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The

ATLAS

Collaboration

a

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i

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l

e

i

n

f

o

a

b

s

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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 LargeHadronColliderusing Pb+Pb and pp datasamples corresponding to integrated

luminositiesof0.14 nb−1and4.0 pb−1,respectively.Jetsare reconstructedusingtheanti-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 in Pb+Pb collisions. The leading and

sub-leading jet transverse momenta are denoted pT1 and pT2.An unfolding 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 asthe 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,was firstobservedattheRelativisticHeavyIonCollider (RHIC)[1,2].Earlymeasurements usingfullyreconstructedjetsin Pb

+

Pb collisionsatthe LHCprovided adirectobservationofthis phenomenon [3]. In Pb

+

Pb collisions the transverse momentum (pT)balancebetweentwojetswasfoundtobedistorted,resulting

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

SubsequentmeasurementsofjetsinPb

+

Pb collisionshave im-provedthe understanding ofpropertiesofquenched jetsandthe empirical features of the quenching mechanism [5–14]. Signifi-canttheoretical advances alsooccurred inthisperiod, andwhile 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

)/(p

T1

+

pT2

)

,wherepT1 andpT2 arethetransverse

momentaofthejetswiththehighestandsecondhighestpTinthe

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

col-lisions morethan isexpectedfromdetector-specificexperimental effects[3,9,10].However, sucheffects,inparticular theresolution of the measured jet pT, must be corrected for in order for the

measurement to be directly comparedto theoretical calculations. Unfoldingprocedureshavebeenappliedtocorrectforsucheffects forsingle-jetmeasurements

[6]

;however,thedijetresultrequires a two-dimensional unfolding to account for migration in the pT

ofeachjetseparately.Themeasurementreportedhereisthefirst unfolded Pb

+

Pb dijet measurement and as such can be directly comparedtotheoreticalmodels.

This Letter presents a measurement of dijet pT correlations

in Pb

+

Pb and pp collisions at a 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 and R

=

0

.

4[15].The analysisisdescribed mostly forthe exampleof R

=

0

.

4 jets. A backgroundsubtraction proce-dure isapplied to account forthe effectsofthe large underlying event(UE)presentin Pb

+

Pb collisionsonthemeasuredjet kine-matics. The momentum balance ofthe dijet systemis 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.

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reduced.Itisthereforeinterestingtocomparetheresultsobtained usingR

=

0

.

3 and R

=

0

.

4 jets,toseeifthesamefeaturesare vis-ible.

2. Experimental set-up

ThemeasurementspresentedinthisLetterareperformedusing theATLASinnerdetector,calorimeterandtriggersystems

[16]

.The inner detector provides measurements of charged-particle tracks overtherange

|

η

|

<

2

.

5.1 Itiscomposedofsiliconpixeldetectors 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)measure chargedparticles over 2

.

1

<

|

η

|

<

3

.

9 using twoplanes ofcountersplacedat z

= ±

3

.

6 m and providetiming measurementsusedintheeventselection[17].

The ATLAS calorimetersystemconsistsof aliquid argon (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 and0

.

2

×

0

.

2 for 2

.

5

<

|

η

|

<

4

.

9.2 TheEM calorimeters

arelongitudinallysegmentedinshowerdepthintothree compart-mentsfollowingapre-samplerlayer(

|

η

|

<

1

.

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

η

granularity (between 0.003 and 0.006)thatcanbeusedtoidentifyphotonsandelectrons.The mid-dlesamplinglayer,whichtypically hasthe largestenergydeposit inEMshowers, hasagranularityof0

.

025

×

0

.

025 over

|

η

|

<

2

.

5. A totaltransverseenergy(TE)triggerisimplementedbyrequiring ahardware-based determinationofthe totaltransverse energyin thecalorimetersystem, EtotT ,tobeaboveathreshold.

Thezero-degreecalorimeters(ZDCs)are locatedsymmetrically atz

= ±

140 mandcover

|

η

|

>

8

.

3. InPb

+

Pb collisionsthe ZDCs primarily measure“spectator” neutrons: neutrons that donot in-teracthadronically when theincident nucleicollide. A ZDC coin-cidencetriggerisimplementedbyrequiringthepulseheightfrom each ZDCto be above a threshold set below the single-neutron peak.

InadditiontotheZDCandTEhardware-based triggers,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 triggerwithathresholdof EtotT

=

20 GeV.A jet reconstruction procedureisthenappliedusingtheanti-kt algorithmwithR

=

0

.

2

andutilisingaUEsubtractionproceduresimilartothatusedinthe offline reconstruction describedin Section4. Eventswithatleast onejetwithET

>

20 GeV attheelectromagneticscale[19]are

se-lected bythejettrigger.Theuseof R

=

0

.

2 forjetsinthetrigger, asopposedto thevaluesof R

=

0

.

3 and 0

.

4 appliedinthe mea-surement, is motivated by the need to define an algorithm that is robustagainst UE fluctuations,which growwith R.The effects ofthedifferentR valuesonthetriggerefficiencyarediscussedin Section 5. The minimum-biastrigger operatedwitha prescale of approximately18whilenoprescalewasappliedtothejettrigger. 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. Theaverage numberofcollisions per bunch-crossing inthe Pb

+

Pb datasamplewas lessthan 0.001,andtheeffectsof multiplecollisionsareneglectedinthedataanalysis.

The centrality of the Pb

+

Pb collisions is characterised by the totaltransverseenergymeasuredintheFCalmodules,



EFCalT .The



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



EFCal

T 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



EFCalT . The centrality boundariesused in thisanalysisare 0%, 10%,20%, 30%, 40%, 60% and80%.

The pp datasample,recordedin2013,wascomposedofevents selected bya jettrigger andused aseriesofdifferent pT

thresh-oldseach selectedwithadifferentprescale. Thejet triggeristhe sameusedinotherATLASmeasurementsin pp collisions[18]and applies the anti-kt algorithm with R

=

0

.

4. The events are

fur-therrequiredtocontainatleastoneprimaryreconstructedvertex. Theaveragenumberofpp collisionsperbunch-crossingvaried be-tween 0.3and0.6during datataking. Thesample corresponds to aluminosityof4

.

0 pb−1.

Theimpactofexperimentaleffectsonthemeasurementis eval-uated using the Geant4-simulateddetector response[22,23] in a MonteCarlo(MC)sampleofpp hard-scatteringevents.Dijetevents at

s

=

2

.

76 TeV are generated using Pythia version 6.423 [24]

withparametervalueschosen accordingtotheAUET2Btune[25]

(3)

the data event that is overlaid. Through this procedure the MC sample contains contributions fromunderlying-event fluctuations andharmonicflowthatmatchthosepresentinthedata.The com-binedsignalisthenreconstructedusingthesameprocedureasis appliedtothedata.So-calledtruthjets aredefinedbyapplyingthe anti-kt algorithm with R

=

0

.

3 and R

=

0

.

4 tostableparticles in

theMC eventgenerator’s output, definedasthose witha proper lifetimegreater than 10 ps, but excluding muons andneutrinos, whichdonotleavesignificantenergydepositsinthecalorimeter.

The detector’s response to quenched jets is studied with an additional sample using Pyquen [30]. This event generator ap-pliesmedium-inducedenergylosstopartonshowersproducedby Pythia.Itisusedtogenerateasample ofjetswithfragmentation functionsthatdifferfromthoseinthenominal Pythia sampleina fashionconsistent withmeasurementsoffragmentationfunctions inquenchedjets[11–13].

4. Jet reconstruction

Theprocedure used to reconstructjets inheavy-ion collisions isdescribed in detailin Ref. [5] andis briefly summarised here. First,energy depositsin the calorimetercells are assembled into



η

× φ =

0

.

1

×

32π logicaltowers.Jetsareformedfromthe tow-ersby applyingtheanti-kt algorithm

[15]

asimplementedinthe

FastJet

softwarepackage

[31]

.

AnestimateoftheUEcontributiontoeachtowerwithinthejet isperformedonan event-by-eventbasis byestimatingthe trans-verseenergydensity,

ρ

(

η

,

φ)

.Globalazimuthal modulationinthe UEarisesduetothephysicsofflow andistraditionallydescribed 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

n

)

]



,

(1)

wherevn 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, butinthismeasurement the 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 from jets is excluded from the estimate ofthebackground.Thetypicalbackgroundenergysubtractedfrom

5. Data analysis

In thisanalysis, jet pairs are formedfrom thetwo highest-pT

jets in the event with pT

>

25 GeV and

|

η

|

<

2

.

1. The pair is

required to have

φ >

/

8, where

≡ |φ

1

− φ

2

|

. For events

selectedbyajet trigger,theleadingjetisrequiredtomatchajet identifiedbythetriggeralgorithmresponsibleforselectingthejet. Thetwo-dimensional(pT1

,

pT2)distributionsobtainedfrom

differ-enttriggeredsamplesarecombinedsuchthatintervalsofpT1 are

populatedby a single trigger.In the pp data analysis, the trigger withthemosteventsthat ismorethan99%efficientforselecting ajet with pT

>

pT1 is used,withthereciprocaloftheluminosity

fortherespectivetriggersamplesusedasaweight.

ThePb

+

Pb jettriggerefficiencyhasabroadturn-onasa func-tion of pT since the triggerjetsare identified using R

=

0

.

2 and

havenoenergyscalecalibrationapplied.Thiseffectisthestrongest incentralcollisionswheretheUEfluctuationsarethelargestand further weaken the correlation between jets reconstructed with differentvaluesof R.Inthemostcentralcollisions,the single-jet-triggerefficiencydoesnotreach aplateauuntil pT

90 GeV.The

jet-triggered sample is used where the efficiency is found to be greater than97%, which occursata pT ofapproximately 85 GeV

inthemostcentralcollisions.A triggerefficiencycorrectionis ap-pliedintheregionwherethereisaninefficiency.

In addition to the dijetsignal, themeasured (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, referredto asUE jets.The rateforsuch occurrencesis high-est in the most central collisions, and the reduction in the true sub-leadingjet pT duetoquenching effectsfurtherenhancesthe

likelihoodofformingacombinatoricpair.

Theshapeofthe

distributionforthecombinatoricjetpairs isinfluencedbytheharmonicflow.Sincethejet pT spectrumfalls

steeply,thejetsmostlikelytobemeasuredatagivenpTvalueare

those lyingon topoflarger-than-average UE. Iftheeffectsof the modulationoftheUEarenotfullyaccountedforinthebackground subtraction,morejetswouldbe observedatanglescorresponding to theflow maxima (

φ

n). Thus combinatoricjet pairs,

with-out anyunderlyingangular correlation,are expectedto acquire a modulationtotheir

distributiondeterminedby thedominant flowharmonics[33].Althoughthesecond-,third- andfourth-order harmonicmodulationsareconsideredevent-by-eventinthejet re-construction proceduredescribed inSection 4,onlytheeffects of thesecond-ordermodulationonthe

distributionareobserved to be completely removed. The residual effectsare an indication that the method ofestimating the modulation of the UE

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

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

areindicatedbyyellowandgreenshadedregions,respectively.Theparametersc3

andc4areobtainedbyfittingthedistributionforjetpairswith|η|>1 in

theregion0<φ <π2,whichisindicatedbytheredsquares(scaledtomatchthe

blackcirclesintheyellowregionforpresentationpurposes).Theerrorbarsdenote statisticalerrors.(Forinterpretationofthereferencestocolourinthisfigure,the readerisreferredtothewebversionofthisarticle.)

neaththejet islessaccurate forthehigher-orderharmonicsthan forn

=

2.

Toaccountforthe residualmodulation,the combinatoric con-tributionisassumedtobeoftheform:

C

(φ)

=

Y

(

1

+

2c3cos 3

+

2c4cos 4

φ) .

(2)

The c3 andc4 valuesare determined by fitting the

distribu-tions over the range 0

<

φ <

π

/

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

<



0

.

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

us-ing jet pairs with a separation of

|

η

|

>

1. Once c3 and c4 are

obtained, the

distribution without this

|

η

|

requirement is integratedover the range 1

<

φ <

1

.

4 toobtain Y .This

proce-forall valuesof xJ.Thisbackgroundsubtractionis notapplied in

the pp databecausethepile-upissmall.

The presence of combinatoric jet pairs also reduces the effi-ciency for genuine pairs. The measured inclusive jet spectrum is used toestimate thelikelihoodthat anotherjetin theevent, un-correlated with the dijet system, is measured with a transverse momentumgreaterthan pT2.Forthe40–60%and60–80%

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

=

25 GeV andincreases

withpT2,reachingunityat45 GeV.Theeffectsofthecombinatoric

jetpairsareaccountedforbyfirstsubtractingtheestimated back-groundandthencorrectingfortheefficiency,

ε

,ineach(pT1

,

pT2)

bin.The numberofjet pairs correctedforsuch effects isdefined tobe:

Ncorr

=

1

ε



Nraw

B



,

where Nraw is thenumberofjetpairs aftercorrectingfortrigger efficiencyandluminosity/prescaleweightingasdescribedabove.

In agiven event, the pT resolutionmayresult inthejet with

the highest true pT beingmeasured with the second highest pT

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

,

pT2)distributions aresymmetrisedprior totheunfolding by

apportioninghalfoftheyieldinagiven(pT1

,

pT2)bin,after

combi-natoricsubtraction,tothebinrelatedtotheoriginalby pT1

pT2.

Thetwo-dimensionaldistributionsaftersymmetrisationareshown in Fig. 2 for central andperipheral Pb

+

Pb collisions and for pp

collisions. The choiceofbinning in(pT1

,

pT2) ismotivatedby the

mappingtothexJ variable,andisdescribedinmoredetailinthe

followingsection.

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

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

(5)

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

Thecalorimetricresponse to jetsisevaluated inthe MC sam-pleby matching truth andreconstructed jets;the nearest recon-structed andtruth jetswithin

R

=



(

η

)

2

+ (φ)

2 of 0

.

3 are

consideredtobeamatch.Thesamerequirementisappliedinboth the R

=

0

.

3 and R

=

0

.

4 versionsofthe analysis.The responseis typically characterisedin terms ofthe jet energyscale (JES) and jetenergyresolution(JER).Thesequantitiesdescribethemeanand widthoftheprecoT distributionsatfixed ptruthT ,expressedasa frac-tionof ptruth

T . Generally, themean of precoT differs from ptruthT by

lessthanapercent,independentofptruth

T andcentrality.This

indi-catesthatthesubtractionoftheaverageUEcontributiontothejet energyisundergoodexperimentalcontrol.TheJERreceives contri-butionsbothfromtheresponseofthecalorimeterandfromlocal UEfluctuationsaboutthemeanintheregionofthejet.Thelatter contributiondominatesatlow pT withtheresolution aslarge as

40%atpT



30 GeV inthemostcentralcollisions.AtthesamepT,

theJER isonly 20% in peripheralcollisions, similar to that in pp

collisions. Atlarger pT values therelative contribution ofthe UE

fluctuationstothejet pTdiminishes,andtheJERisdominatedby

detectoreffects,reaching a constant,centrality-independent value of8%forpT

>

300 GeV.

Themigrationinthetwo-dimensional(pT1

,

pT2)distributionis

accountedfor by applying a two-dimensional Bayesian unfolding tothedata[34,35].Thisprocedure utilizesaresponse matrix ob-tainedbyapplyingthesamepairselectionstothetruthjetsinMC simulationasinthedataanalysis(exceptthetriggerrequirement) andrecording the values of ptruthT1 and ptruthT2 and the transverse momentaofthecorresponding reconstructedjets precoT

1 andp

reco T2 .

Thematchedreconstructedjetsarenotrequiredtohavethe high-est pT inthe event,butaresubjecttoall other requirements

ap-pliedtothedataandtruthjets. Theresponsematrixispopulated symmetricallyin both truth andreconstructed pT. The full

four-dimensionalresponse behaves similarly to the factorised product ofseparatesingle-jetresponsedistributions,andthemigration ef-fectscan be understood in termsof the above discussion. While this provides intuition for the nature of the unfolding problem, suchafactorisationisnotexplicitlyassumed,andanycorrelations betweentheresponseofthetwojetsareaccountedforinthe pro-cedure.

Afterunfolding, theleading/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.Thebinsalong thediagonal,e.g. thosecontaining

pairswithpT2

=

pT1,arenotaffectedbythisprocedure.The

two-dimensional distribution is constructed using binning along each axissuchthattheupperedgeoftheith binobeys,

pT i

=

pT 0

α

i

,

α

=

pT N pT 0

1/N

,

where N is the 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,the binsareofthe samesizewhen plottedwithlogarithmic axes. Withthesechoicesofbinning, the range of xJ values in any given (pT1

,

pT2) bin is fully contained

withintwoadjacentxJbins,whichhaveboundariesatxJ i

=

α

iN.

In thisanalysis, half of the yieldin each (pT1

,

pT2) bin is

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

the diagonal. Thesebins contribute solely to the xJ binwith bin

edges

(

α

−1

,

1

)

.The effectsofsuch amapping onthe x

J

distribu-tionarestudiedandfoundtonotsignificantlydistorttheshapeof thedistributionforavarietyofinputxJdistributions.

The Bayesian unfolding method is an iterative procedure that requiresbothachoiceinanumberofiterations,niter,and

assump-tionofapriorfortheunderlyingtruedistribution.Anincrease in

niterreducessensitivitytothechoiceofpriorbutmayamplify

sta-tisticalfluctuationsthatare alreadypresentintheinput distribu-tion.As Pythia doesnotincludetheeffectsofjetquenching,thexJ

distributionsobtainedfromtheMCsamplearenotexpectedtobe optimalchoicesforthe prior.In particular,the xJ distributions in

PythiaincreasemonotonicallywithxJ,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.

Theeffectsofthereweightingprocedureare shownintheleft panelof

Fig. 3

inthe100

<

pT1

<

126 GeV rangeand0–10%

cen-tralityinterval,wherethelargestdifferencebetweenthedataand Pythiais observed.The“nominal”distribution,orthereweighted distribution,is usedastheprior intheunfolding ofthedata.An

(6)

Fig. 4. Uncertaintiessensitivetothenumberofiterationsintheunfoldingprocedureasafunctionofniterforthe0–10%centralityintervalfor R=0.4 jets.Left:The

combination(solidblack)oftheunfolding(dashedred)andstatistical(dottedblue)uncertainty,√ δ2forthe100<p

T1<126 GeV interval.Right:Thecombineduncertainty

foreachpT1 intervalconsideredinthemeasurement.(Forinterpretationofthereferencestocolourinthisfigure,thereaderisreferredtothewebversionofthisarticle.)

“alternate”reweighting is alsoshown, which hasa shape signifi-cantlydifferentfromthenominal, butdoesnot increaseasmuch asthe Pythia distribution. The features in the dataare observed to be robust with respect to the choice of prior fora broad set of reweighting functions. The systematic uncertainty due to the choice of prior is estimatedby comparing the results ofthe un-foldingsusing the “nominal”and“alternate” xJ distributions. The

resultsofapplyingunfoldingswiththesetwochoicesofpriorsare shownintherightpanelsof

Fig. 3

forthesamepT1 andcentrality

selection.

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

The value ofniter is selected separately in each centrality

in-terval byexamining theuncertainty,

δ

2,in

(

1

/N)

dN

/

dx J after

unfolding considering statistical uncertainties andsystematic un-certaintiesattributedtotheunfoldingprocedure,

δ

2

= δ

2stat

+ δ

prior2

,

andsumming over all xJ bins. Here

δ

prior is the uncertainty due

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

istaken asthestatisticaluncertainty. An additionalcovarianceis obtainedfrom applying the pseudo-experiment procedure to the response matrixandcombinedwiththat obtainedfromapplying theproceduretothe data.The

δ

2stat foreach xJ binistakentobe

thediagonalelementoftheresultingcovariancematrix.The statis-ticalcovariancematricesexhibit similar trendsacross all pT1 and

centrality ranges. Nearby xJ bins show a strong positive

correla-tionthatdiminishesforbinsseparatedinxJ,andisexpectedfrom

theeffectsoftheproceduresforunfoldingandmappingtoxJ.Bins

well separated in xJ show an anti-correlation attributable to the

normalisationof

(

1

/N

)

dN

/

dxJ.

Theleftpanelof

Fig. 4

shows

δ

2asafunctionofn iteralong

withitsvarious contributionsforthe 100

<

pT1

<

126 GeV range

and0–10%centralityinterval.Sincetheunfoldingisperformedin twodimensions,thevalueofnitercannotbechosen separatelyfor

each range of pT1. Athigher valuesof pT1 the effects ofthe

un-foldingare smallerwhilethe effectsofthestatisticalfluctuations canbemoresevere.Therightpanelof

Fig. 4

showsthetotal

δ

2

foreach rangeof pT1 considered inthemeasurement alongwith

thetotalcombinedoverall pT1 ranges.The valueofniterforeach

centrality binand R value ischosen by considering theniter

de-pendence of

δ

2 for each pT

1 bin and selecting a value that

maintainscomparableuncertaintiesacrossallpT1ranges.Themore

central bins requirethemostiterations, resultingfromthe larger jetenergyresolutionintheseevents.Thenumberofiterationsfor

R

=

0

.

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

δ

2 distributions for R

=

0

.

3 jets

showbehaviour similartothosefor R

=

0

.

4 jets inthesame cen-tralitybin.

It is possiblefora third jet presentinthe eventtobe recon-structedasthejetwiththesecondhighest pT throughthe

exper-imental resolution.As achecktostudytheimpactofsuch effects onthemeasurement,analternativeresponsematrixisconstructed whereno

R matching

isrequiredbetweenthetruth and recon-structed jets.A weighting isappliedsuchthatthe pT distribution

of thereconstructed third jet matchesthat observed inthe data. Differencesbetweentheunfoldeddistributionsobtainedwiththis responsematrixandthenominaloneareobservedtobesmalland wellwithinthesystematicuncertaintyassociatedwiththe unfold-ingprocedure.

The

(

1

/N

)

dN

/

dxJ distributions before andafter unfolding are

shownin

Fig. 5

forcentralandperipheralPb

+

Pb collisionsandfor

pp collisionsforjet pairswith100

<

pT1

<

126 GeV.The

system-aticuncertainties indicatedcontain allofthecontributions tothe totalsystematicuncertaintydescribedinSection 7.Inthe pp and

60–80% centralityinterval, theresolution effectsbefore unfolding reduce the sharpness ofthe peak near xJ

1. In thecaseof the

0–10%centralityinterval,theeffectistosmearoutthepeaknear

xJ

0

.

5.ThelowestxJbinsexhibitinstabilityintheunfolding

pro-cedureduetotheMCsamplehavingtoofeweventsinthisregion. However, including thisrangein theunfolding improves the sta-bilityoftheadjacentxJ bins.Thus,afterunfolding,onlytherange

0

.

32

<

xJ

<

1 is reported in the results even though pairs with pT2

>

25 GeV areincludedinthemeasurement.

7. Systematic uncertainties

Systematicuncertaintiesattributedtotheresponsematrixused in theunfoldingarise dueto uncertaintiesin theJESandJER.To account for theseeffects, newresponse matrices are constructed with a systematically varied relationship between the truth and

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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.

Inthe pp data analysis, the JESuncertainty isdescribed by a setof11 independentnuisance parameters;theseincludeeffects fromuncertainties derived through theinsitu calibration[32].In theMC sample usedto determine the calibration,the calorimet-ric response tojets initiated by the fragmentationof quarksand gluonsisobservedtodiffer.PotentialinaccuraciesintheMC sam-pledescribingboththisflavour-dependentresponseandthe rela-tive abundances ofquark andgluon jetsare accounted forusing separate nuisance parameters. A source of uncertaintyrelated to theadaptation oftheinsitu calibrationderived at

s

=

8 TeV to 2.76 TeV dataisalsoincluded.

InthePb

+

Pb dataanalysis, twoadditionaluncertaintiesinthe JESareconsidered.The firstaccountsfordifferencesbetweenthe detector operating conditions in the Pb

+

Pb and pp data, which were recordedin 2011and2013, respectively. Thisis derived by using charged-particle tracks reconstructed in the inner detector toprovideanindependentcheckontheJES,whichonlyuses infor-mationfromthecalorimeter.Foreach jet,allreconstructedtracks within

R

<

0

.

4 andhavingptrkT

>

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

andin the MC sample, and a doubleratio of the two quantities isformed.The doubleratioobtainedinperipheral Pb

+

Pb datais comparedwiththatinpp data.Theprecisionofthecomparisonis limitedbyhavingtoofeweventsintheperipheralPb

+

Pb dataand athighjet pT,anda pT- and

η

-independentuncertaintyof1.46%

isassignedtoaccountforpotentialdifferences.

Thesecondadditionaluncertaintyisacentrality-dependentJES uncertaintytoaccountforpotentialdifferencesinthedetector re-sponseto quenchedjets. This isestimated bycomparing the de-tectorresponse evaluatedinthe Pythia and Pyquen MCsamples. Thisestimate ischeckedindatausingatrack-basedstudysimilar to the one described above, but comparing central and periph-eral Pb

+

Pb collisions andaccounting for the measured variation ofthe fragmentation function with centrality[11–13].An uncer-tainty of up to 1% in the mostcentral collisions and decreasing linearlywithcentrality percentile to 0% in the 60–80%centrality classisassigned.

The uncertainty attributed to the JER is obtained by adding GaussianfluctuationstoeachreconstructedjetpTvaluewhen

pop-ulatingtheresponsematrix.Themagnitudeofthisuncertaintyis fixedbyacomparisonofthedataandMCdescriptions oftheJER

in8 TeV data [36].Since theMCsample isconstructedusingthe data overlay procedure, it is expected that the centrality depen-denceoftheJERshouldbewell describedintheMCsample. This is checked by studying the distribution of UE fluctuations using random,jet-sizedgroupsofcalorimetertowersinPb

+

Pb data.The standard deviationsofthesedistributions describe thetypical UE contribution beneath a jet. The centrality dependence of the UE fluctuationsiscomparedtothatoftheJERintheMCsample,and a systematic uncertaintyis included to account for the observed differences. Asexpected, thesedifferencesare muchsmallerthan thecentrality-independentcontributiontotheJERuncertainty.

Thedata-driven estimatesoftheJESandJERuncertainties de-scribedabovearederivedusingR

=

0

.

4 jets.Additional uncertain-ties are includedin the R

=

0

.

3 jet measurement to account for potential differencesbetweendataandtheMC sampleinthe rel-ative energy scale of R

=

0

.

3 jets with respect to R

=

0

.

4 jets. Theseuncertainties areestimatedfromastudythat matchedjets reconstructedwiththetwo R values andcomparedthe meansof thepRT=0.3

/p

TR=0.4distributionsindataandtheMCsample. Differ-encesmayarisebetweenthedataandMCsamplefromdifferences inthe calorimetricresponse orbecause thejetsin thetwo sam-pleshavedifferentinternalstructure.Thecontributionofthelatter isconstrainedby usingexisting jetshape measurements [37]. An uncertaintyin theenergyscale isapplied to accountfor residual differences, whichare1.5%atthelowest pT anddecreasesharply

asafunctionofpTtoalimitingvalueof0.3%athighpT.A similar

studycomparing thevariancesof the pTR=0.3

/p

TR=0.4 distributions isusedtoconstraintheuncertaintyintherelativeresolution.This uncertaintyisappliedintheR

=

0

.

3 jetmeasurementinthesame fashion as the other JER uncertainties described above. Although larger thanthecentrality-dependentcontribution,it isalsomuch smallerthanthecentrality-independentcontribution.

As the response matrixis sparsely populated (containing 404

bins), statistical fluctuations could introduce instabilities in the unfolding. To evaluate the sensitivity to such effects, along with anyother defectsintheresponse, a newresponse matrixis con-structedasafactorisedproductofsingle-jetresponsedistributions, i.e.assuming the responses in pT1 and pT2 are independent.The

dataareunfoldedusingthisnewresponseandthedifferences be-tweentheunfolded distributionsaretakenasasystematic uncer-tainty.Systematicuncertaintiesintheunfoldingduetothechoice ofpriorareestimatedasdescribedintheprevioussectionandare alsoincluded.

(8)

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 unfoldingandarethusincludedasadditionalcontributionstothe previouslydescribedstatisticaluncertaintiesinthedata.These in-clude statistical uncertainties in

ε

and the uncertainties in the valuesofthefitparametersc3 andc4,accountingfortheir

covari-ance.Uncertaintiesinthe normalisationareestimatedby varying theregion of

usedto estimate Y from1.0–1.4 to1.1–1.5.The uncertaintyduetothiscorrectionissmallerthantheother uncer-taintiesinall pTandcentralitybins,andisonlygreaterthan5%at

valuesofxJ

<

0

.

4.Thiscorrection wasnot appliedtothe pp data

sothereisnocorrespondingsystematicuncertainty.

The breakdownof differentcontributions to the total system-atic uncertainty isshown in the 100

<

pT1

<

126 GeV range for

the0–10% centralityinterval andfor pp collisions in

Fig. 6

. Each contribution to the uncertainty, and thus the total uncertainty, tendstodecreasewithincreasingxJ.ThetotaluncertaintyatxJ

1

reachesapproximately12%inmost pT1 andcentralitybinsinthe

Pb

+

Pb data. ForxJ

<

0

.

4,the relative uncertaintybecomes large,

but thisregion represents only a small contribution to the total

(

1

/N

)

dN

/

dxJ distribution.The JER uncertaintyis thelargest

con-tribution. In the Pb

+

Pb data it reaches values of approximately 10% and15% at xJ

1 and xJ

=

0

.

5,respectively. The JES

contri-butions are the second largest contribution to the uncertainties, typicallybetween5%and10%.Inthemostcentralbinsthe unfold-ing uncertaintycan become aslarge astheJES contribution.The contributions to the uncertainty in the other centrality intervals andinthepp datafollowtrendssimilartothosedescribedforthe 0–10%centralityinterval,butthemagnitudesaresmallerinmore peripheralcollisions. Inthe pp datathey aretypically smallerby a factor of two compared to the 0–10% Pb

+

Pb data. The uncer-taintiesforthe R

=

0

.

3 resultfollowthesametrendsasthosefor 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 isshownin

Fig. 7

.Alsoshownarethe

corre-spondingdistributionsobtainedfromthe Pythia 6sampleusedin the MC studies and also fromPythia 8 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],whichis accurateto next-to-leadingorderin pertur-bativeQCD, andinterfacedwithPythia 8toprovideadescription 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 withtheHerwig++andPowheg+Pythia 8showingthebest agree-mentoverthefullxJrange.

The unfolded

(

1

/N)

dN

/

dxJ distributions in Pb

+

Pb collisions

are shownin Fig. 8, for jet pairs with 100

<

pT1

<

126 GeV for

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

+

Pb dataare consistent withthe pp data. Inmore central Pb

+

Pb collisions, the distributions become significantly broader thanthatinpp collisionsandthepeakatxJ

1,correspondingto

nearly symmetricdijetevents,isreduced.Atlower centrality per-centiles the distribution becomes almost constant overthe range 0

.

6



xJ



1,anddevelopsapeakatxJ

0

.

5 inthe0–10%

(9)

Fig. 8. The(1/N)dN/dxJ distributionsforjetpairswith100<pT1<126 GeV fordifferentcollisioncentralitiesforR=0.4 jets.ThePb+Pb dataareshowninredcircles,

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

Fig. 9showsthe

(

1

/N)

dN

/

dxJ distributions for0–10%

central-ityPb

+

Pb collisions and pp collisionsfor differentselections on

pT1.In pp collisions,thexJ distributionbecomesincreasingly

nar-rowwithincreasingpT1,indicatingthathigher-pTdijetstendtobe

betterbalancedinmomentum (fractionally).Athigher pT1,the xJ

distributionbeginstofallmoresteeplyfromxJ

1,butappearsto

flattenatintermediatevaluesofxJ.Themodificationsobservedin

thePb

+

Pb datalessen withincreasing pT1 andforjetpairs with

pT1

>

200 GeV themaximumatxJ

1 isrestored.

ThedistributionsforR

=

0

.

3 jetsarealsoshownforthe0–10% centralityinterval andfor pp collisionsfordifferentpT1 rangesin Fig. 10.The pT ofan R

=

0

.

3 jetisgenerallylowerthanthatofan R

=

0

.

4 jet originatingfrom 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.Tofacilitateacomparisonbetweenresultsobtainedwiththe two R values,theR

=

0

.

3 jetresultsincludeanadditional pT1

in-terval, 79

<

pT1

<

100 GeV. The differencesbetween the Pb

+

Pb

andpp

(

1

/N)

dN

/

dxJdistributionsarequalitativelysimilartothose

observedforR

=

0

.

4 jets.

Fig. 11

showsthe

(

1

/N)

dN

/

dxJ

distribu-tionsfor79

<

pT1

<

100 GeV fordifferentcollisioncentralitiesbut

forjetsreconstructed withR

=

0

.

3.Thisindicates thatthetrends present in pT1 and centrality are robust with respect to the UE

andthatUEeffectsareproperlyaccountedforbythecombinatoric subtractionandunfoldingproceduresappliedinthedataanalysis. ThedistributionsareflatterforR

=

0

.

3 jetsinall pTandcentrality

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

,

pT2) correlation is weaker forsmaller-R jets

duetotheeffectsofpartonradiationoutsidethenominaljetcone.

9. Conclusion

ThisLetter presentsameasurement ofdijetxJ 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

(10)

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.)

(11)

Fig. 11. The(1/N)dN/dxJdistributionsforjetpairswith79<pT1<100 GeV fordifferentcollisioncentralitiesfor R=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-tributionsandthenprojectedintobinsoffixedratioxJ

=

pT2

/p

T1.

Thedistributions show a largercontribution ofasymmetricdijets inPb

+

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

<

pT1

<

126 GeV,thexJ

distri-butiondevelops a significant peak atxJ

0

.

5 indicating that the

mostprobableconfigurationfordijetsisforthemtobehighly un-balanced.Thisisinsharpcontrasttothesituationinthe pp data

where the most probablevalues are near xJ

1. The

centrality-dependentmodifications evolve smoothly fromcentralto periph-eralcollisions,andtheresultsinthe60–80%centralitybinandthe

pp dataare consistent.At largervaluesof pT1 thexJ distributions

areobservedtonarrowandthedifferencesbetweenthe distribu-tions in central Pb

+

Pb and pp collisions lessen. This is

qualita-tivelyconsistentwithapictureinwhichthefractionalenergyloss decreaseswithincreasingjet pT.Thefeaturesinthedataare

com-patiblewiththoseobservedinpreviousmeasurementsofdijetsin Pb

+

Pb collisions by the ATLAS andCMS collaborations,however, the trends in thismeasurement are more prominent dueto the applicationof the unfoldingprocedure. This resultconstitutesan importantbenchmarkfortheoreticalmodelsofjetquenchingand thedynamicsofrelativisticheavy-ioncollisions.

Acknowledgements

We thank CERN forthe very successfuloperation of the LHC, aswell as thesupport staff fromour institutionswithout whom ATLAScouldnotbeoperatedefficiently.

WeacknowledgethesupportofANPCyT,Argentina;YerPhI, Ar-menia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azer-baijan; SSTC, Belarus; CNPq andFAPESP, Brazil; NSERC, NRC and CFI,Canada; CERN; CONICYT, Chile;CAS, MOSTandNSFC, China;

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theCanadaCouncil,Canarie,CRC,ComputeCanada,FQRNT,andthe OntarioInnovation Trust,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-ESFandtheGreekNSRF;BSF,GIFandMinerva, Israel;BRF, Norway; CERCA Programme Generalitat de Catalunya, Generalitat Valenciana,Spain;theRoyalSocietyandLeverhulmeTrust,United Kingdom.

The crucial computingsupport fromall 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.Majorcontributorsofcomputingresourcesarelisted in Ref.[43].

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(13)

Y. Amaral Coutinho

,

C. Amelung

,

D. Amidei

,

S.P. Amor Dos Santos

, A. Amorim

,

S. Amoroso

32

,

G. Amundsen

25

, C. Anastopoulos

141

,

L.S. Ancu

52

,

N. Andari

19

,

T. Andeen

11

,

C.F. Anders

60b

,

J.K. Anders

77

,

K.J. Anderson

33

,

A. Andreazza

94a

,

94b

, V. Andrei

60a

, S. Angelidakis

9

,

I. Angelozzi

109

,

A. Angerami

38

,

F. Anghinolfi

32

,

A.V. Anisenkov

111

,

c

,

N. Anjos

13

,

A. Annovi

126a

,

126b

,

C. Antel

60a

,

M. Antonelli

50

,

A. Antonov

100

,

,

D.J. Antrim

166

,

F. Anulli

134a

, M. Aoki

69

, L. Aperio Bella

32

,

G. Arabidze

93

,

Y. Arai

69

,

J.P. Araque

128a

, V. Araujo Ferraz

26a

,

A.T.H. Arce

48

,

R.E. Ardell

80

,

F.A. Arduh

74

,

J-F. Arguin

97

,

S. Argyropoulos

66

,

M. Arik

20a

,

A.J. Armbruster

145

, L.J. Armitage

79

,

O. Arnaez

32

,

H. Arnold

51

,

M. Arratia

30

, O. Arslan

23

,

A. Artamonov

99

,

G. Artoni

122

, S. Artz

86

,

S. Asai

157

,

N. Asbah

45

,

A. Ashkenazi

155

, L. Asquith

151

,

K. Assamagan

27

,

R. Astalos

146a

,

M. Atkinson

169

,

N.B. Atlay

143

,

K. Augsten

130

,

G. Avolio

32

, B. Axen

16

, M.K. Ayoub

119

, G. Azuelos

97

,

d

, A.E. Baas

60a

,

M.J. Baca

19

,

H. Bachacou

138

,

K. Bachas

76a

,

76b

, M. Backes

122

,

M. Backhaus

32

,

P. Bagiacchi

134a

,

134b

,

P. Bagnaia

134a

,

134b

,

J.T. Baines

133

,

M. Bajic

39

,

O.K. Baker

179

,

E.M. Baldin

111

,

c

,

P. Balek

175

,

T. Balestri

150

,

F. Balli

138

,

W.K. Balunas

124

,

E. Banas

42

,

Sw. Banerjee

176

,

e

, A.A.E. Bannoura

178

,

L. Barak

32

,

E.L. Barberio

91

,

D. Barberis

53a

,

53b

, M. Barbero

88

,

T. Barillari

103

,

M-S Barisits

32

, T. Barklow

145

,

N. Barlow

30

,

S.L. Barnes

36c

,

B.M. Barnett

133

,

R.M. Barnett

16

, Z. Barnovska-Blenessy

36a

,

A. Baroncelli

136a

, G. Barone

25

,

A.J. Barr

122

, L. Barranco Navarro

170

,

F. Barreiro

85

,

J. Barreiro Guimarães da Costa

35a

,

R. Bartoldus

145

,

A.E. Barton

75

,

P. Bartos

146a

, A. Basalaev

125

,

A. Bassalat

119

,

f

,

R.L. Bates

56

, S.J. Batista

161

, J.R. Batley

30

,

M. Battaglia

139

,

M. Bauce

134a

,

134b

,

F. Bauer

138

, H.S. Bawa

145

,

g

, J.B. Beacham

113

, M.D. Beattie

75

,

T. Beau

83

, P.H. Beauchemin

165

,

P. Bechtle

23

,

H.P. Beck

18

,

h

,

K. Becker

122

,

M. Becker

86

,

M. Beckingham

173

, C. Becot

112

,

A.J. Beddall

20d

, A. Beddall

20b

,

V.A. Bednyakov

68

,

M. Bedognetti

109

,

C.P. Bee

150

,

T.A. Beermann

32

,

M. Begalli

26a

,

M. Begel

27

,

J.K. Behr

45

, A.S. Bell

81

,

G. Bella

155

,

L. Bellagamba

22a

,

A. Bellerive

31

,

M. Bellomo

89

,

K. Belotskiy

100

,

O. Beltramello

32

, N.L. Belyaev

100

,

O. Benary

155

,

,

D. Benchekroun

137a

,

M. Bender

102

,

K. Bendtz

148a

,

148b

,

N. Benekos

10

,

Y. Benhammou

155

,

E. Benhar Noccioli

179

, J. Benitez

66

,

D.P. Benjamin

48

,

M. Benoit

52

, J.R. Bensinger

25

,

S. Bentvelsen

109

,

L. Beresford

122

, M. Beretta

50

,

D. Berge

109

,

E. Bergeaas Kuutmann

168

,

N. Berger

5

, J. Beringer

16

,

S. Berlendis

58

,

N.R. Bernard

89

,

G. Bernardi

83

,

C. Bernius

112

,

F.U. Bernlochner

23

, T. Berry

80

, P. Berta

131

,

C. Bertella

86

,

G. Bertoli

148a

,

148b

,

F. Bertolucci

126a

,

126b

,

I.A. Bertram

75

,

C. Bertsche

45

, D. Bertsche

115

,

G.J. Besjes

39

,

O. Bessidskaia Bylund

148a

,

148b

,

M. Bessner

45

,

N. Besson

138

,

C. Betancourt

51

,

A. Bethani

87

,

S. Bethke

103

,

A.J. Bevan

79

, R.M. Bianchi

127

,

M. Bianco

32

, O. Biebel

102

,

D. Biedermann

17

, R. Bielski

87

,

N.V. Biesuz

126a

,

126b

,

M. Biglietti

136a

, J. Bilbao De Mendizabal

52

,

T.R.V. Billoud

97

,

H. Bilokon

50

,

M. Bindi

57

,

A. Bingul

20b

,

C. Bini

134a

,

134b

, S. Biondi

22a

,

22b

,

T. Bisanz

57

, C. Bittrich

47

,

D.M. Bjergaard

48

,

C.W. Black

152

,

J.E. Black

145

, K.M. Black

24

, D. Blackburn

140

,

R.E. Blair

6

,

T. Blazek

146a

,

I. Bloch

45

,

C. Blocker

25

,

A. Blue

56

, W. Blum

86

,

, U. Blumenschein

79

,

S. Blunier

34a

,

G.J. Bobbink

109

,

V.S. Bobrovnikov

111

,

c

,

S.S. Bocchetta

84

, A. Bocci

48

, C. Bock

102

,

M. Boehler

51

, D. Boerner

178

,

D. Bogavac

102

, A.G. Bogdanchikov

111

,

C. Bohm

148a

,

V. Boisvert

80

, P. Bokan

168

,

i

, T. Bold

41a

,

A.S. Boldyrev

101

, M. Bomben

83

,

M. Bona

79

,

M. Boonekamp

138

,

A. Borisov

132

, G. Borissov

75

,

J. Bortfeldt

32

,

D. Bortoletto

122

,

V. Bortolotto

62a

,

62b

,

62c

, D. Boscherini

22a

,

M. Bosman

13

,

J.D. Bossio Sola

29

,

J. Boudreau

127

,

J. Bouffard

2

,

E.V. Bouhova-Thacker

75

, D. Boumediene

37

,

C. Bourdarios

119

,

S.K. Boutle

56

,

A. Boveia

113

,

J. Boyd

32

,

I.R. Boyko

68

,

J. Bracinik

19

,

A. Brandt

8

,

G. Brandt

57

,

O. Brandt

60a

, U. Bratzler

158

,

B. Brau

89

, J.E. Brau

118

,

W.D. Breaden Madden

56

,

K. Brendlinger

45

,

A.J. Brennan

91

,

L. Brenner

109

,

R. Brenner

168

,

S. Bressler

175

,

D.L. Briglin

19

,

Figure

Fig. 2. The two-dimensional (p T 1 , p T 2 ) distributions after correction and symmetrisation for Pb + Pb data in the 0–10% (left) and 60–80% (centre) centrality bins and for pp data (right) for R = 0
Fig. 3. Left: the ( 1 / N ) dN / dx J distributions used as priors in the unfolding of the R = 0
Fig. 4. Uncertainties sensitive to the number of iterations in the unfolding procedure as a function of n iter for the 0–10% centrality interval for R = 0
Fig. 5. The ( 1 / N ) dN / dx J distributions for R = 0 . 4 jets before (black) and after (red) unfolding for the 100 &lt; p T 1 &lt; 126 GeV interval for the Pb + Pb 0–10% (left) and Pb + Pb 60–80% (middle) centrality ranges and for pp collisions (right)
+5

References

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