Article
Reference
Measurement of transverse energy–energy correlations in multi-jet events in pp collisions at √s = 7 TeV using the ATLAS detector and
determination of the strong coupling constant αs(mZ)
ATLAS Collaboration
ANCU, Lucian Stefan (Collab.), et al .
Abstract
High transverse momentum jets produced in pp collisions at a centre of mass energy of 7 TeV are used to measure the transverse energy–energy correlation function and its associated azimuthal asymmetry. The data were recorded with the ATLAS detector at the LHC in the year 2011 and correspond to an integrated luminosity of 158 pb −1 . The selection criteria demand the average transverse momentum of the two leading jets in an event to be larger than 250 GeV. The data at detector level are well described by Monte Carlo event generators.
They are unfolded to the particle level and compared with theoretical calculations at next-to-leading-order accuracy. The agreement between data and theory is good and provides a precision test of perturbative Quantum Chromodynamics at large momentum transfers. From this comparison, the strong coupling constant given at the Z boson mass is determined to be αs(mZ)=0.1173±0.0010 (exp.) −0.0026+0.0065 (theo.) .
ATLAS Collaboration, ANCU, Lucian Stefan (Collab.), et al . Measurement of transverse energy–energy correlations in multi-jet events in pp collisions at √s = 7 TeV using the ATLAS detector and determination of the strong coupling constant αs(mZ). Physics Letters. B , 2015, vol. 750, p. 427-447
DOI : 10.1016/j.physletb.2015.09.050
Available at:
http://archive-ouverte.unige.ch/unige:75554
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Measurement of transverse energy–energy correlations in multi-jet events in pp collisions at √
s = 7 TeV using the ATLAS detector and determination of the strong coupling constant αs( m
Z)
.ATLASCollaboration
a r t i c l e i n f o a b s t ra c t
Articlehistory:
Received7August2015
Receivedinrevisedform10September 2015
Accepted19September2015 Availableonlinexxxx Editor:W.-D.Schlatter
Hightransversemomentumjetsproducedinppcollisionsatacentreofmassenergyof7 TeVareused tomeasurethetransverse energy–energycorrelationfunctionand itsassociated azimuthalasymmetry.
The data wererecorded withthe ATLASdetector atthe LHCin theyear 2011and correspondtoan integrated luminosity of 158 pb−1.The selection criteria demand the average transverse momentum of the two leading jetsin an event to be largerthan 250 GeV.The data at detector level are well described by Monte Carlo event generators. They are unfolded to the particle level and compared withtheoreticalcalculationsatnext-to-leading-orderaccuracy.Theagreementbetweendataandtheory is good and providesaprecision test of perturbativeQuantumChromodynamics atlarge momentum transfers.Fromthiscomparison,thestrongcouplingconstantgivenatthe Zbosonmassisdetermined tobeαs(mZ)=0.1173±0.0010 (exp.)+−00..00650026(theo.).
©2015PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
1. Introduction
Thestudyofjet productionattheLHCprovidesa quantitative testofQuantumChromodynamics,QCD,atthehighestmomentum transfers.Theoreticalcalculationsforjetcross-sectionsinhadronic collisionshavebeencarriedoutuptonext-to-leadingorder(NLO) accuracyinthestrongcouplingconstant αs [1–3]andextensively compared with the data [4–10]. These calculations are valid for configurationswithuptofourjetsinthefinalstate.
Event shape variables havebeen measured in all major e+e− experiments,aswellasinexperimentsattheelectron–protoncol- liderHERA.Thesestudieswererecentlyextendedtohadroncollid- erswithmeasurementsofthetransversethrustandthetransverse minor[11,12]attheTevatron[13]andtheLHC[14,15].
Energy–energy correlations (EEC), i.e. measurements of the energy-weighted angular distributions of hadron pairs produced ine+e− annihilation,were proposed in Refs. [16,17] asan alter- nativeeventshapevariablenotbasedonthedeterminationofthe thrust principal axis [18] or the sphericity tensor [19]. The EEC functionanditsasymmetry,AEEC,weresubsequentlycalculatedin O(αs2)[20–22],andtheirmeasurements[23–35]havehadsignifi- cantimpactontheprecisiontestsofperturbative QCDandinthe determination ofthe strong coupling constant in e+e− annihila- tionexperiments;arecentreviewisgiveninRef.[36].TheEECare
E-mailaddress:atlas.publications@cern.ch.
by construction notaffected by softdivergences,andasa conse- quenceofthistheyarecalculableathighorders.
The transverse energy–energy correlation function, TEEC, and its asymmetry, ATEEC, were proposed as the analogousvariables athadron colliderexperimentsin Ref. [37],where predictions to leadingorder(LO)werealsopresented.TheNLOcorrectionswere calculatedrecentlyinRef. [38] usingNLOJet++[2,3].Thesecalcu- lationsallowforanumericaldeterminationoftheNLOpredictions for theTEEC andATEEC, i.e.the coefficientsof the second order polynomialsinthestrongcouplingconstant.Theyareusedinthis paperforquantitative precisiontestsofQCDincludingadetermi- nationofthestrongcouplingconstant.TheTEECisdefinedas:
1
σ
d d(cosφ)= 1
σ
i j
dσ
dxTidxTjd(cosφ)xTixTjdxTidxTj, (1)
where thesum runsover all pairs of jetsin the final state with azimuthal1 angular difference φ=ϕi j and xTi=ETi/ET is the transverseenergycarriedbyjeti inunitsofthesumofjettrans- verse energies ET=
iETi. In order to cancel uncertainties that
1 ATLASuses aright-handedcoordinatesystemwith itsoriginat thenominal interactionpoint(IP)inthecentreofthedetectorandthez-axisalongthebeam pipe.Thex-axispointsfromtheIPtothecentreoftheLHCring,andthe y-axis pointsupward.Cylindricalcoordinates (r,ϕ)areusedinthe transverseplane,ϕ beingtheazimuthalanglearoundthebeampipe.Thepseudorapidityisdefinedin termsofthepolarangleθasη= −ln tan(θ/2).
http://dx.doi.org/10.1016/j.physletb.2015.09.050
0370-2693/©2015PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
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are constant over cosφ∈ [−1,1], it is useful to define the az- imuthalasymmetryoftheTEEC(ATEEC)as
1
σ
dasym d(cosφ)≡ 1
σ
d d(cosφ)
φ
− 1 σ
d d(cosφ)
π−φ
. (2)
ThisLetterpresentsameasurementoftheTEECanditsassociated asymmetryusinghigh-energyjets.
2. TheATLASdetector
TheATLASdetector[39]isamulti-purposeparticlephysicsde- tector with a forward–backward symmetric cylindrical geometry andasolidanglecoverageofalmost4π.
The inner tracking system covers the pseudorapidity range
|η|<2.5, and consists of a silicon pixel detector, a silicon mi- crostripdetector,and, for|η|<2.0,a transitionradiation tracker.
It is surrounded by a thin superconducting solenoid providing a 2 T magnetic field along the beam direction. A high-granularity liquid-argon sampling electromagneticcalorimeter covers the re- gion |η|<3.2. An iron/scintillator tile hadronic calorimeter pro- videscoverage intherange|η|<1.7.Theendcapandforwardre- gions,spanning1.5<|η|<4.9,areinstrumentedwithliquid-argon calorimetersforelectromagneticandhadronicmeasurements.The muonspectrometersurroundsthecalorimeters.Itconsistsofthree large air-core superconducting toroid systems and separate trig- gerandhigh-precisiontrackingchambersprovidingaccuratemuon trackingfor|η|<2.7.
Thetriggersystem[40]hasthreeconsecutivelevels:level 1 (L1), level2(L2)andtheeventfilter(EF).TheL1triggersarehardware- based anduse coarse detector informationto identify regions of interest,whereas the L2triggers are software-basedandperform a fastonline datareconstruction. Finally, the EFuses reconstruc- tionalgorithmssimilartotheofflineversionswiththefulldetector granularity.
3. MonteCarlosamples
Multi-jetproductioninppcollisionsisrepresentedbythecon- volution ofthe production cross-sectionsfor parton–parton scat- tering with the parton distribution functions. Monte Carlo (MC) generators differinthe approximationsused tocalculatethe un- derlying short-distance QCD process, in the way parton showers arebuilttotakeintoaccounthigher-ordereffectsandinthefrag- mentation scheme responsible for long-distance effects. For this analysis, two different MC approaches are used, depending on whether the underlying hard process is considered to be 2→2 ormulti-legged.Thegeneratedeventsarethenprocessedwiththe ATLASfulldetectorsimulation[41]basedonGeant4[42].
ThebaselineMCsamplesaregeneratedusingPythia6.423[43]
withthematrixelementsfortheunderlying2→2 processescal- culatedatLOusingtheMRST2007LO*partondistributionfunctions (PDF)[44] andmatched totransverse-momentum-ordered parton showers.TheAUET2Btune[45,46]isusedtomodeltheunderlying event(UE) andthe hadronisation follows the Lund string model [47].
AdditionalsamplesaregeneratedwithHerwig++2.5.1[48],us- ingtheCTEQ6.6PDF[49]andtheUE7000tunefortheunderlying event[50].Herwig++usesangular-orderedpartonshowers,aclus- terhadronisationschemeanditsownunderlying-eventparameter- isationgivenbyJimmy[51].
A different approach to simulate multi-jet final states is fol- lowed by Alpgen [52]. This approach is based on LO matrix- element calculations for 2→n multi-parton final states, with n≤6, interfaced withHerwig+Jimmy [53,51] to providethe par- tonshower,hadronisationandunderlying-eventmodels.Alpgenis
known to providea good descriptionof themulti-jet final states asmeasuredbyATLAS[54].
4. Eventselectionandjetcalibration
The datausedinthisanalysiswere recordedin2011at√ s= 7 TeV and collected usinga single-jet trigger. It requires atleast one jet, reconstructed with the anti-kt algorithm [55] with ra- dius parameter R=0.4 as implemented in FastJet [56]. The jet transverse energy, ET = Esinθ, is required to be greater than 135 GeVatthetriggerlevel.Thistriggerisfullyefficientatrecon- structed transverse energies above 240 GeV. Taking into account theprescalefactorofthistrigger,thedatacollectedcorrespondto aneffectiveintegratedluminosityofLeff=158 pb−1 [57].
Events are required to haveat leastone primary vertex, with five or more associated tracks with transverse momentum pT>
400 MeV. If there is more than one primary vertex, the vertex maximising
p2T is chosen. MC simulated events are subject to areweighting algorithminordertomatchtheaveragenumberof interactionsperbunch-crossingobservedinthedata.
Intheanalysis,jetsarereconstructedwiththesamealgorithm asusedinthetrigger,theanti-kt algorithmwithradiusparameter R=0.4.Theinputobjectstothejetalgorithmaretopologicalclus- tersofenergydepositsinthecalorimeters[58].Thebaselinecali- brationfortheseclusterscorrectstheirenergyusinglocalhadronic calibration [59,60]. The four-momentum ofan uncalibrated jet is defined asthe sum of thefour-momenta of its constituent clus- ters,whichareconsideredmassless.Theresultingjetsaremassive.
However, the effectofthismass ismarginal forjetsin thekine- maticrangeconsideredinthispaper.
The jet calibration procedure includes energy corrections for multiple ppinteractionsinthesameorneighbouringbunchcross- ings, termed “pileup” inthefollowing, aswell asangular correc- tions to ensure that the jet originates from the primary vertex.
Effects due toenergy lossesininactive material, shower leakage, the magnetic field, as well as inefficiencies in energy clustering and jet reconstruction, are taken into account. This is done us- inganMC-basedcorrection,inbinsof ηandpT,derivedfromthe relationofthereconstructedjetenergytotheenergyofthecorre- spondinghadron-leveljet,notincludingmuonsornon-interacting particles.Inafinalstep,aninsitucalibrationcorrectsforresidual differencesinthejetresponsebetweentheMCsimulationandthe datausingmomentum-balancetechniquesfordijet, γ + jet, Z + jet andmulti-jet final states.This so-calledjet energyscale (JES) [61]issubjecttouncertaintiesincludingthoseaffectingtheenergy ofwell-measuredobjects,likeZ bosonsandphotons.ThetotalJES uncertaintyisgivenbyasetofindependentsources,correlatedin pT.Theuncertaintyinthe pT ofindividualjetsduetotheJESin- creasesfrom(1–4)%for|η|<1.8,to5% for1.8<|η|<4.5.
The selected events must have at least two jets with trans- verse momentum pT>50 GeV andpseudorapidity |η|<2.5. The twoleadingjetsarefurtherrequiredtofulfil pT1+pT2>500 GeV.
In addition,jetsare requiredto satisfy quality criteriathat reject beam-inducedbackgrounds[62],aswellascriteriaforthefraction of the momentum of tracks within the jet which arise from the primary interactionvertex.Thenumberofselectedeventsindata is 3.8×105,withan averagejet multiplicityNjet=2.6.There- sulting distributionfor (pT1+pT2)/2 extendsup to1.3 TeV with anaveragevalueof305 GeV.
5. Resultsatthedetectorlevel
TheselectedeventsareusedtomeasuretheTEECanditsasso- ciated asymmetryATEEC,asdefinedinEquations(1)and(2).The
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Fig. 1.Thedetector-level distributionsforthe transverseenergy–energycorrelationTEEC(left)anditsasymmetryATEEC(right)alongwith comparisonstoMCmodel expectations.Theuncertaintiesshownarestatisticalonly.ThefirstbinoftheATEECdistributionhasanegativevalueandisthereforenotincludedinthefigure.
TEEC distributionfor asample of N eventsis obtainedby calcu- latingthe cosines of the angles inthe transverse plane between allpossiblepairsofjetsineachevent.Everypair(i,j)represents anentryinthedistribution,whichisthenweightedwiththenor- malised product of the transverse energies. The weights wi j are definedas
wi j=xTixTj=ETiETj
kETk
2, (3) suchthat fora giveneventtheir sumisalways unity, asthe self correlationsi= j arealsotakenintoaccount.The resultingdistri- butionisthendividedbythenumberofevents,whichnormalises ittounitarea.Thisweightingprocedurereducesthesensitivityto thejetenergyscaleandresolution.
Fig. 1showstheTEECandATEECdistributionsalongwithcom- parisonstodetector-levelPythia,HerwigandAlpgenexpectations.
The TEEC exhibitspeaks atcosφ=1 (self correlations) andnear cosφ= −1, with a rather flat central region around cosφ=0.
Thesefeaturesaresimilar tothoseobservedine+e−annihilation, asdescribedinRef.[31].Thecentralregionisexpectedtobedom- inatedbyhardradiationprocesseswhilemultiplesoftradiationis expectedtobeimportantinthecosφ ±1 regions.
ThedescriptionoftheTEEC isgoodintheback-to-backregion cosφ −1 for both Pythia 6andAlpgen.Differences up to 10%
are observed in the central part, while the region of small an- glesshowsdifferences aslarge as about15%. The description by Herwig++is poorer.The ATEECexhibits asteep fall-off, whichis reproducedby bothPythia6andAlpgen.Herwig++showssome discrepanciesaslargeas30%.
6. Correctiontoparticlelevel
Thedataarecorrectedtotheparticlelevelinordertotakeinto account detectorefficiencies andresolutions. Thisallows a direct comparisonwiththeoreticalcalculations,aswellaswithmeasure- mentsofotherexperiments.
Particle-leveljetsarereconstructedinMCeventsusingallpar- ticleswithaveragelifetime τ>10−11s,includingmuonsandneu- trinos. The kinematic selection criteria are the same as for the detector-level distribution. The unfolding relies on a bin-by-bin correctiongivenbytheratiosoftheparticle-leveltodetector-level distributionsinthePythiaAUET2Bsample,whichisthenapplied to the detector-level distributions in data. To check the effect of bin migrations on the unfolding procedure, an iterativeBayesian method[63]asimplementedinRooUnfold[64]isalsoused.The convergencecriteriaisfulfilledwhenthelinearsumoverallbins oftheabsoluterelativedifferencesfromoneiteration tothenext dropsbelow10−2.Themethodconvergesafterfiveiterations.The differencesbetweenthetwo approachesarenegligible,compared tothestatisticaluncertainties,inthefullrangeofcosφ.Thisisex- pectedduetothehighazimuthalresolutionofthejetaxis,which is10mrad.
The followingexperimental sources of uncertaintyare consid- eredforthismeasurement:
• Jetenergyscale:The uncertainty dueto thejet energyscale (JES)[61] iscalculated usingMC techniquesby varying each jetenergyandmomentumbyonestandarddeviationforeach of the 63 independent sources of the JES uncertainty, and propagated to the TEEC. These uncertainties depend on the jettransversemomentumandpseudorapidity.Thetotaluncer- taintyduetotheJESiscalculatedasthesuminquadratureof allindependentuncertainties.Inordertoinvestigatetheeffect of possible correlations between JES sources in the analysis, two alternative scenarios with weaker and stronger correla- tions have been considered [61]. The impact of the change ofcorrelation configurations,aswell asofthe numberofJES independent sources, onthe value of αs(mZ) andits experi- mentalerrorisfoundtobenegligible.
ThevaluesoftheJESuncertaintyaretypicallyasymmetricfor boththeTEECandATEECdistributions,althoughthevaluesfor
