A study on A study on AlpGen and SherpaAlpGen and Sherpa

in Z+jets eventsin Z+jets events

Piergiulio LenziUniversità di Firenze & INFN

HERA-LHC workshopCERN

27-05-2008

OutlineOutline

­ The­Matrix­Element­–­Parton­Shower­matching­problem

­ Two­different­approaches­to­the­matching:­ CKKW­(Catani,­Kuhn,­Krauss,­Webber),­the­SHERPA­

way

­ MLM­(M.­Mangano),­the­AlpGen­way

­ Production­of­Z+jets­events­at­LHC­(14­TeV)­ Sherpa­and­its­systematics

­ AlpGen­and­its­systematics

­ A­comparison­between­the­two

IntroductionIntroduction

­ This­work­is­part­of­my­“MCnet short term studentship”­work­at­University­College­London­(UCL),­supervised­by­Prof.­Jon­Butterworth

­ the­RIVET­package­has­been­used­for­this­comparison­http://projects.hepforge.org/rivet/trac/wiki/

­ RIVET­(Robust Independent Validation of Experiment and Theory)­is­part­of­the­CEDAR­(Combined e-Science Data Analysis Resource)­[1]­project

­ It­will­be­used­by­the­JetWeb[2]­facility­to­make­comparison­between­theory­and­experimental­data­stored­in­the­HEP-DATA­[3]­database

­ It­can­be­used­also­as­a­standalone­tool­for­MC­validation/tuning­and­comparison­with­experimental­results

[1] J.M. Butterworth et al. “The CEDAR Project”, hep-ph/0412139[2] http://jetweb.cedar.ac.uk/[3] http://hepdata.cedar.ac.uk

RIVETRIVET

­ Interface­to­many­generators­is­provided­by­the­separate­­AGILe­library­http://projects.hepforge.org/agile/

­ RIVET­is­a­C++­package,­with­two­main­kind­of­objects

­ Projections:­these­classes­calculate­event­observables.­Projections­are­handled­through­a­smart­caching­system­avoiding­the­same­observable­being­calculated­twice­for­the­same­event

­ Analyses: rivet­analyses­distributed­in­the­release­are­mainly­intended­to­reproduce­at­the­generator­level­experimental­results­corrected­for­detector­effects.­User­analyses­can­of­course­also­be­written­to­compare/tune­different­event­generators­­

­ The­default­RIVET­plot­output­format­is­AIDA-xml,­the­same­used­when­exporting­experimental­results­from­HEP-DATA­database­

­ Version­1.0­has­been­released­on­­11-02-2008

The ME-PS matching The ME-PS matching problemproblem

­ The­PS­response­coincides­with­the­ME­in­the­soft/collinear­region­xi~1

­ The­divergence­of­the­cross­section­in­this­region­is­tamed­in­the­PS­using­a­cutoff­and­a­reweighting­factor­called­Sudakov­form­factor

­ It­would­be­very­convenient­to­use­the­ME­to­predict­hard­parton­configuration­and­the­PS­to­describe­the­evolution­of­jets

­ BUT­beware­double­counting­and­holes­in­the­phase­space!

SHERPA SHERPA approachapproach to the to the matching: CKKWmatching: CKKW

­ Jet­production­and­­jet­evolution­regions­are­well­separated­using­a­kt­measure­(y=min(Pt1

2,­Pt22)*ΔR2/D2)­­

cutoff­ycut=Qcut2/Ecm

2­

­ The­following­recipe­is­used:­ Calculate­the­ME­cross­sections­for­all­the­desired­parton­

multiplicities;­ycut­is­used­to­cutoff­divergences;­a­fixed­sME

­is­

used

­ events­are­produced­according­to­the­ME­cross­sections­and­a­“shower­history”­is­reconstructed­through­kt­clustering­

until­a­22­process­is­found In­other­words­this­answers­to­the­question:­“How­could­a­PS­

have­produced­this­parton­configuration?”

­ A­running­coupling­correction­weight­is­applied­­

­ Apply­a­Sudakov­form­factor­correction­for­each­clustering The­effect­of­this­correction­is­to­weight­the­event­as­if­it­were­

produced­by­a­PS

­ Evolve­the­event­with­a­PS,­vetoing­emission­above­the­cut

Cluste

r

AlpGen approach to the AlpGen approach to the matching: MLMmatching: MLM

­ The­MLM­algorithm­proceeds­exactly­as­the­CKKW­up­to­the­reweighting­of­s

­ Events­are­fully­showered­using­a­conventional­shower­(PYTHIA­or­HERWIG)

­ Partons­are­clustered­into­jets­(with­a­cone­algorithm­in­the­AlpGen­implementation)

­ Jets­are­matched­to­original­partons­ If­not­all­the­jets­match­to­the­original­partons­event­is­

rejected

­ This­effectively­reproduces­Sudakov­reweighting

­ Effectively­vetoes­PS­emission­above­the­merging­scale

Z+jets event Z+jets event generationgeneration

­ SHERPA­ SHERPA-MC-1.0.11­was­used­ pp­­­e+­e-­+­up­to­3­jets­at­14TeV­ CTEQ6l­pdf­ No­underlying­event­ 66.­GeV­<­mass(e+­e-)­<­116.­GeV­ Matching­parameter­Qcut­=­20GeV

­ AlpGen­ V2.13­was­used­ pp­­­e+­e-­+­n­jets­(n­=­0,­1,­2,­3)­at­14TeV­ CTEQ6l­pdf­ 66.GeV­<­mass(e+­e-)­<­116.­GeV­ -­Matching­parameters:

Et(clus)­=­25­GeV R(clus)­=­0.7 ηmax­=­5

­ Pythia­and­Herwig­UE­was­switched­off

AnalysisAnalysis

­ Final­state­particles­with­|η|­<­5­were­selected­ No­pt­cut­on­the­final­state­particles­ Kt­jets­were­reconstructed­using­the­FastJets­package­by­M.­Cacciari,­G.­Salam­

­ Ptmin­=­30­GeV,­D­=­0.4

­ ΔRll>0.2,­ΔRlj>0.4,­ΔRjj>0.7

­ Many­lepton­and­jet­observables­have­been­calculated

­ For­each­generator­a­collection­of­observables­is­shown­and­the­effect­of­a­change­in­the­matching­parameters­and­in­the­scale­choice­is­described

­ A­comparison­between­AlpGen­and­Sherpa­is­shown

Sherpa, Lepton Sherpa, Lepton observablesobservables

Pt lepton pair

Pt e-

η lepton pair

η e-

Sherpa, jet Sherpa, jet observablesobservables

Sherpa, differential jet Sherpa, differential jet ratesrates

­ Distribution­of­the­kt­resolution­variable­making­a­n­jet­turn­into­a­­n-1­jet­event

­ Little­bumps­observed­around­the­resolution­cut­(log10(20)~1.3)

­ The­ME­kinematics­is­altered­by­the­PS,­so­mismatches­around­the­cut­can­occur­

MEPS

Sherpa systematics: Sherpa systematics: change of the matching change of the matching

scalescale­ Three­values­for­Qcut­were­tried:­20GeV­(default),­30GeV,­50GeV

­ The­effect­on­the­overall­cross­section­is­summarized­below

­ The­effect­on­lepton­observables,­and­the­relative­difference­with­respect­to­the­default­is­shown­in­the­plots­below

­ As­the­Qcut­is­increased,­the­ME­phase­space­fraction­is­reduced

­ Since­the­ME­is­responsible­for­the­hardest­parton­kinematics­the­increase­in­the­merging­scale­results­in­spectra­with­softer­tails

Qcut=20GeV

Qcut=30GeV

Qcut=50GeV

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Pt lepton pair Pt e-

Change of the matching Change of the matching scale (continued)scale (continued)

­ Jet­observables:­ The­mean­multiplicity­

decreases­as­the­merging­scale­grows

­ Diff­jet­rates­are­depleted­in­the­ME­region,­and­are­enhanced­in­the­PS­region

­ The­smoothest­transition­seems­to­be­the­one­for­the­highest­merging­scale­used

Sherpa systematics: Sherpa systematics: change of scaleschange of scales

­ Sherpa­was­run­with­the­default­choice­for­renormalization­(R)­and­factorization­(F)­scales,­R­­and­F­times­0.5­and­R­and­F­times­2

­ The­effect­on­the­overall­cross­secion­is­summarized­below:Default scales­

Scales*0.5­ Scales*2­

1594.1 pb­ 1292.4 pb 1646.5 pb­

­ The­effect­is­more­evident­in­the­first­bins­where­the­0­jet­contribution­dominates

­ The­effect­changes­sign­for­higher­boson­pt

­ This­agrees­with­previous­studies,­where­it­was­shown­that­the­LO­cross­section­for­0­jets­grows­with­the­scale,­while­the­LO­cross­section­for­>0jets­decreases­as­the­scale­grows­

[hep-ph/0308195]­­­

Pt lepton pair

AlpGen systematics, AlpGen systematics, change of the merging change of the merging

scalescale­ Two­values­were­used­for­the­Et(min)­of­the­cone­

algorithm­used­to­steer­the­matching:­25GeV­and­40­GeV­ The­overall­cross­section­effect­is­summarized­below

­ The­effect­on­lepton­observables­is­almost­negligible

Et(min)=25GeV Et(min)=40GeV

1534.5 pb 1516.4 pb

Change of the merging Change of the merging scale (continued)scale (continued)

­ Leading­jet­Pt­show­a­bump­around­40­GeV­for­the­non-default­sample

­ Small­differences­observed­in­the­jet­multiplicity

­ Differential­jet­rate­plots­show­some­modification­at­the­merging­scale

AlpGen systematics, AlpGen systematics, Change of scalesChange of scales

­ AlpGen+Pythia­was­run­with­the­default­scale­choice,­R­times­0.5­and­R­times­2

­ The­effect­on­the­overall­cross­section­is­summarized­below: Default

scales Scale*0.5 Scale*2

1534.5­pb­ 1449.1­pb­ 1672.2­pb­

­ The­effect­is­similar­to­the­one­observed­in­Sherpa

­ The­low­pt­region,­dominated­by­the­0jet­contribution­seems­to­be­less­affected­than­in­Sherpa­though

Change of scales Change of scales (continued)(continued)

­ The­effect­on­the­jet­multiplicity:­ The­scales*0.5­sample­shows­the­highest­jet­

multiplicity,­while­the­scales*2­samples­shows­the­smallest

­ This­agrees­with­what­was­observed­in­the­boson­pt­spectrum,­where­the­tail­due­to­>0­jet­events­was­enhanced­in­the­scales*0.5­case­and­depleted­in­the­scales*2­case­

­ The­effect­of­the­jet­pt­spectrum­is­not­very­evident

AlpGen-SHERPA AlpGen-SHERPA comparisons:comparisons:

lepton observableslepton observables­ AlpGen­has­been­showered­both­with­Pythia­and­Herwig­ The­inclusive­cross­sections­are

­ Sherpa­shows­the­hardest­spectrum,­Pythia­the­softest­ Differences­between­Pythia­and­Herwig­are­due­to­the­different­way­

the­two­PS­alter­the­ME­kinematics

­ The­Pt­spectrum­differences­translate­into­the­η­spectrum,­with­PYTHIA­showing­the­less­central­Z­and­SHERPA­the­most­central­one

SHERPA AlpGen+PYTHIA

AlpGen+Herwig

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Lepton observables Lepton observables (continued)(continued)

­ As­for­the­Z­spectrum­,­the­e-­Pt­spectrum­is­harder­for­Sherpa­and­softer­for­Pythia

­ The­e-­η­are­similar­(within­8%)

AlpGen-SHERPA AlpGen-SHERPA comparisons:comparisons:

jet observablesjet observables­ Sherpa­shows­a­harder­leading­jet­spectrum­ The­jet­multiplicity­is­maximum­for­Sherpa­and­minimum­for­AlpGen+Pythia

ConclusionsConclusions­ AlpGen­and­SHERPA­implement­two­different­approaches­

to­the­matching­of­ME­and­PS­predictions­ A­study­of­the­“theoretical­uncertainties”­has­been­

carried­out­for­both­generators,­varying­the­matching­parameters­and­the­scales

­ The­change­on­the­shape­of­the­distributions­is­similar­for­the­two­generators­when­changing­the­scales

­ When­changing­the­matching­parameters­AlpGen­shows­minor­changes­in­the­shape­of­the­distributions­than­Sherpa

­ When­comparing­AlpGen­with­SHERPA,­some­not­negligible­differences­have­been­spotted:

­ The­boson­lepton­and­jet­spectra­are­harder­for­SHERPA­ The­Sherpa­mean­jet­multiplicity­is­higher­then­the­AlpGen­

one

­ It­might­be­interesting­to­see­how­differential­jet­rates­look­on­data,­and­see­how­well­the­MC­can­reproduce­these­plots,­since­these­observables­are­very­sensitive­to­the­way­in­which­the­phase­space­is­filled

BackupBackup

The PS formulaeThe PS formulae

Divergent in z = 0 and z = 1

Divergencies are tamed with a cutoff .

Evolving the shower a big splitting probability will turn into big probabilities for successive branchings. If we want to conserve total probability the splitting probability abc at scale Q has to be multiplied by the probability that that splitting did not happen before (at > Q).

This “non branching probability” is the

“Sudakov form factor”

The ME-PS matching The ME-PS matching problemproblem

­ Matrix­Element­calculations:✓­Can­be­done­with­up­to­several­partons­in­the­final­state,­as­long­

as­tree­level­results­are­asked­for✓­Describe­well­separated­jets­configurations✕­Run­into­troubles­in­the­soft­and­collinear­regions✕­Can’t­describe­the­internal­structure­of­jets

- ­Parton­Shower­calculations:✓­PS­is­universal,­given­the­basic­hard­process­the­PS­recipe­will­

produce­reasonable­parton­configurations✓­The­use­of­Sudakov­form­factors­ensures­controlled­behavior­in­

the­soft­and­collinear­region,­so­jet­evolution­is­well­described✕­Cannot­steer­the­shower­evolution­too­much,­some­regions­of­

the­phase­space­are­not­efficiently­fillied,­e.g.­welll­separated­parton­configurations

- A­combined­use­of­the­two­approaches­is­desiderable,­BUT­beware­double­counting­and­holes­in­the­phase­space

PYTHIA approach to the PYTHIA approach to the matching: ME matching: ME correctionscorrections

­ Let’s­consider­the­LO­e+e-qqbar­and­the­NLO­real­emission­one­e+e-qqbar­g

­ If­the­shower­populates­the­phase­space­according­to­WPS,­then­a­factor­WME/WPS­needs­to­be­applied

­ WME­is­substituted­to­WPS­in­the­Sudakov­form­factor

­ In­the­hard­region,­where­the­Sudavov­~1,­the­ME­results­holds,­in­the­soft­region,­where­WME­~WPS­the­PS­result­holds

CKKW (continued)CKKW (continued)

­ For­each­internal­line­in­the­“shower­history”­connecting­scale­i­to­scale­k­reweight­events­with­a­factor­

­ For­each­external­line­reweight­events­with­a­factor ­Δk(qi,­qj)­is­the­Sudakov­form­factor­associated­to­

clustering­k,­connecting­scales­qi­and­qj

The­net­effect­of­this­procedure­is­similar­to­what­is­achieved­with­the­Pythia’s­ME­corrections:­the­splitting­functions­present­in­the­Sudakov­form­factor­are­replaced­by­their­ME­version

­ The­PS­is­then­applied­to­the­weighted­events,­with­a­VETO­on­hard­(avove­the­merging­scale)­emission

AlpGen+Pythia,AlpGen+Pythia, default settings default settings­ Lepton­observables

Pt lepton pair

η lepton pair

Pt e- η e-

AlpGen+Pythia,AlpGen+Pythia,default settingsdefault settings

­ Jet­observables

AlpGen+Pythia,AlpGen+Pythia,default settingsdefault settings

Jet observables Jet observables (continued)(continued)­ The­differential­jet­rates­show­

many­differences:­ AlpGen+Pythia­and­

AlpGen+Herwig­show­similar­rates­for­21­and­32­transition,­while­the­shape­is­quite­different­for­10

­ Sherpa­always­fills­the­ME­region­more

­ This­seems­to­be­in­agreement­with­the­harder­spectra­observed­for­sherpa,­since­the­ME­is­responsible­for­the­hardest­parton­kinematics