A study on A study on AlpGen and SherpaAlpGen and Sherpa

in Z+jets eventsin Z+jets events

Piergiulio LenziUniversità di Firenze & INFN

CTEQ-MCnet Summer SchoolDebrecen, 8-16 August 2008

IntroductionIntroduction

­ I’m­a­PhD­student­based­in­Florence;­I’m­in­my­third­year­(the­last­in­Italy),­working­on­CMS­ Florence­group­has­been­deeply­involved­in­the­CMS­Inner­Tracker­construction,­so­I’ve­been­working­on:­ Construction­and­commissioning­of­the­detector­ Development­of­track­reconstruction­algorithms

­ In­the­last­year­we­dedicated­more­effort­on­the­physics,­and­we­have­chosen­the­Z+jets­channel­ As­I­was­starting­to­study­the­new­subject­the­­­­“MCnet short-term studentship”­announcement­appeared­on­one­of­the­CMS­mailing­lists!!­ I­immediately­decided­to­apply!

OutlineOutline

­ Something­about­what­I­used­to­do­before­my­studentship…­ Building­the­CMS­tracker

­ Track­Reconstruction­@­CMS

­ The­Matrix­Element­–­Parton­Shower­matching­problem

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

­ MLM­(M.­Mangano),­the­AlpGen­way

­ Production­of­Z+jets­events­at­LHC­(14­TeV)­ Sherpa­and­its­systematics

­ AlpGen­and­its­systematics

­ A­comparison­between­the­two

CMS Tracker CMS Tracker constructionconstruction

I’ve­been­involved­in­all­the­steps­of­the­tracker­construction,­from­sensor­quality­tests­to­the­full­detector­commissioning

Beam test, Oct 2004

Cosmic rays in a tracker prototype, June 2005

Layer assembly, Feb 2006

Final Inner Barrel assembly, Oct 2007

Final assembly and tests, Mar-Jul 2007

Track reconstructionTrack reconstruction

­ I’ve­worked­on­the­development­of­CMS­track­reconstruction­algorithms;­in­particular­ Commissioning­of­detector­and­reconstruction­software­with­cosmic­ray­real­data

Track reconstruction efficiencyon cosmic rays as a function of track θ. Black simulation; Red data

­ Development­of­the­Kalman­Filter­based­pattern­recognition

­ Development­of­track­fitting­methods­based­on­soft­hit-to-track­assignment­(DAF).­Should­perform­better­in­dense­or­noisy­environment

Transverse and longitudinal impact parameter resolution; Blue standard tracking Red DAF

preliminary

My studentshipMy studentship

­ I­spent­my­studentship­at­University­College­London­(UCL)­from­Jan­to­Apr­2008,­supervised­by­Prof.­Jon­Butterworth­ I­was­working­in­close­contact­with­developers­of­the­RIVET­package­and­with­MC­experts­­http://projects.hepforge.org/rivet/trac/wiki/­ RIVET­(Robust Independent Validation of Experiment and

Theory)­is­part­of­the­CEDAR­(Combined e-Science Data Analysis Resource)­[1]­project

­ Rivet­main­objective­is­to­provide­a­general­framework­for­MC­validation/tuning­and­comparison­with­experimental­results

­ The­main­idea­is­to­reproduce­in­Rivet­experimental­analyses;­results­obtained­running­such­analyses­on­MC­samples­are­then­easily­compared­with­experimental­results­stored­in­HEP-DATA­DB­[2]

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

RIVETRIVET

­ Interface­to­many­generators­is­provided­by­the­separate­­AGILe­library­http://projects.hepforge.org/agile/­ RIVET­is­a­C++­package,­with­two­main­kind­of­objects­ Projections:­these­classes­calculate­event­observables.­Projections­are­handled­through­a­smart­caching­system­avoiding­the­same­observable­being­calculated­twice­for­the­same­event

­ Analyses: RIVET­comes­with­many­analyses­that­reproduce­experimental­papers­from­LEP,­HERA,­TVT.­

User­analyses­can­be­easily­plugged­in­the­RIVET­framework­with­a­plugin­system

­ Comparison­with­experimental­results­is­straightforward,­thanks­to­the­use­of­the­low­weight­AIDA-xml­plot­format,­the­same­used­when­exporting­experimental­results­from­HEP-DATA­database

ME and PSME and PS

­ Matrix­Element­(ME)­calculations­are­based­on­the­computation­of­the­Feynman­amplitudes­of­the­processes­contributing­to­the­final­state

­ Parton­showers­(PS)­describe­the­final­state­starting­from­a­hard­22­process­­as­a­successive­series­of­12­splittings.

­ Splitting­probability­is­calculated­in­the­limit­of­collinear­emission­

­ Divergences­in­this­limit­are­tamed­imposing­the­conservation­of­total­probability­using­form­factors­(Sudakov)

The ME-PS matching The ME-PS matching problemproblem

­ Matrix­Element­calculations:✓Describe­well­separated­jets­configurations✓­Are­exact­at­a­given­order✕­Run­into­troubles­in­the­soft­and­collinear­regions✕­Can’t­describe­the­internal­structure­of­jets

- ­Parton­Shower­calculations:✓­PS­is­universal,­given­the­basic­hard­process­the­PS­recipe­will­produce­reasonable­parton­configurations

✓­The­use­of­Sudakov­form­factors­ensures­controlled­behavior­in­the­soft­and­collinear­region,­so­jet­evolution­is­well­described

✕­Cannot­steer­the­shower­evolution­too­much,­some­regions­of­the­phase­space­are­not­efficiently­filled,­e.g.­well­separated­parton­configurations

- It­would­be­very­convenient­to­use­the­ME­to­predict­hard­parton­configuration­and­the­PS­to­describe­the­evolution­of­jets,­but­beware­double­counting­and­holes­in­the­phase­space

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

­ Jet­production­and­­jet­evolution­regions­are­well­separated­using­a­kt­measure­(y=min(Pt12,­Pt22)*ΔR2/D2)­­cutoff­

ycut=Qcut2/Ecm

2­

­ Calculate­the­ME­cross­sections­for­all­the­desired­parton­multiplicities;­ycut­is­used­to­cutoff­divergences;­a­fixed­s

ME­is­used

­ Select­one­parton­multiplicity­according­to­ME­cross­sections­and­produce­jet­momenta­according­to­the­corresponding­ME­squared

­ a­“shower­history”­is­reconstructed­through­kt­clustering­until­a­

22­process­is­found In­other­words­this­answers­to­the­question:­“How­could­a­PS­have­

­­­produced­this­parton­configuration?”

­ A­running­coupling­correction­weight­is­applied­­

­ Apply­a­Sudakov­form­factor­correction­for­each­clustering The­effect­of­this­correction­is­to­weight­the­event­as­if­it­were­produced­by­a­PS­but­substituting­the­collinear­splitting­function­with­the­exact­ME

­ Evolve­the­event­with­a­PS,­vetoing­emission­above­the­cut

Cluste

r A

bove

y

cut

Bel

ow

ycu

t

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

­ The­MLM­algorithm­proceeds­exactly­as­the­CKKW­up­to­the­reweighting­of­s

­ Events­emerging­from­the­ME­are­fully­showered­using­a­conventional­shower­(PYTHIA­or­HERWIG)­ Partons­are­clustered­into­jets­(with­a­cone­algorithm­in­the­AlpGen­implementation)­ Jets­are­matched­to­original­partons

­ If­not­all­the­jets­match­to­the­original­partons­event­is­rejected

­ 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

­ Many­lepton­and­jet­observables­have­been­calculated­ For­each­generator­a­collection­of­observables­is­shown­and­the­effect­of­a­change­in­the­matching­parameters­and­in­the­scale­choice­is­described­ A­comparison­between­AlpGen­and­Sherpa­is­shown

Sherpa observablesSherpa observables

Pt lepton pairPt e-

Jet multiplicity Pt leading jet

Sherpa, differential jet Sherpa, differential jet ratesrates

­ Distribution­of­the­kt­resolution­variable­making­a­n­jet­turn­into­a­­n-1­jet­event

­ Critical­region­around­the­cut­(log10(20)~1.3)

­ The­ME­kinematics­is­altered­by­the­PS,­so­mismatches­around­the­cut­can­occur­

MEPS

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

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

­ The­effect­on­the­overall­cross­section­is­summarized­below

­ The­effect­on­lepton­observables,­and­the­relative­difference­with­respect­to­the­default­is­shown­in­the­plots­below­ As­the­Qcut­is­increased,­the­ME­phase­space­fraction­is­reduced

­ Since­the­ME­is­responsible­for­the­hardest­parton­kinematics­the­increase­in­the­merging­scale­results­in­spectra­with­softer­tails

Qcut=20GeV

Qcut=30GeV

Qcut=50GeV

1594.1 pb 1411.3 pb 1399.8 pb

Pt lepton pair Pt e-

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)­of­the­cone­algorithm­used­to­steer­the­matching:­25GeV­and­40­GeV

­ The­overall­cross­section­effect­is­summarized­below

­ The­effect­on­lepton­observables­is­almost­negligible

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

1534.5 pb 1516.4 pb

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,­dominated­by­the­0jet­contribution­shows­a­behavior­similar­to­Sherpa

AlpGen-SHERPA AlpGen-SHERPA comparisons:comparisons:

lepton observableslepton observables­ AlpGen­has­been­showered­both­with­Pythia­and­Herwig­ The­inclusive­cross­sections­are

­ Sherpa­shows­the­hardest­spectrum,­Pythia­the­softest­ Differences­between­Pythia­and­Herwig­are­due­to­the­different­way­the­two­PS­alter­the­ME­kinematics

­ The­Pt­spectrum­differences­translate­into­the­η­spectrum,­with­PYTHIA­showing­the­less­central­Z­and­SHERPA­the­most­central­one

SHERPA AlpGen+PYTHIA

AlpGen+Herwig

1594.1 pb 1534.5 pb 1523.0 pb

AlpGen-SHERPA AlpGen-SHERPA comparisons:comparisons:

jet observablesjet observables­ Sherpa­shows­a­harder­leading­jet­spectrum­ The­jet­multiplicity­is­maximum­for­Sherpa­and­minimum­for­AlpGen+Pythia

ConclusionConclusion

­ About­my­work­ AlpGen­and­SHERPA­implement­two­different­approaches­to­the­matching­of­ME­and­PS­predictions

­ A­study­of­the­“theoretical­uncertainties”­has­been­carried­out­for­both­generators,­varying­the­matching­parameters­and­the­scales

­ When­comparing­AlpGen­with­SHERPA,­some­not­negligible­differences­have­been­spotted

­ And­in­general­about­my­studentship:­ I­worked­in­close­contact­with­MC­experts­ I­got­an­insight­on­the­differences­among­some­of­the­MC­tools­available,­and­on­the­systematics­of­such­tools

­ ….and­I­spent­some­nice­time­in­London!

­ Many thanks to Jon Butterworth, James Monk, Andy Buckley, Frank Krauss, Frank Siegert

BackupBackup

Track reconstructionTrack reconstruction­ Track­reconstruction­is­a­complex­pattern­recognition­problem­ A­combinatorial­approach­together­with­a­Kalman­filter­estimation­of­track­parameters­is­used

pixelpixel

Inner BarrelInner Barrel

Outer BarrelOuter Barrel

EndcapEndcap

ss

Inn

er

Dis

ksIn

ner

Dis

ks

5.6 m5.6 m

1.2 1.2

mm

­ Track­candidates­found­in­this­way­are­then­fitted­in­order­to­estimate­track­parameters­on­each­surface

The ME-PS matching The ME-PS matching problemproblem

­ The­PS­response­coincides­with­the­ME­in­the­soft/collinear­region­xi~1

­ The­divergence­of­the­cross­section­in­this­region­is­tamed­in­the­PS­using­a­reweighting­factor­called­Sudakov­form­factor

­ It­would­be­very­convenient­to­use­the­ME­to­predict­hard­parton­configuration­and­the­PS­to­describe­the­evolution­of­jets

­ BUT­beware­double­counting­and­holes­in­the­phase­space!

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”

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)­is­the­Sudakov­form­factor­associated­to­clustering­k,­connecting­scales­qi­and­qj

The­net­effect­of­this­procedure­is­similar­to­what­is­achieved­with­the­Pythia’s­ME­corrections:­the­splitting­functions­present­in­the­Sudakov­form­factor­are­replaced­by­their­ME­version

­ The­PS­is­then­applied­to­the­weighted­events,­with­a­VETO­on­hard­(avove­the­merging­scale)­emission

Sherpa, jet Sherpa, jet observablesobservables

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

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

­ Jet­observables:­ The­mean­multiplicity­decreases­as­the­merging­scale­grows

­ Diff­jet­rates­are­depleted­in­the­ME­region,­and­are­enhanced­in­the­PS­region

­ The­smoothest­transition­seems­to­be­the­one­for­the­highest­merging­scale­used

Jet observables Jet observables (continued)(continued)­ The­differential­jet­rates­show­

many­differences:­ AlpGen+Pythia­and­AlpGen+Herwig­show­similar­rates­for­21­and­32­transition,­while­the­shape­is­quite­different­for­10

­ Sherpa­always­fills­the­ME­region­more

­ This­seems­to­be­in­agreement­with­the­harder­spectra­observed­for­sherpa,­since­the­ME­is­responsible­for­the­hardest­parton­kinematics

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

­ Leading­jet­Pt­show­a­bump­around­40­GeV­for­the­non-default­sample

­ Small­differences­observed­in­the­jet­multiplicity

­ Differential­jet­rate­plots­show­some­modification­at­the­merging­scale

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

­ The­effect­on­the­jet­multiplicity:­ The­scales*0.5­sample­shows­the­highest­jet­multiplicity,­while­the­scales*2­samples­shows­the­smallest

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

­ The­effect­of­the­jet­pt­spectrum­is­not­very­evident

Lepton observables Lepton observables (continued)(continued)

­ As­for­the­Z­spectrum­,­the­e-­Pt­spectrum­is­harder­for­Sherpa­and­softer­for­Pythia­ The­e-­η­are­similar­(within­8%)

ConclusionsConclusions­ AlpGen­and­SHERPA­implement­two­different­approaches­to­the­matching­of­ME­and­PS­predictions

­ A­study­of­the­“theoretical­uncertainties”­has­been­carried­out­for­both­generators,­varying­the­matching­parameters­and­the­scales­ The­change­on­the­shape­of­the­distributions­is­similar­for­the­two­generators­when­changing­the­scales

­ When­changing­the­matching­parameters­AlpGen­shows­minor­changes­in­the­shape­of­the­distributions­than­Sherpa

­ When­comparing­AlpGen­with­SHERPA,­some­not­negligible­differences­have­been­spotted:­ The­boson­lepton­and­jet­spectra­are­harder­for­SHERPA­ The­Sherpa­mean­jet­multiplicity­is­higher­then­the­AlpGen­one

­ It­might­be­interesting­to­see­how­differential­jet­rates­look­on­data,­and­see­how­well­the­MC­can­reproduce­these­plots,­since­these­observables­are­very­sensitive­to­the­way­in­which­the­phase­space­is­filled