Measurement of transverse energy–energy correlations in multi-jet events in $\mathit{pp}$ collisions at $\sqrt{s}=7$ TeV using the ATLAS detector and determination of the strong coupling constant $\alpha _{s}(m_{z})$

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Physics Letters B

www.elsevier.com/locate/physletb

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 α

_s

( 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 Availableonline26September2015 Editor:W.-D.Schlatter

Hightransversemomentumjetsproducedinpp collisionsatacentreofmassenergyof7 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 Z bosonmassisdetermined tobeαs(mZ)=⁰.1173±⁰.0010 (exp.)⁺₋⁰₀^._.⁰⁰⁶⁵₀₀₂₆(theo.).

©²⁰¹⁵^CERN^for^the^benefitôf^theÂTLASCollaboration.PublishedbyElsevierB.V.Thisisanopen accessarticleundertheCCBYlicense(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(α_s²)[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] using NLOJet++[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

dxTidxT jd(cosφ)^x^Ti^x^{T j}^dx^Ti^dx^{T j}, (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 E_T=

iE_Ti. 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/©²⁰¹⁵^CERN^for^the^benefitôf^theÂTLASCollaboration.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

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are constant over cosφ∈ [−¹,1]^, ît îs ûseful ^to ^define ^the âz- imuthalasymmetryoftheTEEC(ATEEC)as

1

σ

d^asym 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 region |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-jetproductioninpp collisionsisrepresentedbythecon- volution ofthe production cross-sectionsfor parton–parton scat- tering with the parton distribution functions. Monte Carlo (MC) generators differinthe approximationsused tocalculatethe underlying 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]basedon Geant4[42].

ThebaselineMCsamplesaregeneratedusing Pythia 6.423[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].

Additionalsamplesaregeneratedwith Herwig++2.5.1[48],us- ingtheCTEQ6.6PDF[49]andthe UE7000tunefortheunderlying event[50]. Herwig++usesangular-orderedpartonshowers,aclus- terhadronisationschemeanditsownunderlying-eventparameter- isationgivenby Jimmy[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, înterfaced with Herwig+Jimmy [53,51] to providethe par- tonshower,hadronisationandunderlying-eventmodels. Alpgen is

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 = ^{E sin}θ, 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 p_T>

400 MeV. If there is more than one primary vertex, the vertex maximising

p²_T is chosen. MC simulated events are subject to areweighting algorithminordertomatchtheaveragenumberof interactionsperbunch-crossingobservedinthedata.

Intheanalysis,jetsarereconstructedwiththesamealgorithm asusedinthetrigger,theanti-k_t 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 pp interactionsinthesameorneighbouringbunchcross- ings, termed “pileup” inthefollowing, aswell asangular corrections 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 p_T.Theuncertaintyinthe p_T ofindividualjetsduetotheJESin- creasesfrom(1–4)%for|η_|<1.8,to5% for1.8<|η_|<4.5.

The selected events must have at least two jets with transverse momentum pT>50 GeV andpseudorapidity |η_|<2.5. The twoleadingjetsarefurtherrequiredtofulﬁl p_T1+^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^,^with^an ^average^jet multiplicity^Njet=².6.There- sulting distributionfor (p_T1+^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=xTixT j=^E^Ti^E^{T j}

kETk

2, (3)

suchthat fora giveneventtheir sumisalways unity, asthe self correlationsi= ^{j are}âlso^takenîntoâccount.^The ^resulting^distri- butionisthendividedbythenumberofevents,whichnormalises ittounitarea.Thisweightingprocedurereducesthesensitivityto thejetenergyscaleandresolution.

Fig. 1showstheTEECandATEECdistributionsalongwithcom- parisonstodetector-level Pythia, Herwig and Alpgen expectations.

The TEEC exhibitspeaks atcosφ=^{1 (self} correlations) andnear cosφ= −^1, ^with â ^rather ^flat ^central ^region âround ^cosφ=^0.

Thesefeaturesaresimilar tothoseobservedine⁺e⁻annihilation, asdescribedinRef.[31].Thecentralregionisexpectedtobedom- inatedbyhardradiationprocesseswhilemultiplesoftradiationis expectedtobeimportantinthecosφ ±^{1 regions.}

ThedescriptionoftheTEEC isgoodintheback-to-backregion cosφ −^{1 for} both Pythia 6and Alpgen.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 both Pythia 6and Alpgen. 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 distributionsinthe Pythia AUET2Bsample,whichisthenapplied to the detector-level distributions in data. To check the effect of bin migrations on the unfolding procedure, an iterativeBayesian method[63]asimplementedin RooUnfold[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:

• ^Jet^energy^{scale: 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 correlations have been considered [61]. The impact of the change ofcorrelation conﬁgurations,aswell asofthe numberofJES independent sources, onthe value of αs(m_Z) andits experi- mentalerrorisfoundtobenegligible.

ThevaluesoftheJESuncertaintyaretypicallyasymmetricfor boththeTEECandATEECdistributions,althoughthevaluesfor