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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,resultingfromconfigurationsinwhichthetwojetssufferdifferentamounts 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 andprovid- E-mailaddress:atlas.publications@cern.ch.
ing testable predictions. Measurements of the dijet asymmetry,
AJ
≡ (
pT1−
pT2)/(p
T1+
pT2)
,wherepT1 andpT2 arethetransversemomentaofthejetswiththehighestandsecondhighestpTinthe
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 pTofeachjetseparately.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 parametervalues 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 expressedhttps://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. 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-nalinshowerdepthandhasaη
×φ
granularityof0.
1×
0.
1 for|
η
|
<
2.
5 and0.
2×
0.
2 for 2.
5<
|
η
|
<
4.
9.2 TheEM calorimetersarelongitudinallysegmentedinshowerdepthintothree compart-mentsfollowingapre-samplerlayer(
|
η
|
<
1.
8).TheEM calorime-terhasagranularitythatvarieswithlayerandpseudorapidity,but whichisgenerallymuchfinerthanthat ofthehadronic calorime-ter. The first layer has highη
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.
2andutilisingaUEsubtractionproceduresimilartothatusedinthe offline reconstruction describedin Section4. Eventswithatleast onejetwithET
>
20 GeV attheelectromagneticscale[19]arese-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 .TheEFCalT distribution obtained in minimum-bias collisions is par-titioned into separate ranges of
EFCalT 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 arefur-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]
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 intheMC 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]
asimplementedintheFastJet
softwarepackage[31]
.AnestimateoftheUEcontributiontoeachtowerwithinthejet isperformedonan event-by-eventbasis byestimatingthe trans-verseenergydensity,
ρ
(
η
,
φ)
.Globalazimuthal modulationinthe UEarisesduetothephysicsofflow andistraditionallydescribed in terms of the Fourier expansion of theφ
dependence of the transverseenergydensity.Inthesubtractionprocedure,theUE es-timateisassignedaφ
dependenceusingthemeasuredmagnitudes andphasesofthemodulation:ρ
(
η
, φ)
=
ρ
(
η
)
×
1+
2 n vncos[
n(φ
−
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 ofη
. 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.Thetypicalbackgroundenergysubtractedfrom5. 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 isrequired to have
φ >
7π/
8, whereφ
≡ |φ
1− φ
2|
. For eventsselectedbyajet trigger,theleadingjetisrequiredtomatchajet identifiedbythetriggeralgorithmresponsibleforselectingthejet. Thetwo-dimensional(pT1
,
pT2)distributionsobtainedfromdiffer-enttriggeredsamplesarecombinedsuchthatintervalsofpT1 are
populatedby a single trigger.In the pp data analysis, the trigger withthemosteventsthat ismorethan99%efficientforselecting ajet with pT
>
pT1 is used,withthereciprocaloftheluminosityfortherespectivetriggersamplesusedasaweight.
ThePb
+
Pb jettriggerefficiencyhasabroadturn-onasa func-tion of pT since the triggerjetsare identified using R=
0.
2 andhavenoenergyscalecalibrationapplied.Thiseffectisthestrongest incentralcollisionswheretheUEfluctuationsarethelargestand further weaken the correlation between jets reconstructed with differentvaluesof R.Inthemostcentralcollisions,the single-jet-triggerefficiencydoesnotreach aplateauuntil pT
∼
90 GeV.Thejet-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
φ
distributionforthecombinatoricjetpairs isinfluencedbytheharmonicflow.Sincethejet pT spectrumfallssteeply,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
φ
distributiondeterminedby thedominant flowharmonics[33].Althoughthesecond-,third- andfourth-order harmonicmodulationsareconsideredevent-by-eventinthejet re-construction proceduredescribed inSection 4,onlytheeffects of thesecond-ordermodulationontheφ
distributionareobserved to be completely removed. The residual effectsare an indication that the method ofestimating the modulation of the UEunder-Fig. 1. Theφdistributionfor R=0.4 jetpairswith89<pT1<100 GeV inthe
0–10%centralityinterval.Thedistributionforalljetpairsisindicatedbytheblack circles.ThecombinatoriccontributiongivenbyEq.(2)isshownasablueline.The rangesofφusedtofixthevalueofY andtodefinethesignalregion(φ >78π)
areindicatedbyyellowandgreenshadedregions,respectively.Theparametersc3
andc4areobtainedbyfittingtheφdistributionforjetpairswith|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 3φ
+
2c4cos 4φ) .
(2)The c3 andc4 valuesare determined by fitting the
φ
distribu-tions over the range 0
<
φ <
π
/
2 where the real dijet contri-bution is expected to be small. The region 0<
φ
0.
8 is also expectedtoreceiverealdijetcontributionsarisingfromparton ra-diationwhichresultsinpairs ofjetsatnearbyangles.Toremove thiscontribution,thefittoobtainc3 andc4 isperformedonlyus-ing jet pairs with a separation of
|
η
|
>
1. Once c3 and c4 areobtained, the
φ
distribution without this|
η
|
requirement is integratedover the range 1<
φ <
1.
4 toobtain Y .Thisproce-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 andincreaseswithpT2,reachingunityat45 GeV.Theeffectsofthecombinatoric
jetpairsareaccountedforbyfirstsubtractingtheestimated back-groundandthencorrectingfortheefficiency,
ε
,ineach(pT1,
pT2)bin.The numberofjet pairs correctedforsuch effects isdefined tobe:
Ncorr
=
1ε
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 byapportioninghalfoftheyieldinagiven(pT1
,
pT2)bin,aftercombi-natoricsubtraction,tothebinrelatedtotheoriginalby pT1
↔
pT2.Thetwo-dimensionaldistributionsaftersymmetrisationareshown in Fig. 2 for central andperipheral Pb
+
Pb collisions and for ppcollisions. The choiceofbinning in(pT1
,
pT2) ismotivatedby themappingtothexJ 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.
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 areconsideredtobeamatch.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 ptruthT . 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)distributionisaccountedfor 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 eachbin with pT2
>
pT1 the yield is moved to the corresponding binwith pT2
<
pT1.Thebinsalong thediagonal,e.g. thosecontainingpairswithpT2
=
pT1,arenotaffectedbythisprocedure.Thetwo-dimensional distribution is constructed using binning along each axissuchthattheupperedgeoftheith binobeys,
pT i
=
pT 0α
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 containedwithintwoadjacentxJbins,whichhaveboundariesatxJ i
=
α
i−N.In thisanalysis, half of the yieldin each (pT1
,
pT2) bin isappor-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 xJ
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
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 andcentralityselection.
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 afterunfolding considering statistical uncertainties andsystematic un-certaintiesattributedtotheunfoldingprocedure,
δ
2= δ
2stat+ δ
prior2,
andsumming over all xJ bins. Here
δ
prior is the uncertainty dueto 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 binistakentobethediagonalelementoftheresultingcovariancematrix.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 iteralongwithitsvarious contributionsforthe 100
<
pT1<
126 GeV rangeand0–10%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
2foreach 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 pT1 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 jetsshowbehaviour 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 distributionof thereconstructed third jet matchesthat observed inthe data. Differencesbetweentheunfoldeddistributionsobtainedwiththis responsematrixandthenominaloneareobservedtobesmalland wellwithinthesystematicuncertaintyassociatedwiththe unfold-ingprocedure.
The
(
1/N
)
dN/
dxJ distributions before andafter unfolding areshownin
Fig. 5
forcentralandperipheralPb+
Pb collisionsandforpp collisionsforjet pairswith100
<
pT1<
126 GeV.Thesystem-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 the0–10%centralityinterval,theeffectistosmearoutthepeaknear
xJ
∼
0.
5.ThelowestxJbinsexhibitinstabilityintheunfoldingpro-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
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 withinR
<
0.
4 andhavingptrkT>
2 GeV,arematchedto thejet andthescalarsumofthetracktransversemomentaisevaluated. The ratio of this sum to the jet’s pT is evaluated both in dataandin 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- andη
-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 anddecreasesharplyasafunctionofpTtoalimitingvalueof0.3%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.
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,accountingfortheircovari-ance.Uncertaintiesinthe normalisationareestimatedby varying theregion of
φ
usedto estimate Y from1.0–1.4 to1.1–1.5.The uncertaintyduetothiscorrectionissmallerthantheother uncer-taintiesinall pTandcentralitybins,andisonlygreaterthan5%atvaluesofxJ
<
0.
4.Thiscorrection wasnot appliedtothe pp datasothereisnocorrespondingsystematicuncertainty.
The breakdownof differentcontributions to the total system-atic uncertainty isshown in the 100
<
pT1<
126 GeV range forthe0–10% centralityinterval andfor pp collisions in
Fig. 6
. Each contribution to the uncertainty, and thus the total uncertainty, tendstodecreasewithincreasingxJ.ThetotaluncertaintyatxJ∼
1reachesapproximately12%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 thelargestcon-tribution. In the Pb
+
Pb data it reaches values of approximately 10% and15% at xJ∼
1 and xJ=
0.
5,respectively. The JEScontri-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 for100
<
pT1<
126 GeV isshowninFig. 7
.Alsoshownarethecorre-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 collisionsare shownin Fig. 8, for jet pairs with 100
<
pT1<
126 GeV fordifferent 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,correspondingtonearly symmetricdijetevents,isreduced.Atlower centrality per-centiles the distribution becomes almost constant overthe range 0
.
6xJ1,anddevelopsapeakatxJ∼
0.
5 inthe0–10%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 onpT1.In pp collisions,thexJ distributionbecomesincreasingly
nar-rowwithincreasingpT1,indicatingthathigher-pTdijetstendtobe
betterbalancedinmomentum (fractionally).Athigher pT1,the xJ
distributionbeginstofallmoresteeplyfromxJ
∼
1,butappearstoflattenatintermediatevaluesofxJ.Themodificationsobservedin
thePb
+
Pb datalessen withincreasing pT1 andforjetpairs withpT1
>
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.
4jets are expected to appear at lower values of pT1 for R
=
0.
3jets.Tofacilitateacomparisonbetweenresultsobtainedwiththe two R values,theR
=
0.
3 jetresultsincludeanadditional pT1in-terval, 79
<
pT1<
100 GeV. The differencesbetween the Pb+
Pbandpp
(
1/N)
dN/
dxJdistributionsarequalitativelysimilartothoseobservedforR
=
0.
4 jets.Fig. 11
showsthe(
1/N)
dN/
dxJdistribu-tionsfor79
<
pT1<
100 GeV fordifferentcollisioncentralitiesbutforjetsreconstructed withR
=
0.
3.Thisindicates thatthetrends present in pT1 and centrality are robust with respect to the UEandthatUEeffectsareproperlyaccountedforbythecombinatoric subtractionandunfoldingproceduresappliedinthedataanalysis. ThedistributionsareflatterforR
=
0.
3 jetsinall pTandcentralitybins,includingin pp collisions.Thisisconsistentwiththe expec-tationthat the(pT1
,
pT2) correlation is weaker forsmaller-R jetsduetotheeffectsofpartonradiationoutsidethenominaljetcone.
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 usingFig. 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 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,thexJdistri-butiondevelops a significant peak atxJ
∼
0.
5 indicating that themostprobableconfigurationfordijetsisforthemtobehighly un-balanced.Thisisinsharpcontrasttothesituationinthe pp data
where the most probablevalues are near xJ
∼
1. Thecentrality-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 isqualita-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;
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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