jet matching –ME vs. PS
Jet matchingschemes
Matching inMadGraph /MadEvent
Conclusions
Jet matching – ME vs. PS
Matrix elements
1 Fixed order calculation
2 Computationally expensive
3 Limited number ofparticles
4 Valid when partons arehard and well separated
5 Quantum interferencecorrect
6 Needed for multi-jetdescription
Parton showers
1 Resums logs to all orders
2 Computationally cheap
3 No limit on particlemultiplicity
4 Valid when partons arecollinear and/or soft
5 Partial quantum interferencethrough angular ordering
6 Needed for hadronization/detector simulation
Matrix element and Parton showers complementary approaches
Both necessary in high-precision studies of multijet processes
Need to combine without double-counting
3 / 19
MatchingME+Pythia
Johan Alwall
Jet matching –ME vs. PS
Jet matchingschemes
CKKW matching
MLM matching
Differencesbetween CKKWand MLM
Matching inMadGraph /MadEvent
Conclusions
Jet matching schemesThe simple idea behind matching
Use matrix element description for well separated jets,and parton showers for collinear jets
Phase-space cutoff to separate regions
=⇒ No double-counting between jet multiplicities
Difficulties
Get smooth transition between regions
No/small dependence from precise cutoff
No/small dependence from largest multiplicity sample
How to accomplish this
CKKW matching (Catani, Krauss, Kuhn, Webber)
MLM matching (M.L. Mangano)
(Interesting newcomers: SCET Schwartz,GenEvA Bauer, Tackman, Thaler)
4 / 19
MatchingME+Pythia
Johan Alwall
Jet matching –ME vs. PS
Jet matchingschemes
CKKW matching
MLM matching
Differencesbetween CKKWand MLM
Matching inMadGraph /MadEvent
Conclusions
CKKW matchingCatani, Krauss, Kuhn, Webber [hep-ph/0109231], Krauss [hep-ph/0205283]
Imitate parton shower procedure for matrix elements
1 Choose a cutoff scale dini
2 Generate multiparton event with dmin = dini
3 Cluster event with kT algorithm to find “parton showerhistory”
4 Use di ' k2T in each vertex as scale for αs
5 Weight event with Sudakov factor ∆(di , dj) for each partonline between vertices i and j
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)R(i , j)
R(i , j) = cosh∆ηij − cos ∆φij
5 / 19
MatchingME+Pythia
Johan Alwall
Jet matching –ME vs. PS
Jet matchingschemes
CKKW matching
MLM matching
Differencesbetween CKKWand MLM
Matching inMadGraph /MadEvent
Conclusions
Final-state showers:Combination of NLL Sudakov factors and vetoed NLLshowers guarantees independence of qini to NLL order
Initial-state showers: Proof by example (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
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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
different dini, compared to averaged reference curve
[hep-ph/0503280]
6 / 19
MatchingME+Pythia
Johan Alwall
Jet matching –ME vs. PS
Jet matchingschemes
CKKW matching
MLM matching
Differencesbetween CKKWand MLM
Matching inMadGraph /MadEvent
Conclusions
MLM matchingM.L. Mangano [2002, Alpgen home page, arXiv:0706.2569]
Use shower hardness to separate ME/PS
1 Generate multiparton event with cut on jet pT , η and ∆R2 Cluster event and use k2
T for αs scale (as in CKKW)3 Shower event (using Pythia or Herwig)4 Collect showered partons in cone jets with
pT ,min(jet) > pT ,min(parton)5 Keep event only if each jet corresponds to one parton
(“matched”)6 For highest multiplicity sample, allow extra jets with
pT < ppartonTmin
Keep Discard unless highest multiplicity7 / 19
MatchingME+Pythia
Johan Alwall
Jet matching –ME vs. PS
Jet matchingschemes
CKKW matching
MLM matching
Differencesbetween CKKWand MLM
Matching inMadGraph /MadEvent
Conclusions
Differences between CKKW and MLM
CKKW scheme: Assumes intimate knowledge of andmodifications to parton shower. Needs analytical form forparton shower Sudakovs.
MLM scheme: Effective Sudakov suppression directly fromparton shower
However: MLM not sensitive to parton types of internal lines(remedied by pseudoshower approach, see below)
Factorization scale: In CKKW jet resolution scale, in MLMcentral scale.
Highest multiplicity treatment – less obvious in MLM than inCKKW
MLM only for hadronic collisions (so far)
CKKW with pseudoshowers
Lonnblad [hep-ph/0112284] (ARIADNE)Mrenna, Richardsson [hep-ph/0312274]
Apply parton shower stepwize to clustered event, reject eventif too hard emission
Apply vetoed parton shower as in the CKKW approach
8 / 19
MatchingME+Pythia
Johan Alwall
Jet matching –ME vs. PS
Jet matchingschemes
Matching inMadGraph /MadEvent
Old and NewPythia showers
Impact of showeron matching
pT (W ) at theTevatron
Summary ofshower impact
“Shower kT ”scheme
Conclusions
Matching in MadGraph / MadEventJ.A. et al. [arXiv:0706.2569], [work in progress](cf. Mrenna, Richardsson [hep-ph/0312274])
CKKW scheme (for Sherpa showers) (with S. Hoche)
MLM scheme (Pythia showers, old & new)
MLM scheme with kT jets (Pythia showers, old & new)
“Shower kT scheme” (Pythia showers, new)
Details of MadEvent kT MLM scheme
1 Generate multiparton event with kT clustering cutoff dcut
2 Cluster event and use kT for αs scale3 Shower event with Pythia4 Perform jet clustering with kT algorithm, dmin(jet) > dcut
5 Match clustered jets to partons (d(jet, parton) < dmin(jet))6 Discard events where jets not matched7 For highest multiplicity sample, jets matched if
d(jet, parton) < dmin(parton, parton)
9 / 19
MatchingME+Pythia
Johan Alwall
Jet matching –ME vs. PS
Jet matchingschemes
Matching inMadGraph /MadEvent
Old and NewPythia showers
Impact of showeron matching
pT (W ) at theTevatron
Summary ofshower impact
“Shower kT ”scheme
Conclusions
Advantages with kT jets
Immediate comparison with CKKW scheme
One matching parameter (d jetmin vs. pT ,min,∆Rmin)
Easy to check smoothness by plotting jet rates djet
Allows to use “shower kT scheme”
Allows straightforward investigations of parton showers
Shower kT scheme
Keep/reject event based on kT of hardest shower emission (asreported by Pythia)
Highest multiplicity treatment as in CKKW, use min dparton ascutoff
No jet clustering
No need of “fiducial region”, can use kmatchT = dME
cut
Need similar kT definitions in ME and PS (only “new”,pT -ordered showers at present)
10 / 19
MatchingME+Pythia
Johan Alwall
Jet matching –ME vs. PS
Jet matchingschemes
Matching inMadGraph /MadEvent
Old and NewPythia showers
Impact of showeron matching
pT (W ) at theTevatron
Summary ofshower impact
“Shower kT ”scheme
Conclusions
Old and New Pythia showers
Parton showers
Sudakov form factors for non-branching probability betweenscales
∆(t1, t2) = exp
{−
∫ t1
t2
dt ′
t ′
∫ 1−ε(t)
ε(t)
dzαs(t)
2πP(z)
}
QCD splitting functions Pa→b(z) for z distribution
Different choice of evolution variable t=⇒ “Old” Pythia showers: Q2
=⇒ “New” Pythia showers: p2T (dipole-inspired)
Can give quite different distributions
11 / 19
MatchingME+Pythia
Johan Alwall
Jet matching –ME vs. PS
Jet matchingschemes
Matching inMadGraph /MadEvent
Old and NewPythia showers
Impact of showeron matching
pT (W ) at theTevatron
Summary ofshower impact
“Shower kT ”scheme
Conclusions
Comparisons between old and new Pythia showers
Differential jet rates in W production at the Tevatron
) (GeV)2
log(Qpar0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2
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Unmatched "new" Pythia
Unmatched "old" Pythia
) (GeV)1
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1Unmatched "new" Pythia
Unmatched "old" Pythia
0→ 1 jet rate 1→ 2 jet rate
pT (W ) in W production at the Tevatron
(W), GeV/cTP0 20 40 60 80 100 120 140
pb
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1
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Unmatched "new" PythiaUnmatched "old" Pythia
D0 data
(W), GeV/cTP0 5 10 15 20 25 30 35 40 45 50
pb
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10
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Unmatched "new" PythiaUnmatched "old" Pythia
D0 data
12 / 19
MatchingME+Pythia
Johan Alwall
Jet matching –ME vs. PS
Jet matchingschemes
Matching inMadGraph /MadEvent
Old and NewPythia showers
Impact of showeron matching
pT (W ) at theTevatron
Summary ofshower impact
“Shower kT ”scheme
Conclusions
Impact of shower on matching
) (GeV)1
log(Qpar0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2
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Matched sum, new showers0-jet sample1-jet2-jet3-jet4-jetMatched sum, old showers
) (GeV)1
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in)
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Matched sum, old showers0-jet sample
1-jet
2-jet
3-jet
4-jet
“Old” Pythia showers “New” Pythia showers
dmatch (13 GeV) dmatch (13 GeV)
) (GeV)1
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Matched sum, new showers0-jet sample1-jet2-jet3-jet4-jet
=13 GeVmatch
Matched sum, d
Matched sum, old showers
) (GeV)1
log(Qpar0 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 contributions0-jet sample1-jet2-jet3-jet4-jet
=13 GeVmatch
Matched sum, d
dmatch (30 GeV) dmatch (30 GeV)
Differential 0→ 1 jet rate
13 / 19
MatchingME+Pythia
Johan Alwall
Jet matching –ME vs. PS
Jet matchingschemes
Matching inMadGraph /MadEvent
Old and NewPythia showers
Impact of showeron matching
pT (W ) at theTevatron
Summary ofshower impact
“Shower kT ”scheme
Conclusions
) (GeV)2
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Matched sum, new showers0-jet sample1-jet2-jet3-jet4-jetMatched sum, old showers
) (GeV)2
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in)
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Matched sum, old showers0-jet sample
1-jet
2-jet
3-jet
4-jet
“Old” Pythia showers “New” Pythia showers
dmatch (13 GeV) dmatch (13 GeV)
) (GeV)2
log(Qpar0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2
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in)
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Matched sum, new showers0-jet sample1-jet2-jet3-jet
=13 GeVmatch
Matched sum, d
Matched sum, old showers
) (GeV)2
log(Qpar0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2
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Matched sum, old shower0-jet sample1-jet2-jet3-jet4-jet
=13 GeVmatch
Matched sum, d
dmatch (30 GeV) dmatch (30 GeV)
Differential 1→ 2 jet rate
Old showers smooth for small cutoff, new showers for larger cutoff14 / 19
MatchingME+Pythia
Johan Alwall
Jet matching –ME vs. PS
Jet matchingschemes
Matching inMadGraph /MadEvent
Old and NewPythia showers
Impact of showeron matching
pT (W ) at theTevatron
Summary ofshower impact
“Shower kT ”scheme
Conclusions
pT (W ) at the Tevatron
(W), GeV/cTP0 5 10 15 20 25 30 35 40 45 50
pb
/GeV
10
210
Matched sum, new showers0-jet sample1-jet2-jet3-jet4-jetD0 data
(W), GeVTP0 5 10 15 20 25 30 35 40 45 50
pb
/GeV
10
210
Matched sum, old showers0-jet sample1-jet2-jet3-jet4-jetD0 data
“Old” Pythia showers “New” Pythia showers
dmatch (13 GeV) dmatch (30 GeV)
(W), GeV/cTP0 20 40 60 80 100 120 140 160 180 200
pb
/GeV
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1
10
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Matched sum, new showers0-jet sample1-jet2-jet3-jet4-jetMatched sum, old showersD0 data
(W), GeV/cTP0 20 40 60 80 100 120 140 160 180 200
pb
/GeV
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1
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Matched sum, old showers0-jet sample1-jet2-jet3-jet4-jetD0 data
dmatch (13 GeV) dmatch (30 GeV)
Tail well described by both, but head best by new shower
15 / 19
MatchingME+Pythia
Johan Alwall
Jet matching –ME vs. PS
Jet matchingschemes
Matching inMadGraph /MadEvent
Old and NewPythia showers
Impact of showeron matching
pT (W ) at theTevatron
Summary ofshower impact
“Shower kT ”scheme
Conclusions
Summary of shower impact
Different showers have very different behavior, especiallyat low kT
Strongly affects matching – need different treatment(e.g. cutoffs) for different showers
Matching stabilizes tail, but overall normalization isstrongly affected by shower=⇒ Normalizing overall cross section to e.g. NLO valuedangerous
New pythia showers seem to agree better with W/Z data– but why “step” in matching for low kT ?
16 / 19
MatchingME+Pythia
Johan Alwall
Jet matching –ME vs. PS
Jet matchingschemes
Matching inMadGraph /MadEvent
Old and NewPythia showers
Impact of showeron matching
pT (W ) at theTevatron
Summary ofshower impact
“Shower kT ”scheme
Conclusions
“Shower kT” schemeComparison with kT and cone jet MLM schemes
) (GeV)4
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) (GeV)3
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) (GeV)2
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Matched sum shower kT0-jet sample1-jet2-jet3-jet4-jetMLM kT jetsMLM cone jets
) (GeV)1
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dmatch (30 GeV) dmatch (30 GeV)
Excellent agreement with MLM methods17 / 19
MatchingME+Pythia
Johan Alwall
Jet matching –ME vs. PS
Jet matchingschemes
Matching inMadGraph /MadEvent
Old and NewPythia showers
Impact of showeron matching
pT (W ) at theTevatron
Summary ofshower impact
“Shower kT ”scheme
Conclusions
Dependence on highest multiplicity
) (GeV)4
log(Qpar0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2
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) (GeV)3
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) (GeV)2
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Max mult 2j0-jet sample1-jet2-jetMax mult 4j Max mult 1j
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Surprisingly small dependence with “shower kT” method!
18 / 19
MatchingME+Pythia
Johan Alwall
Jet matching –ME vs. PS
Jet matchingschemes
Matching inMadGraph /MadEvent
Conclusions
Conclusions
Have presented investigation of shower and schemedependence for the benchmark case W + jets
Shower dependence larger than expected (should beequivalent for small kT !?)
Needs care with e.g. cutoff values (pT or kT )
New “shower kT” scheme presented, with many niceproperties:−→ More efficient than standard MLM since no “fiducialregion” needed−→ Agrees with MLM schemes−→ Remarkable insensitivity to highest multiplicitysample−→ No need for special treatment of e.g. top or b quarks
So far only for “new” Pythia shower
19 / 19