Measurement of jet p(T) correlations in Pb+Pb and pp collisions at √sNN=2.76 TeV with the ATLAS detector

Citation for this paper:

Aaboud, M.; Aad, G.; Abbott, B.; Abdallah, J.; Abdinov, O.; Abeloos, B.; … &

Zwalinski, L. (2017). Measurement of jet p(T) correlations in Pb+Pb and pp

collisions at √sNN=2.76 TeV with the ATLAS detector. Physics Letters B, 774,

379-402. DOI: 10.1016/j.physletb.2017.09.078

_____________________________________________________________

Measurement of jet p(T) correlations in Pb+Pb and pp collisions at √sNN=2.76 TeV

with the ATLAS detector

M. Aaboud et al. (The ATLAS Collaboration)

2017

© 2017 Aaboud et al. This is an open access article distributed under the terms of the

Creative Commons Attribution License.

http://creativecommons.org/licenses/by/4.0

This article was originally published at:

.

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ATLAS

Collaboration

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Articlehistory:

Received29June2017

Receivedinrevisedform13September 2017

Accepted26September2017 Availableonline29September2017 Editor: D.F.Geesaman

Measurements of dijet pT correlations in Pb+Pb and pp collisions at a nucleon–nucleon

centre-of-mass energy of √sNN=2.76 TeV are presented. The measurements are performed with the ATLAS

detector atthe LargeHadronColliderusingPb+Pb and pp datasamples correspondingto integrated luminositiesof0.14 nb−1and4.0 pb−1,respectively.Jetsarereconstructedusingtheanti-kt algorithm

with radius parameter values R=0.3 and R=0.4. A background subtraction procedure is applied to correct the jetsfor the large underlyingevent present inPb+Pb collisions.The leading and sub-leading jet transverse momenta are denoted pT1 and pT2. Anunfolding procedure is applied to the two-dimensional(pT1,pT2)distributionstoaccountforexperimentaleffectsinthemeasurementofboth jets.Distributionsof(1/N)dN/dxJ,wherexJ=pT2/pT1,arepresentedasafunctionofpT1 andcollision centrality.ThedistributionsarefoundtobesimilarinperipheralPb+Pb collisionsandpp collisions,but highlymodifiedincentralPb+Pb collisions.SimilarfeaturesarepresentinboththeR=0.3 andR=0.4 results,indicatingthattheeffectsoftheunderlyingeventareproperlyaccountedforinthemeasurement. Theresultsarequalitativelyconsistentwithexpectationsfrompartonicenergylossmodels.

©2017TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

Jets have long been considered an important tool for study-ing the matter produced in ultra-relativistic heavy-ion collisions. In these collisions, a hot medium of deconfined colour charges is produced, known as the quark–gluon plasma (QGP). Jets pro-duced in the initial stage of the collision lose energy as they

propagate through the medium. This phenomenon, known as jet

quenching,wasfirstobservedattheRelativisticHeavyIonCollider (RHIC) [1,2].Earlymeasurementsusingfullyreconstructedjetsin Pb

+

Pb collisions attheLHC providedadirect observationofthis phenomenon [3]. In Pb

+

Pb collisions the transverse momentum (pT)balancebetweentwojetswasfoundtobedistorted,resulting

fromconfigurationsinwhichthetwojetssufferdifferentamounts ofenergyloss.Thismeasurementwastheexperimental confirma-tionofsomeoftheinitialpicturesofjetquenchingandsignatures ofadeconfinedmedium[4].

SubsequentmeasurementsofjetsinPb

+

Pb collisionshave im-proved the understandingofpropertiesof quenchedjetsand the empirical features of the quenching mechanism [5–14]. Signifi-cant theoreticaladvances also occurredinthis period,and while a complete description of jet quenching is not available, some models are capable of reproducing its key features and

provid- _{E-mailaddress:atlas.publications@cern.ch.}

ing testable predictions. Measurements of the dijet asymmetry,

AJ

≡ (

pT1

−

pT2

)/(

pT1

+

pT2

)

,wherepT1 and pT2 arethetransverse

momentaofthejetswiththehighestandsecondhighest pTinthe

event,respectively,havebeencrucialinfacilitatingthese develop-ments. The experimental results demonstratethat the measured asymmetriesincentral collisions,wherethegeometric overlapof thecollidingnucleiisalmostcomplete,differfromthoseinpp

col-lisions morethanisexpectedfromdetector-specificexperimental effects[3,9,10].However,such effects,inparticulartheresolution of the measured jet pT, must be corrected for in order for the

measurement tobe directlycompared to theoreticalcalculations. Unfoldingprocedureshavebeenappliedtocorrectforsucheffects forsingle-jetmeasurements[6];however,thedijetresult requires a two-dimensional unfolding to account for migration in the pT

ofeachjetseparately.Themeasurementreportedhereisthefirst unfolded Pb

+

Pb dijetmeasurement and as such can be directly comparedtotheoreticalmodels.

This Letter presents a measurement of dijet pT correlations

in Pb

+

Pb and pp collisions ata nucleon–nucleoncentre-of-mass energy of 2.76 TeV performed with the ATLAS detector. Jets are reconstructed with the anti-kt algorithm with radius parameter values R

=

0

.

3 andR

=

0

.

4[15].Theanalysisisdescribedmostly fortheexampleof R

=

0

.

4 jets.A backgroundsubtraction proce-dure isapplied to accountforthe effectsof thelarge underlying event(UE) presentinPb

+

Pb collisionsonthemeasured jet kine-matics. The momentum balance of the dijet system is expressed https://doi.org/10.1016/j.physletb.2017.09.078

0370-2693/©2017TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

reduced.Itisthereforeinterestingtocomparetheresultsobtained usingR

=

0

.

3 and R

=

0

.

4 jets,toseeifthesamefeaturesare vis-ible.

2. Experimentalset-up

ThemeasurementspresentedinthisLetterareperformedusing theATLASinnerdetector,calorimeterandtriggersystems[16].The inner detector provides measurements of charged-particle tracks overtherange

|

η

|

<

2

.

5.1Itiscomposedofsiliconpixeldetectors in the innermost layers, followed by silicon microstrip detectors and a straw-tube tracker, all immersed in a 2 T axial magnetic field provided by a solenoid. The minimum-biastrigger scintilla-tors(MBTS) measurecharged particlesover 2

.

1

<

|

η

|

<

3

.

9 using twoplanesofcountersplacedat z

= ±

3

.

6 m and providetiming measurementsusedintheeventselection[17].

TheATLAS calorimeter systemconsists of a liquidargon (LAr) electromagnetic (EM) calorimeter (

|η|

<

3

.

2), a steel–scintillator samplinghadroniccalorimeter(

|

η

|

<

1

.

7),a LArhadronic calorime-ter(1

.

5

<

|η|

<

3

.

2),andaforwardcalorimeter(FCal)(3

.

2

<

|η|

<

4

.

9).Thehadroniccalorimeterhasthreesamplinglayers longitudi-nalinshowerdepthandhasa



η

×φ

granularityof0

.

1

×

0

.

1 for

|

η

|

<

2

.

5 and 0

.

2

×

0

.

2 for2

.

5

<

|

η

|

<

4

.

9.2 TheEM calorimeters arelongitudinallysegmentedinshowerdepthintothree compart-mentsfollowingapre-samplerlayer(

|

η

|

<

1

.

8).TheEM calorime-terhasagranularitythatvarieswithlayerandpseudorapidity,but whichisgenerallymuchfinerthanthatofthehadronic calorime-ter. The first layer has high

η

granularity (between 0.003 and 0.006)thatcanbeusedtoidentifyphotonsandelectrons.The mid-dlesamplinglayer, whichtypicallyhasthelargestenergydeposit inEMshowers,hasagranularity of0

.

025

×

0

.

025 over

|η|

<

2

.

5. A totaltransverseenergy(TE)triggerisimplementedbyrequiring ahardware-based determinationofthetotaltransverse energyin thecalorimetersystem, Etot_T ,tobeaboveathreshold.

Thezero-degreecalorimeters(ZDCs)are locatedsymmetrically atz

= ±

140 m andcover

|

η

|

>

8

.

3.InPb

+

Pb collisionsthe ZDCs primarilymeasure “spectator”neutrons: neutrons that donot in-teracthadronically whenthe incidentnuclei collide.A ZDC coin-cidencetriggerisimplementedbyrequiringthepulseheightfrom each ZDC to be above a threshold set below the single-neutron peak.

InadditiontotheZDC andTE hardware-basedtriggers,a soft-ware-based high-level trigger is used to further reduce the

ac-1 _{ATLASusesaright-handedcoordinatesystemwithitsoriginatthenominal}

in-teractionpoint(IP)inthecentreofthedetectorandthez-axisalongthebeampipe. Thex-axispointsfromtheIPtothecentre oftheLHCring,andthey-axispoints upward.Cylindricalcoordinates(r,φ)areusedinthetransverseplane,φbeingthe azimuthalanglearoundthebeampipe.Thepseudorapidityisdefinedintermsof thepolarangleθasη= −ln tan(θ/2).

2 _{Anexceptionisthethirdsamplinglayer,whichhasasegmentationof0.2×0.1}

upto|η|=1.7.

emptyevents.Thejettrigger[18]firstselectseventssatisfyingthe TE triggerwitha thresholdof Etot_T

=

20 GeV.A jet reconstruction procedureisthenappliedusingtheanti-kt algorithmwith R

=

0

.

2 andutilisingaUEsubtractionproceduresimilartothatusedinthe offline reconstructiondescribed inSection 4.Eventswith atleast onejetwith ET

>

20 GeV attheelectromagneticscale[19]are

se-lectedbythejettrigger.TheuseofR

=

0

.

2 forjetsinthetrigger, as opposedtothe valuesof R

=

0

.

3 and0

.

4 applied inthe mea-surement, is motivated by the need to define an algorithm that isrobust against UEfluctuations, whichgrowwith R. Theeffects ofthedifferentR valuesonthetriggerefficiencyarediscussedin Section 5.The minimum-biastrigger operatedwith aprescale of approximately18whilenoprescalewas appliedtothejettrigger. After accounting for these prescales, the recorded events corre-spondtointegratedluminositiesof8 μb−1 and0

.

14 nb−1 forthe minimum-biasandjet-triggeredsamples,respectively.

Eventsarefurthersubjectedtocriteriadesignedtoremove non-collisionbackgroundandinelasticelectromagneticinteractions be-tweenthenuclei.Eventsarerequiredtohaveareconstructed pri-maryvertexandhaveatimingdifferenceoflessthan5 nsbetween thetimesmeasuredbythetwoMBTSplanes.Afterthetriggerand eventselectioncriteria,theresultingdatasamplescontain53and 14millioneventsintheminimum-biasandjettriggeredsamples, respectively. Theaveragenumberofcollisions per bunch-crossing inthePb

+

Pb datasample wasless than0.001,and theeffectsof multiplecollisionsareneglectedinthedataanalysis.

The centrality of the Pb

+

Pb collisions ischaracterised by the totaltransverseenergymeasuredintheFCalmodules,



EFCal_T .The



EFCal_T distribution obtained in minimum-bias collisions is par-titioned into separate ranges of



E_TFCal referred to as centrality classes[17,20,21].Eachclassisdefinedbythefractionofthe dis-tributioncontainedbytheinterval,e.g.the0–10%centralityclass, whichcorrespondstothemostcentralcollisions,containsthe10% of minimum-bias events with the largest



EFCal_T . The centrality boundaries used inthisanalysis are0%, 10%, 20%,30%, 40%, 60% and80%.

The pp datasample,recordedin2013,wascomposedofevents selectedby ajet triggerand useda seriesofdifferent pT

thresh-oldseach selectedwith adifferentprescale.Thejet triggeristhe sameusedinotherATLASmeasurementsinpp collisions[18]and applies the anti-kt algorithm with R

=

0

.

4. The events are fur-therrequiredtocontainatleastoneprimaryreconstructedvertex. Theaveragenumberofpp collisionsperbunch-crossingvaried be-tween 0.3and 0.6during datataking.The samplecorresponds to aluminosityof4

.

0 pb−1.

Theimpactofexperimentaleffectsonthemeasurementis eval-uated usingthe Geant4-simulated detectorresponse [22,23]in a MonteCarlo(MC)sampleofpp hard-scatteringevents.Dijetevents at

√

s

=

2

.

76 TeV are generated using Pythia version 6.423 [24]

with parametervalueschosenaccording tothe AUET2Btune [25]

the data event that is overlaid. Through this procedure the MC sample contains contributionsfrom underlying-event fluctuations andharmonicflowthatmatchthosepresentinthedata.The com-binedsignal isthen reconstructedusingthesameprocedureasis appliedtothedata.So-calledtruthjets aredefinedbyapplyingthe anti-kt algorithmwith R

=

0

.

3 and R

=

0

.

4 tostable particles in the MC event generator’s output,definedas thosewith a proper lifetime greater than 10 ps, but excluding muons and neutrinos, whichdonotleavesignificantenergydepositsinthecalorimeter.

The detector’s response to quenched jets is studied with an additional sample using Pyquen [30]. This event generator ap-pliesmedium-inducedenergylosstopartonshowersproducedby Pythia.Itisusedtogenerateasampleofjetswith fragmentation functionsthatdifferfromthoseinthenominal Pythia sampleina fashion consistentwith measurements offragmentationfunctions inquenchedjets[11–13].

4. Jetreconstruction

The procedure usedto reconstructjets inheavy-ion collisions is described in detail in Ref. [5]and isbriefly summarised here. First, energydeposits inthe calorimeter cells are assembled into



η

× φ =

0

.

1

×

₃₂π logicaltowers.Jetsareformedfromthe tow-ersby applyingtheanti-kt algorithm[15] as implementedinthe

FastJet

softwarepackage[31].

AnestimateoftheUEcontributiontoeachtowerwithinthejet isperformed onan event-by-eventbasis byestimating the trans-verseenergydensity,

ρ

(

η

,

φ)

.Globalazimuthal modulationinthe UEarisesduetothephysicsofflowandistraditionallydescribed

in terms of the Fourier expansion of the

φ

dependence of the

transverseenergydensity.Inthesubtractionprocedure,theUE es-timateisassigneda

φ

dependenceusingthemeasuredmagnitudes andphasesofthemodulation:

ρ

(

η

, φ)

=

ρ

(

η

)

×



1

+

2



n vncos

[

n

(φ

−

n

)

]



,

(1)

where vn and

n arethemagnitudesandphasesoftheharmonic modulation, respectively, and

ρ

(

η

)

is the average transverse en-ergy density measured from energy deposits in the calorimeter as a function of

η

. In Ref. [5], only the second-order harmonic modulation (n

=

2) was considered,butinthis measurementthe

procedure has been extended to account for n

=

3 and 4

har-monic modulations as well. The subtraction is applied to each towerwithinthejet.ThequantitiesinEq.(1)maybebiasedifthe energyinajetisincludedintheircalculation,whichresultsinan over-subtractionoftheaverageUEcontributiontothejetenergyor incompleteremovaloftheharmonicmodulation.Tomitigatesuch effects, the contribution fromjets is excluded from the estimate ofthebackground.Thetypicalbackgroundenergysubtractedfrom

5. Dataanalysis

Inthis analysis, jetpairs are formed fromthetwo highest-pT

jets in the event with pT

>

25 GeV and

|η|

<

2

.

1. The pair is

required to have

φ >

7

π

/

8, where

φ

≡ |φ

1

− φ

2

|

. For events

selectedbyajettrigger,theleadingjet isrequiredtomatchajet identifiedbythetriggeralgorithmresponsibleforselectingthejet. Thetwo-dimensional(pT1

,

pT2) distributionsobtainedfrom

differ-enttriggeredsamplesarecombinedsuchthatintervalsofpT1 are

populatedby a singletrigger. Inthe pp data analysis,the trigger withthemosteventsthatismorethan99%efficientforselecting ajet with pT

>

pT1 isused,with thereciprocaloftheluminosity

fortherespectivetriggersamplesusedasaweight.

ThePb

+

Pb jettriggerefficiencyhasabroadturn-onasa func-tion of pT since thetrigger jetsare identifiedusing R

=

0

.

2 and

havenoenergyscalecalibrationapplied.Thiseffectisthestrongest incentralcollisionswheretheUEfluctuationsarethelargestand further weaken the correlation between jets reconstructed with differentvaluesofR.Inthemostcentralcollisions,the single-jet-triggerefficiencydoes notreachaplateauuntil pT

∼

90 GeV. The

jet-triggered sample is used where the efficiency is found to be greater than97%, whichoccursata pT ofapproximately85 GeV

inthemostcentralcollisions.A triggerefficiencycorrectionis ap-pliedintheregionwherethereisaninefficiency.

In addition to thedijet signal, the measured (pT1

,

pT2)

distri-butionreceivescontributionsfromso-calledcombinatoric jetpairs. Suchpairsarisewhentwojets,whicharenotfromthesame hard-scattering process, fulfil the pair requirements through random association. Jetsforming such pairs mayoriginate from indepen-denthardscatteringsorfromupwardUEfluctuationsidentifiedas jets,referred toas UEjets. Therate forsuchoccurrencesis high-est in the most central collisions, and the reduction in the true sub-leadingjet pT dueto quenching effectsfurther enhances the

likelihoodofformingacombinatoricpair.

Theshapeofthe

φ

distributionforthecombinatoricjetpairs isinfluencedbytheharmonicflow.Sincethejet pT spectrumfalls

steeply,thejetsmostlikelytobemeasuredatagivenpTvalueare

thoselying ontop oflarger-than-averageUE. Iftheeffects ofthe modulationoftheUEarenotfullyaccountedforinthebackground subtraction,morejetswouldbeobservedatanglescorresponding to theflow maxima(

φ

∼

n).Thus combinatoric jet pairs, with-out anyunderlyingangularcorrelation, areexpectedto acquire a modulationtotheir

φ

distributiondeterminedby thedominant flowharmonics[33].Althoughthesecond-,third- andfourth-order harmonicmodulationsareconsideredevent-by-eventinthejet re-constructionprocedure describedinSection 4,onlythe effectsof thesecond-ordermodulationonthe

φ

distributionareobserved to be completely removed. The residual effects are an indication that the method of estimating the modulationof the UE

under-Fig. 1. TheφdistributionforR=0.4 jetpairswith89<pT1<100 GeV inthe

0–10%centralityinterval.Thedistributionforalljetpairsisindicatedbytheblack circles.ThecombinatoriccontributiongivenbyEq.(2)isshownasablueline.The rangesofφusedtofixthevalueofY andtodefinethesignalregion(φ >78π)

areindicatedbyyellowandgreenshadedregions,respectively.Theparametersc3

andc4 areobtainedbyfittingtheφdistributionforjetpairswith|η|>1 in

theregion0<φ <π₂,whichisindicatedbytheredsquares(scaledtomatchthe blackcirclesintheyellowregionforpresentationpurposes).Theerrorbarsdenote statisticalerrors.(Forinterpretationofthereferencestocolourinthisfigure,the readerisreferredtothewebversionofthisarticle.)

neaththejetisless accurateforthehigher-orderharmonicsthan forn

=

2.

Toaccountfortheresidualmodulation,the combinatoric con-tributionisassumedtobeoftheform:

C

(φ)

=

Y

(1

+

2c3cos 3φ

+

2c4cos 4φ) . (2)

The c3 and c4 values are determinedby fitting the

φ

distribu-tions over the range 0

<

φ <

π

/

2 where the real dijet contri-bution is expectedto be small. The region 0

<

φ



0

.

8 is also expectedtoreceiverealdijetcontributionsarisingfromparton ra-diationwhichresultsinpairsofjetsatnearbyangles.Toremove thiscontribution,thefittoobtainc3 andc4 isperformedonly

us-ing jet pairs with a separation of

|

η

|

>

1. Once c3 and c4 are

obtained, the

φ

distribution without this

|

η

|

requirement is integratedover therange 1

<

φ <

1

.

4 to obtain Y .This

proce-forall valuesof xJ.This backgroundsubtraction isnot appliedin

the pp databecausethepile-upissmall.

The presence of combinatoric jet pairs also reduces the effi-ciency for genuine pairs.The measured inclusive jet spectrum is usedto estimatethelikelihood thatanotherjet intheevent, un-correlated with the dijet system, is measured with a transverse momentumgreaterthanpT2.Forthe40–60%and60–80%

central-ity intervals the effect is negligible. In the 0–10% centrality bin theefficiencyisapproximately0.9forpT2

=

25 GeV andincreases

with pT2,reachingunityat45 GeV.Theeffectsofthecombinatoric

jetpairsareaccountedforbyfirstsubtractingtheestimated back-groundand thencorrectingfortheefficiency,

ε

,ineach(pT1

,

pT2)

bin.The numberofjet pairscorrected forsuch effectsisdefined tobe:

Ncorr

=

1

ε



Nraw

−

B



,

where Nraw _{isthe numberofjet pairsaftercorrectingfortrigger}

efficiencyandluminosity/prescaleweightingasdescribedabove. In agivenevent, the pT resolution mayresult inthe jetwith

the highest true pT being measured with the second highest pT

and vice-versa. To properly account for such migration effects, (pT1

,

pT2)distributions aresymmetrisedpriortothe unfoldingby

apportioninghalfoftheyieldinagiven(pT1

,

pT2)bin,after

combi-natoricsubtraction,tothebinrelatedtotheoriginalbypT1

↔

pT2.

Thetwo-dimensionaldistributionsaftersymmetrisationareshown in Fig. 2 for central and peripheral Pb

+

Pb collisions and for pp

collisions. Thechoice ofbinning in(pT1

,

pT2) ismotivatedby the

mappingtothexJ variable,and isdescribedinmoredetailinthe

followingsection.

Fig. 2. Thetwo-dimensional(pT1,pT2)distributionsaftercorrectionandsymmetrisationforPb+Pb datainthe0–10%(left)and60–80%(centre)centralitybinsandfor

pp data(right)for R=0.4 jets.Thedashedlinesindicatetheboundariesusedinselectingthedifferenttriggers.ThePb+Pb datadistributionshavetheircombinatoric contributionsubtracted.

Fig. 3. Left:the(1/N)dN/dxJ distributionsusedaspriorsintheunfoldingofthe R=0.4 jetsforthenominal(dashedred)andalternatevariation(dottedblue)forthe

100<pT1<126 GeV and0–10%centralityinterval.Thesamedistributionobtainedfromthe Pythia MCsampleisshowninsolidblack.Right:unfolded (1/N)dN/dxJ

distributionsfromdataforthesamepT1 andcentralityrangesusingthenominal(redcircles)andalternate(bluediamonds)priorsshownintheleftpanel.Theratioof

nominaltoalternateisshowninthebottompanel.Inthebottompanelontherightthefirsttwobinsareoffscalewithbinscentres ofxJ=0.34 and0.38andbinscontents

of2.49and1.82,respectively.Statisticalerrorsarenotshown.(Forinterpretationofthereferencestocolourinthisfigure,thereaderisreferredtothewebversionofthis article.)

6. Unfolding

The calorimetricresponseto jetsisevaluated inthe MC sam-ple by matchingtruth and reconstructedjets; thenearest recon-structed and truth jetswithin



R

=



(

η

)

2

_{+ (φ)}

2 _of0

_.

_{3 are}

consideredtobeamatch.Thesamerequirementisappliedinboth the R

=

0

.

3 andR

=

0

.

4 versionsoftheanalysis.The responseis typically characterised interms of the jet energyscale (JES) and jetenergyresolution(JER).Thesequantitiesdescribethemeanand widthofthe preco

T distributionsatfixedptruthT ,expressedasa

frac-tion of ptruth_T . Generally,the meanof preco_T differs from ptruth_T by lessthanapercent,independentofptruth_T andcentrality.This indi-catesthatthesubtractionoftheaverageUEcontributiontothejet energyisundergoodexperimentalcontrol.TheJERreceives contri-butions bothfromtheresponseofthecalorimeterand fromlocal UEfluctuationsaboutthemeanintheregionofthejet.Thelatter contributiondominates atlow pT with the resolutionas large as

40%atpT



30 GeV inthemostcentralcollisions.AtthesamepT,

the JERis only 20% inperipheral collisions, similarto that in pp

collisions. At larger pT valuesthe relativecontribution ofthe UE

fluctuationstothejet pT diminishes,and theJERisdominatedby

detectoreffects,reachinga constant,centrality-independent value of8%forpT

>

300 GeV.

Themigrationinthetwo-dimensional(pT1

,

pT2)distributionis

accounted forby applying a two-dimensional Bayesian unfolding to thedata[34,35].Thisprocedureutilizesaresponse matrix ob-tainedbyapplyingthesamepairselectionstothetruthjetsinMC simulationasinthedataanalysis(exceptthetriggerrequirement) and recording the values of ptruth_T1 and ptruth_T2 and the transverse momenta ofthecorrespondingreconstructedjets preco_T

1 and p

reco T2 .

Thematchedreconstructedjetsarenotrequiredtohavethe high-est pT intheevent, butare subjectto allother requirements

ap-pliedtothedataand truthjets.Theresponsematrixispopulated symmetrically in both truth and reconstructed pT. The full

four-dimensional response behaves similarlyto the factorised product ofseparatesingle-jetresponsedistributions,andthemigration ef-fects can be understoodin terms ofthe above discussion. While this provides intuition for the nature of the unfolding problem, suchafactorisationisnotexplicitlyassumed,andanycorrelations betweentheresponseofthetwojetsareaccountedforinthe pro-cedure.

After unfolding,the leading/sub-leading distinctionis restored by reflecting the distribution over the line pT1

=

pT2: for each

bin with pT2

>

pT1 the yield is moved to the corresponding bin

with pT2

<

pT1.Thebinsalongthediagonal,e.g.thosecontaining

pairswith pT2

=

pT1,arenotaffectedby thisprocedure.The

two-dimensional distribution isconstructed using binning along each axissuchthattheupperedgeoftheith binobeys,

pT i

=

pT 0

α

i

,

α

=

pT N pT 0

1/N

,

where N isthe total number of bins and pT 0 and pT N are the

minimum and maximum bin edges covered by the binning,

re-spectively.As aconsequence, thebinsare ofthesamesizewhen plotted with logarithmic axes.Withthesechoices ofbinning, the range of xJ values in any given (pT1

,

pT2) bin is fully contained

withintwoadjacentxJ bins,whichhaveboundaries atxJ i

=

α

i−N.

In thisanalysis, half ofthe yield in each (pT1

,

pT2) bin is

appor-tioned to each of the xJ bins.The exceptionsare the bins along

the diagonal.These bins contribute solelyto the xJ bin with bin

edges

(

α

−1

_,

₁

₎

_{.Theeffects ofsucha mappingonthe x}

J

distribu-tionarestudiedandfoundtonotsignificantlydistorttheshapeof thedistributionforavarietyofinputxJdistributions.

The Bayesian unfolding method isan iterative procedure that requiresbothachoiceinanumberofiterations,niter,and

assump-tionofapriorfortheunderlyingtruedistribution.Anincrease in

niterreducessensitivitytothechoiceofpriorbutmayamplify

sta-tisticalfluctuationsthat arealreadypresentintheinput distribu-tion.As Pythia doesnotincludetheeffectsofjetquenching,thexJ

distributionsobtainedfromtheMCsamplearenotexpectedtobe optimalchoices fortheprior. Inparticular, thexJ distributions in

Pythiaincreasemonotonicallywithx_J,whereasthedistributionsin thedatabecomeflatteranddevelopapeaknearxJ

∼

0

.

5 inlower

pT1 intervalsandinthemostcentralcollisions.The(pT1

,

pT2)

dis-tributions from Pythia are reweighted in a centrality-dependent way to obtain features that qualitatively match those present in thedata.

Theeffectsofthereweightingprocedureareshownintheleft panelofFig. 3inthe100

<

pT1

<

126 GeV rangeand 0–10%

cen-tralityinterval,wherethelargestdifferencebetweenthedataand Pythiaisobserved.The “nominal”distribution,orthereweighted distribution,isused asthe priorinthe unfoldingofthe data.An

Fig. 4. Uncertaintiessensitivetothe numberofiterationsintheunfoldingprocedureasafunctionofniter forthe0–10%centralityintervalfor R=0.4 jets.Left:The

combination(solidblack)oftheunfolding(dashedred)andstatistical(dottedblue)uncertainty,√δ2_forthe100<pT

1<126 GeV interval.Right:Thecombineduncertainty

foreachpT1intervalconsideredinthemeasurement.(Forinterpretationofthereferencestocolourinthisfigure,thereaderisreferredtothewebversionofthisarticle.)

“alternate” reweightingis alsoshown, which hasa shape signifi-cantlydifferentfromthenominal,butdoes notincreaseas much as the Pythia distribution. The features inthe dataare observed to be robust with respect to the choice ofprior for a broad set of reweighting functions. The systematic uncertainty due to the choice ofprior is estimatedby comparingthe results ofthe un-foldingsusing the“nominal” and “alternate” xJ distributions.The

resultsofapplyingunfoldingswiththesetwochoicesofpriorsare shownintherightpanelsofFig. 3forthesamepT1 andcentrality

selection.

An alternative study is performed in the MC sample to vali-datetheestimationofthisuncertainty.The“alternate”reweighting isapplied toobtaininputtruthandreconstructeddistributionsin whichnopeakstructureispresent.Thereconstructeddistribution isthenunfoldedusingthenominal prior.Theunfoldeddistribution doesnotdevelopthestrongpeakpresentinthenominalprior.The differencesbetweentheunfoldedresultandtheinputtruth distri-butionaresimilartotheuncertaintyobtainedbyvaryingtheprior usedtounfoldthedata.

The value of niter is selected separately ineach centrality

in-tervalby examiningthe uncertainty,

√

δ

2_,in

₍

₁

_/

_N

₎

_dN

_/

_dx J after

unfoldingconsidering statistical uncertainties and systematic un-certaintiesattributedtotheunfoldingprocedure,

δ

2

= δ

_stat2

+ δ

2_prior

,

and summing over all xJ bins. Here

δ

prior is the uncertainty due

to the choice of prior, obtained using the procedure described above.The statistical uncertainties are evaluatedusing a pseudo-experiment technique. Stochastic variations of the data are gen-erated based on its statistical uncertainty and each variation is unfoldedandprojectedintoxJ.Thestatisticalcovarianceoftheset

istakenas the statistical uncertainty.An additionalcovariance is obtainedfrom applyingthe pseudo-experiment procedure to the responsematrixand combined with thatobtainedfrom applying theproceduretothedata.The

δ

2stat foreach xJbinistakentobe

thediagonalelementoftheresultingcovariancematrix.The statis-ticalcovariance matrices exhibit similartrendsacross all pT1 and

centralityranges. Nearby xJ bins show a strong positive

correla-tionthatdiminishesforbinsseparatedinxJ,andisexpectedfrom

theeffectsoftheproceduresforunfoldingandmappingtoxJ.Bins

well separated in xJ show an anti-correlationattributable to the

normalisationof

(

1

/

N

)

dN

/

dxJ.

TheleftpanelofFig. 4shows

√

δ

2_{asafunctionofn} iter along

withits variouscontributions forthe 100

<

pT1

<

126 GeV range

and0–10%centralityinterval.Sincetheunfoldingisperformedin twodimensions,thevalueofniter cannotbechosenseparatelyfor

each rangeof pT1.At highervalues of pT1 theeffects ofthe

un-foldingare smallerwhiletheeffectsofthe statisticalfluctuations canbemoresevere.TherightpanelofFig. 4showsthetotal

√

δ

2

foreach rangeof pT1 considered inthe measurementalongwith

thetotalcombinedoverall pT1 ranges.Thevalueofniter foreach

centrality binand R value is chosen by considering the niter

de-pendence of

√

δ

2 _{for each pT}

1 bin and selecting a value that

maintainscomparableuncertaintiesacrossallpT1 ranges.Themore

central binsrequire the most iterations,resultingfromthe larger jetenergyresolutionintheseevents.Thenumberofiterationsfor

R

=

0

.

4 jets is at most 20 for 0–10% centrality and at the least 6 for 60–80%centrality. The

√

δ

2 _{distributions for R}

₌

₀

_.

_{3 jets}

showbehavioursimilartothoseforR

=

0

.

4 jetsinthesame cen-tralitybin.

It ispossible fora thirdjet present inthe event to be recon-structedas thejet withthesecondhighest pT throughthe

exper-imentalresolution.Asacheck tostudytheimpactofsucheffects onthemeasurement,analternativeresponsematrixisconstructed whereno



R matchingisrequiredbetween thetruthand recon-structedjets. A weightingisappliedsuchthat the pT distribution

of thereconstructed thirdjet matches that observedin thedata. Differencesbetweentheunfoldeddistributionsobtainedwiththis responsematrixandthenominaloneareobservedtobesmalland wellwithinthesystematicuncertaintyassociatedwiththe unfold-ingprocedure.

The

(

1

/

N

)

dN

/

dxJ distributions before and after unfolding are

showninFig. 5forcentralandperipheralPb

+

Pb collisionsandfor

pp collisions forjetpairswith 100

<

pT1

<

126 GeV.The

system-aticuncertainties indicatedcontainall ofthe contributionstothe totalsystematic uncertaintydescribed inSection 7.Inthe pp and

60–80% centralityinterval,the resolutioneffectsbefore unfolding reduce the sharpnessof thepeak near xJ

∼

1.In thecase ofthe

0–10%centralityinterval,theeffectistosmearoutthepeaknear

xJ

∼

0

.

5.ThelowestxJbinsexhibitinstabilityintheunfolding

pro-cedureduetotheMCsamplehavingtoofeweventsinthisregion. However, includingthisrange inthe unfoldingimproves the sta-bilityoftheadjacentxJbins.Thus,afterunfolding,onlytherange

0

.

32

<

xJ

<

1 is reported in the results even though pairs with

pT2

>

25 GeV areincludedinthemeasurement.

7. Systematicuncertainties

Systematicuncertaintiesattributedtotheresponsematrixused inthe unfoldingarise duetouncertainties intheJESand JER.To account for theseeffects, newresponse matrices are constructed with a systematically varied relationship between the truth and

Fig. 5. The(1/N)dN/dxJdistributionsforR=0.4 jetsbefore(black)andafter(red)unfoldingforthe100<pT1<126 GeV intervalforthePb+Pb 0–10%(left)andPb+Pb

60–80%(middle)centralityrangesandforpp collisions(right).Statisticaluncertaintiesareindicatedbyverticalerrorbars(notvisibleinmostcases).Systematicuncertainties intheunfoldedresultareindicatedbytheredshadedboxes.(Forinterpretationofthereferencestocolourinthisfigure,thereaderisreferredtothewebversionofthis article.)

reconstructedjetkinematics.Thedataarethenunfoldedusingthe newresponseandtheresultiscomparedwiththenominal.

In the pp dataanalysis, the JESuncertainty is described by a set of11independent nuisanceparameters; theseincludeeffects fromuncertainties derived through theinsitu calibration[32].In the MC sample used to determinethe calibration,the calorimet-ric response to jetsinitiated by the fragmentation of quarksand gluonsisobservedtodiffer.PotentialinaccuraciesintheMC sam-pledescribing boththisflavour-dependentresponseand the rela-tive abundances of quark and gluon jets are accountedforusing separate nuisanceparameters. A source of uncertaintyrelated to the adaptationofthe insitu calibrationderivedat

√

s

=

8 TeV to 2.76 TeV dataisalsoincluded.

InthePb

+

Pb dataanalysis,twoadditionaluncertaintiesinthe JESare considered.Thefirstaccounts fordifferencesbetween the detector operating conditions in the Pb

+

Pb and pp data, which were recorded in2011and 2013, respectively. Thisis derived by using charged-particle tracks reconstructed in the inner detector toprovideanindependentcheckontheJES,whichonlyuses infor-mationfromthecalorimeter.Foreachjet,allreconstructedtracks within



R

<

0

.

4 andhavingptrk_T

>

2 GeV,arematchedto thejet and thescalarsumofthetrack transversemomentaisevaluated. The ratio of this sum to the jet’s pT is evaluated both in data

and inthe MC sample, and a double ratioof the two quantities is formed.Thedoubleratioobtainedinperipheral Pb

+

Pb datais comparedwiththatinpp data.Theprecisionofthecomparisonis limitedbyhavingtoofeweventsintheperipheralPb

+

Pb dataand athigh jet pT,and a pT- and

η

-independentuncertaintyof1.46%

isassignedtoaccountforpotentialdifferences.

Thesecondadditionaluncertaintyisacentrality-dependentJES uncertaintytoaccountforpotentialdifferencesinthedetector re-sponse to quenchedjets. Thisis estimatedby comparingthe de-tector responseevaluated inthe Pythia and Pyquen MCsamples. Thisestimateischeckedindatausingatrack-basedstudy similar to the one described above, but comparing central and periph-eral Pb

+

Pb collisions and accounting for the measured variation of the fragmentation function with centrality [11–13].An uncer-tainty of up to 1% in the most central collisions and decreasing linearly with centralitypercentile to 0% in the 60–80%centrality classisassigned.

The uncertainty attributed to the JER is obtained by adding GaussianfluctuationstoeachreconstructedjetpTvaluewhen

pop-ulatingtheresponse matrix.The magnitudeofthisuncertaintyis fixed byacomparisonofthedataandMCdescriptions oftheJER

in8 TeV data[36].SincetheMC sampleis constructedusingthe data overlay procedure, it is expected that the centrality depen-denceoftheJERshouldbewelldescribedintheMCsample.This is checked by studying the distribution of UE fluctuations using random,jet-sizedgroupsofcalorimetertowersinPb

+

Pb data.The standarddeviations ofthesedistributions describethe typicalUE contribution beneath a jet. The centralitydependence of the UE fluctuationsiscomparedtothatoftheJERintheMCsample,and a systematic uncertainty is includedto account for the observed differences. Asexpected, thesedifferencesare muchsmallerthan thecentrality-independentcontributiontotheJERuncertainty.

Thedata-drivenestimatesoftheJESand JERuncertainties de-scribedabovearederivedusingR

=

0

.

4 jets.Additional uncertain-tiesare included in the R

=

0

.

3 jet measurement to account for potentialdifferences betweendataand theMCsampleinthe rel-ative energy scale of R

=

0

.

3 jets with respect to R

=

0

.

4 jets. Theseuncertaintiesare estimatedfroma studythat matchedjets reconstructedwith thetwo R valuesand comparedthemeansof thepR=0.3

T

/

pTR=0.4distributionsindataandtheMCsample.

Differ-encesmayarisebetweenthedataandMCsamplefromdifferences inthe calorimetricresponseor becausethe jetsinthetwo sam-pleshavedifferentinternalstructure.Thecontributionofthelatter isconstrained by usingexistingjet shapemeasurements [37]. An uncertaintyinthe energyscaleis appliedto account forresidual differences,whichare1.5%atthelowest pT anddecreasesharply

asafunctionofpTtoalimitingvalueof0.3%athigh pT.A similar

study comparingthe variancesofthe p_TR=0.3

/

p_TR=0.4 distributions isusedtoconstraintheuncertaintyintherelativeresolution.This uncertaintyisappliedintheR

=

0

.

3 jetmeasurementinthesame fashion as the other JERuncertainties described above. Although largerthan thecentrality-dependent contribution, itisalso much smallerthanthecentrality-independentcontribution.

As the response matrix is sparsely populated (containing 404 bins), statistical fluctuations could introduce instabilities in the unfolding. To evaluate the sensitivity to such effects, along with anyotherdefects intheresponse,a newresponse matrixis con-structedasafactorisedproductofsingle-jetresponsedistributions, i.e. assuming theresponses in pT1 and pT2 are independent. The

dataareunfoldedusingthisnewresponseandthedifferences be-tweentheunfoldeddistributionsaretakenasa systematic uncer-tainty.Systematicuncertaintiesintheunfoldingduetothechoice ofpriorareestimatedasdescribedintheprevioussectionandare alsoincluded.

Fig. 6. Thetotalsystematicuncertaintyanditsvariouscomponentsfor100<pT1<126 GeV forR=0.4 jetsinPb+Pb collisionswith0–10%centrality(left)andpp collisions

(right).Inthefigureontheleftthefirsttwobinsareoffscalewithbinscentres ofxJ=0.34 and0.38andbinscontentsof1.25and0.75,respectively.

Uncertaintiesduetothecorrectionforthecombinatoriceffects described in Section 5 affect the number of jet pairs before the unfoldingand arethusincludedasadditionalcontributionstothe previouslydescribedstatisticaluncertaintiesinthedata.These in-clude statistical uncertainties in

ε

and the uncertainties in the valuesofthefitparametersc3 andc4,accountingfortheir

covari-ance.Uncertainties inthenormalisationare estimatedby varying theregionof

φ

usedtoestimate Y from1.0–1.4 to1.1–1.5.The uncertaintyduetothiscorrectionissmallerthantheother uncer-taintiesinallpTandcentralitybins,andisonlygreaterthan5%at

valuesof xJ

<

0

.

4.Thiscorrectionwas notappliedtothe pp data

sothereisnocorrespondingsystematicuncertainty.

Thebreakdown ofdifferent contributions tothe total system-aticuncertainty is shown inthe 100

<

pT1

<

126 GeV range for

the0–10%centrality intervaland for pp collisions inFig. 6. Each contribution to the uncertainty, and thus the total uncertainty, tendstodecreasewithincreasingxJ.ThetotaluncertaintyatxJ

∼

1

reachesapproximately12%inmost pT1 and centralitybinsinthe

Pb

+

Pb data.For xJ

<

0

.

4, therelative uncertaintybecomes large,

butthis region represents only a small contribution to the total

(

1

/

N

)

dN

/

dxJ distribution. TheJER uncertaintyis thelargest

con-tribution. In the Pb

+

Pb data it reaches values of approximately 10% and 15% at xJ

∼

1 and xJ

=

0

.

5, respectively.The JES

contri-butions are the second largest contribution to the uncertainties, typicallybetween5%and10%.Inthemostcentralbinsthe unfold-inguncertainty canbecome as large as the JEScontribution.The contributions to the uncertainty in the other centrality intervals andinthepp datafollowtrendssimilartothosedescribedforthe 0–10%centralityinterval,butthemagnitudesaresmallerinmore peripheralcollisions. Inthe pp data they aretypically smallerby a factor oftwo compared to the 0–10% Pb

+

Pb data. The uncer-taintiesforthe R

=

0

.

3 result followthesametrendsasthosefor theR

=

0

.

4 resultbutareslightlylargerduetothetwoadditional sourcesincludedinthatmeasurementtodescribetherelative en-ergyscaleandresolutionbetweenthetwo R values.

8. Results

The unfolded

(

1

/

N

)

dN

/

dxJ distribution in pp collisions for

100

<

pT1

<

126 GeV isshowninFig. 7.Alsoshownarethe

corre-spondingdistributionsobtainedfromthe Pythia 6sampleusedin

the MC studies and also from Pythia8 using the AU2 tune and

Herwig++ [38] with the UE-EE-3 [39] tune. An additional

sam-ple,referredtoasPowheg+Pythia8isgeneratedusingPowheg-Box 2.0[40–42],whichisaccurate tonext-to-leadingorderin pertur-bativeQCD,and interfacedwithPythia 8toprovidea description

of the parton shower and hadronisation. All samples used the

Fig. 7. The(1/N)dN/dxJdistributionforR=0.4 jetsinpp collisionsforthe100<

pT1<126 GeV intervalisshowninblackpointswiththegreyshadedboxes

indi-catingthesystematicuncertainties.Alsoshownareresultsobtainedfromvarious MCeventgenerators: Pythia 6(redsquares),Pythia 8(bluediamonds),Herwig++ (greencrosses)andPowheg+Pythia 8(purplestars).TheratioofeachMCresultto thedataisshowninthebottompanelwherethesystematicuncertaintiesofthe dataareindicatedbyashadedbandcentredatunity.(Forinterpretationofthe ref-erencestocolourinthisfigure,thereaderisreferredtothewebversionofthis article.)

CTEQ6L1PDFset[26]exceptthePowheg+Pythia 8,whichusedthe CT10 PDF set [29]. All four models describe the data fairly well with theHerwig++andPowheg+Pythia 8showingthebest agree-mentoverthefullxJrange.

The unfolded

(

1

/

N

)

dN

/

dxJ distributions in Pb

+

Pb collisions

are shown in Fig. 8, forjet pairs with 100

<

pT1

<

126 GeV for

different centrality intervals. The distribution in pp collisions is shownoneachpanelforcomparison.Inthe60–80%centralitybin, where the effects of quenching are expected to be the smallest, the Pb

+

Pb dataare consistentwith the pp data.In morecentral Pb

+

Pb collisions, the distributions become significantly broader thanthatinpp collisionsandthepeakatxJ

∼

1,correspondingto

nearly symmetricdijet events,isreduced. Atlowercentrality per-centiles the distributionbecomes almost constant over therange 0

.

6



xJ



1,anddevelopsapeakatxJ

∼

0

.

5 inthe0–10%

Fig. 8. The(1/N)dN/dxJdistributionsforjetpairswith100<pT1<126 GeV fordifferentcollisioncentralitiesfor R=0.4 jets.ThePb+Pb dataareshowninredcircles,

whilethepp distributionisshownforcomparisoninbluediamonds,andisthesameinallpanels.Statisticaluncertaintiesareindicatedbytheerrorbarswhilesystematic uncertaintiesareshownwithshadedboxes.(Forinterpretationofthereferencestocolourinthisfigure,thereaderisreferredtothewebversionofthisarticle.)

Fig. 9 showsthe

(

1

/

N

)

dN

/

dxJ distributions for0–10%

central-ity Pb

+

Pb collisions and pp collisions fordifferent selections on

pT1.In pp collisions,thexJdistributionbecomesincreasingly

nar-rowwithincreasing pT1,indicatingthathigher-pTdijetstendtobe

better balancedinmomentum(fractionally).Athigher pT1,the xJ

distributionbeginstofallmoresteeplyfromxJ

∼

1,butappearsto

flattenatintermediate valuesofxJ.Themodificationsobservedin

the Pb

+

Pb datalessenwith increasing pT1 and forjetpairs with

pT1

>

200 GeV themaximumatxJ

∼

1 isrestored.

ThedistributionsforR

=

0

.

3 jetsarealsoshownforthe0–10% centralityintervalandfor pp collisionsfordifferentpT1 rangesin Fig. 10.ThepTofan R

=

0

.

3 jetisgenerallylowerthanthatofan

R

=

0

.

4 jet originating from the same hard scattering, and thus features observed in the

(

1

/

N

)

dN

/

dxJ distributions for R

=

0

.

4

jets are expected to appear at lower values of pT1 for R

=

0

.

3

jets. Tofacilitatea comparisonbetween resultsobtainedwith the two R values,the R

=

0

.

3 jetresultsincludeanadditional pT1

in-terval, 79

<

pT1

<

100 GeV. The differences between the Pb

+

Pb

andpp

(

1

/

N

)

dN

/

dxJdistributionsarequalitativelysimilartothose

observedforR

=

0

.

4 jets.Fig. 11showsthe

(

1

/

N

)

dN

/

dxJ

distribu-tionsfor79

<

pT1

<

100 GeV fordifferentcollisioncentralitiesbut

forjetsreconstructedwith R

=

0

.

3.Thisindicatesthatthe trends present in pT1 and centrality are robust with respect to the UE

andthatUEeffectsareproperlyaccountedforbythecombinatoric subtractionandunfoldingproceduresappliedinthedataanalysis. ThedistributionsareflatterforR

=

0

.

3 jetsinallpTandcentrality

bins,includingin pp collisions. Thisisconsistentwith the expec-tationthat the (pT1

,

pT2) correlationis weaker forsmaller-R jets

duetotheeffectsofpartonradiationoutsidethenominaljetcone. 9. Conclusion

ThisLetterpresentsa measurementofdijet xJ distributions in

4

.

0 pb−1 of pp and 0

.

14 nb−1 of Pb

+

Pb collisions at

√

sNN

=

2

.

76 TeV.Themeasurementisperformeddifferentiallyin leading-jet transverse momentum, pT1, and in collision centrality using

Fig. 9. The(1/N)dN/dxJdistributionsforR=0.4 jetswithdifferentselectionsonpT1,shownforthe0–10%centralitybin(redcircles)andforpp (bluediamonds).Statistical

uncertaintiesareindicatedbytheerrorbarswhilesystematicuncertaintiesareshownwithshadedboxes.(Forinterpretationofthereferencestocolourinthisfigure,the readerisreferredtothewebversionofthisarticle.)

Fig. 10. The(1/N)dN/dxJdistributionsforR=0.3 jetswithdifferentselectionsonpT1,shownforthe0–10%centralitybin(redcircles)andforpp (bluediamonds).Statistical

uncertaintiesareindicatedbytheerrorbarswhilesystematicuncertaintiesareshownwithshadedboxes.(Forinterpretationofthereferencestocolourinthisfigure,the readerisreferredtothewebversionofthisarticle.)

Fig. 11. The(1/N)dN/dxJdistributionsforjetpairswith79<pT1<100 GeV fordifferentcollisioncentralitiesforR=0.3 jets.ThePb+Pb dataareshowninredcircles,

whilethepp distributionisshownforcomparisoninbluediamonds,andisthesameinallpanels.Statisticaluncertaintiesareindicatedbytheerrorbarswhilesystematic uncertaintiesareshownwithshadedboxes.(Forinterpretationofthereferencestocolourinthisfigure,thereaderisreferredtothewebversionofthisarticle.)

data from the ATLAS detector at the LHC. The measured distri-butions are unfolded to account for the effects of experimental resolutionandinefficienciesonthetwo-dimensional(pT1

,

pT2)

dis-tributionsand thenprojectedintobinsoffixedratioxJ

=

pT2

/

pT1.

The distributions showa larger contributionofasymmetricdijets inPb

+

Pb datacomparedtothatinpp data,a featurethatbecomes morepronouncedinmorecentralcollisionsandisconsistentwith expectationsofmedium-inducedenergylossduetojetquenching. Inthe0–10%centralitybinfor100

<

pT1

<

126 GeV,thexJ

distri-bution developsa significant peak atxJ

∼

0

.

5 indicatingthat the

mostprobableconfigurationfordijetsisforthemtobehighly un-balanced.Thisisinsharpcontrasttothesituationinthe pp data

where the most probable values are near xJ

∼

1. The

centrality-dependent modificationsevolve smoothly fromcentralto periph-eralcollisions,andtheresultsinthe60–80%centralitybinandthe

pp dataareconsistent.Atlargervaluesof pT1 thexJ distributions

are observedtonarrowandthedifferences betweenthe distribu-tions in central Pb

+

Pb and pp collisions lessen. This is

qualita-tivelyconsistentwithapictureinwhichthefractionalenergyloss decreaseswithincreasingjetpT.Thefeaturesinthedataare

com-patiblewiththoseobservedinpreviousmeasurementsofdijetsin Pb

+

Pb collisions by theATLAS and CMS collaborations, however,

the trends in this measurement are more prominent due to the

application of theunfolding procedure.This result constitutes an importantbenchmarkfortheoreticalmodelsofjet quenchingand thedynamicsofrelativisticheavy-ioncollisions.

Acknowledgements

We thankCERN for thevery successful operationof the LHC, as well as the support stafffromour institutions withoutwhom ATLAScouldnotbeoperatedefficiently.

WeacknowledgethesupportofANPCyT,Argentina;YerPhI,

Ar-menia; ARC, Australia; BMWFW and FWF, Austria; ANAS,

Azer-baijan; SSTC, Belarus;CNPq and FAPESP, Brazil; NSERC, NRC and CFI,Canada; CERN; CONICYT,Chile; CAS,MOST and NSFC, China;

OntarioInnovationTrust,Canada; EPLANET,ERC,ERDF,FP7,

Hori-zon 2020 and Marie Skłodowska-Curie Actions, European Union;

Investissements d’Avenir Labex and Idex, ANR, Région Auvergne andFondationPartagerleSavoir,France;DFGandAvHFoundation, Germany;Herakleitos,ThalesandAristeiaprogrammesco-financed byEU-ESFandtheGreek NSRF;BSF,GIFandMinerva, Israel;BRF, Norway; CERCA Programme Generalitat de Catalunya, Generalitat Valenciana,Spain;theRoyalSocietyandLeverhulmeTrust,United Kingdom.

The crucialcomputing support from all WLCG partners is ac-knowledged gratefully, in particular from CERN, the ATLAS

Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway,

Swe-den),CC-IN2P3(France),KIT/GridKA(Germany),INFN-CNAF(Italy), NL-T1(Netherlands),PIC(Spain),ASGC(Taiwan),RAL(UK)andBNL (USA),theTier-2facilitiesworldwideandlargenon-WLCGresource providers.Major contributorsofcomputing resourcesarelistedin Ref.[43].

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C. Anastopoulos

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19

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77

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33

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V. Andrei

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S. Angelidakis

9

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I. Angelozzi

109

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A. Angerami

38

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F. Anghinolfi

32

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A.V. Anisenkov

111

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13

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A. Annovi

126a

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C. Antel

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M. Antonelli

50

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A. Antonov

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M. Aoki

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L. Aperio Bella

32

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G. Arabidze

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G. Avolio

32

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B. Axen

16

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M.K. Ayoub

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F. Balli

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E. Banas

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C. Blocker

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A. Blue

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W. Blum

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U. Blumenschein

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S. Blunier

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G.J. Bobbink

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C. Bock

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D. Boerner

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A.G. Bogdanchikov

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M. Bomben

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M. Bona

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M. Boonekamp

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J. Bortfeldt

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M. Bosman

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J.D. Bossio Sola

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J. Boudreau

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J. Bouffard

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D. Boumediene

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C. Bourdarios

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A. Boveia

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J. Boyd

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I.R. Boyko

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J. Bracinik

19

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A. Brandt

8

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G. Brandt

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O. Brandt

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U. Bratzler

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B. Brau

89

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J.E. Brau

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W.D. Breaden Madden

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