Matching with MadEvent-Pythia Johan Alwall Why Matching? Matching schemes Matching of Matrix Elements and Parton Showers Results with MadEvent and Pythia Conclusions Johan Alwall SLAC LoopFest ’07, Fermilab, April 18, 2007 1 / 28
Matching with Outline MadEvent-Pythia Johan Alwall Why Matching? Matching schemes Results Why Matching? 1 Conclusions Matching schemes 2 Results 3 Conclusions 4 2 / 28
Matching with Why Matching? – Matrix elements vs. parton showers MadEvent-Pythia Johan Alwall Why Matching? Matrix elements vs. parton showers Matrix elements Parton showers Parton showering Matrix element generators Fixed order calculation Resums large logs 1 1 Matching schemes Limited number of particles No limit on particle multiplicity 2 2 Results Valid when partons are hard Valid when partons are 3 Conclusions 3 and well separated collinear and/or soft Quantum interference Partial quantum interference 4 4 correct through angular ordering Needed for multi-jet 5 Needed for hadronization/ 5 description 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 with Parton showering MadEvent-Pythia Johan Alwall QCD strahlung from soft/collinear emission approximation Why Matching? Matrix elements Evolves down from hard interaction scale to hadronization vs. parton showers Parton showering scale/initial state hadron scale Matrix element generators Sudakov form factors gives non-branching probability between scales Matching schemes ( ) Z t 1 Z 1 − ǫ ( t ) Results dt ′ dz α s ( t ) b Conclusions ∆ LL ( t 1 , t 2 ) = exp − P ( z ) t ′ 2 π t 2 ǫ ( t ) t 2 distribution from − d ∆( t 1 , t 2) dt 2 z distribution from QCD splitting functions P a → bc ( z ) For initial state radiation (backward evolution), extra factor of f ( x , t 2 ) / f ( x , t 1 ) at each splitting to account for parton content at different scales Different choice of evolution variable t in different generators Pythia: Q 2 (old), p 2 T (new) – Herwig E 2 θ 2 – Ariadne p 2 T (2 → 3) 4 / 28
Matching with Matrix element generators MadEvent-Pythia Johan Alwall Use complete matrix element Why Matching? Matrix elements vs. parton showers Parton showering Matrix element generators Matching schemes Results Conclusions Diagrams for u ¯ d → e + ν e u ¯ ug by MadGraph Get appropriate description for well separated jets (away from collinear region) Get interference effects/correlations correctly Examples: MadGraph/MadEvent, Alpgen, HELAC, Sherpa 5 / 28
Matching with Matching schemes MadEvent-Pythia Johan Alwall The simple idea behind matching Use matrix element description for well separated jets, and parton Why Matching? showers for collinear jets Matching schemes CKKW matching Phase-space cutoff to separate regions MLM matching Differences between CKKW This allows to combine different jet multiplicities from matrix elements and MLM Matching schemes without double counting with parton shower emissions in MadEvent Results Difficulties Conclusions 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 with CKKW matching MadEvent-Pythia Johan Alwall Catani, Krauss, Kuhn, Webber [hep-ph/0109231] , Krauss [hep-ph/0205283] Imitate parton shower procedure for matrix elements Why Matching? Matching schemes Choose a cutoff (jet resolution) scale d ini 1 CKKW matching MLM matching Generate multiparton event with d min = d ini and 2 Differences factorization scale d ini between CKKW and MLM Matching schemes Cluster event with k T algorithm to find “parton shower history” 3 in MadEvent Use d i ≃ k 2 Results T in each vertex as scale for α s 4 Conclusions Weight event with NLL Sudakov factor ∆( d j , d ini ) / ∆( d i , d ini ) for 5 each parton line between vertices i and j ( d j can be d ini ) Shower event, allowing only emissions with k T < d ini (“vetoed 6 shower”) For highest multiplicity sample, use min( d i ) of event as d ini 7 Boost-invariant k T measure: d iB = p 2 T , i d ij = min( p 2 T , i , p 2 T , j ) F ij F ij = cosh( η i − η j ) − cos( φ i − φ j ) 7 / 28
Matching with MadEvent-Pythia Johan Alwall Sudakov reweighting Why Matching? Telescopic product – in the Matching schemes example: CKKW matching MLM matching Differences [∆ q ( d 3 , d ini )] 2 ∆ g ( d 2 , d ini ) between CKKW and MLM ∆ g ( d 1 , d ini ) Matching schemes in MadEvent × ∆ q ( d 1 , d ini )∆ q ( d 1 , d ini ) Results Conclusions Vetoed showers Start shower for parton at scale of mother node ( cf. upper scale for Sudakov suppression) Veto (forbid) emissions with d > d ini , but continue shower as if emission happened Allow emissions below d ini 8 / 28
Matching with MadEvent-Pythia PDF factors in the Krauss algorithm Johan Alwall Want to account for probability of PS configuration in ME correction weight Why Matching? For ISR process shown, get PS probability: Matching schemes CKKW matching ∆ q ( t , t ini ) 2 ∆ g ( t 1 , t ini )∆ g ( t 2 , t ini ) MLM matching Differences between CKKW × q ( x 2 , t ini ) q ( x 1 / z 1 z 2 , t ini ) and MLM Matching schemes q ( x 2 , t ) q ( x 1 / z 1 z 2 , t 2 ) in MadEvent Results x t × q ( x 1 / z 1 z 2 , t 2 ) α s ( t 2 ) P qq ( z 2 ) /z t 1 Conclusions x q ( x 1 / z 1 , t 1 ) 2 π z 2 1 x /z z t 2 × q ( x 1 / z 1 , t 1 ) α s ( t 1 ) P qq ( z 1 ) 1 2 q ( x 1 , t ) 2 π z 1 gives, combined with LO cross-section q ( x 1 , t )¯ q ( x 2 , t ) d ˆ σ q ¯ q → ll : d σ DY + gg = ∆ q ( t , t ini ) 2 ∆ g ( t 1 , t ini )∆ g ( t 2 , t ini ) q ( x ′ 1 , t ini )¯ q ( x 2 , t ini ) × α s ( t 1 ) α s ( t 2 ) P qq ( z 1 ) P qq ( z 2 ) d ˆ σ q ¯ q → ll (ˆ s / z 1 z 2 ) 2 π 2 π z 1 z 2 σ PS q → llgg ( x ′ x 1 Red: Correction weight Blue: PDFs Green: d ˆ 1 = z 1 z 2 , x 2 ) q ¯ 9 / 28
Matching with MadEvent-Pythia For final-state showers ( e + e − collision ): Johan Alwall Combination of NLL Sudakov factors and vetoed NLL showers guarantees independence of q ini to NLL order Why Matching? For initial-state showers: No proof but seems to work ok (Sherpa) Matching schemes CKKW matching Problem in practice: No NLL shower implementation! MLM matching Differences (Sherpa uses Pythia-like showers and adapted Sudakovs) between CKKW and MLM Matching schemes in MadEvent /GeV) /GeV) /GeV) Q =15 GeV Q =30 GeV Q =100 GeV Results cut cut cut 1 1 1 1 1 1 /dlog(Q /dlog(Q /dlog(Q Conclusions 10 -1 10 -1 10 -1 σ σ σ d d d σ σ σ 1/ 1/ 1/ 10 -2 10 -2 10 -2 -3 -3 -3 10 10 10 -4 -4 -4 10 10 10 SHERPA SHERPA SHERPA -0.5 0 0.5 1 1.5 2 2.5 3 -0.5 0 0.5 1 1.5 2 2.5 3 -0.5 0 0.5 1 1.5 2 2.5 3 log(Q /GeV) log(Q /GeV) log(Q /GeV) 1 1 1 Differential 0 → 1 jet rate by Sherpa in pp → Z + jets for three different cutoffs d ini , compared to averaged reference curve [hep-ph/0503280] 10 / 28
Matching with MLM matching MadEvent-Pythia Johan Alwall M.L. Mangano [2002, Alpgen home page, hep-ph/0602031] Use parton shower to choose events Why Matching? Matching schemes Generate multiparton event with cut on jet p T min , η max and ∆ R min , 1 CKKW matching and factorizations scale = “central scale” (e.g. transverse mass) MLM matching Differences Cluster event (according to color) and use k 2 T for α s scale between CKKW 2 and MLM Matching schemes Shower event (using Pythia or Herwig) starting from fact. scale 3 in MadEvent Results Collect showered partons in cone jets with same ∆ R min and 4 Conclusions p T cut > p T min Keep event only if each jet matched to one parton 5 (∆ R ( jet , parton < 1 . 5∆ R ) For highest multiplicity sample, allow extra jets with p T < p parton 6 Tmin Keep only if highest Keep Discard 11 / 28 multiplicity
Matching with MadEvent-Pythia Differences between CKKW and MLM Johan Alwall CKKW scheme: Assumes intimate knowledge of and modifications to parton shower. Needs analytical form for parton shower Sudakovs. Why Matching? Matching schemes MLM scheme: Effective Sudakov suppression directly from parton CKKW matching shower MLM matching Differences However: MLM not sensitive to parton types of internal lines between CKKW and MLM (remedied by pseudoshower approach, see below) Matching schemes in MadEvent Factorization scale: In CKKW jet resolution scale, in MLM central Results scale. Not clear (?) which is better. Conclusions Highest multiplicity treatment – less obvious in MLM than in CKKW CKKW with pseudoshowers L¨ onnblad [hep-ph/0112284] (ARIADNE) Mrenna, Richardsson [hep-ph/0312274] Apply parton shower stepwize to clustered event, reject event if too hard emission Apply vetoed parton shower as in the CKKW approach 12 / 28
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