Azimuthal anisotropy of charged jet production in sNN=2.76 TeV Pb-Pb collisions

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Physics

Letters

B

www.elsevier.com/locate/physletb

Azimuthal

anisotropy

of

charged

jet

production

in

√

s

_NN

=

2

.

76 TeV

Pb–Pb

collisions

.ALICE

Collaboration



a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received 5 October 2015

Received in revised form 30 November 2015 Accepted 16 December 2015

Available online 18 December 2015 Editor: M. Doser

Wepresentmeasurementsoftheazimuthaldependenceofchargedjetproductionincentraland semi-central √sNN=2.76 TeV Pb–Pbcollisions withrespecttothesecondharmonic eventplane,quantified

as vch jet₂ .Jetfindingisperformedemployingtheanti-kTalgorithmwitharesolutionparameterR=0.2

usingcharged tracksfromtheALICE tracking system.The contributionoftheazimuthalanisotropy of the underlyingeventis takenintoaccountevent-by-event. Theremaining(statistical) region-to-region fluctuations are removedonanensemblebasis byunfoldingthe jetspectra fordifferentevent plane orientations independently. Significant non-zero vch jet₂ is observed insemi-central collisions (30–50% centrality)for20<pch jet_T <90 GeV/c.Theazimuthaldependenceofthechargedjetproductionissimilar tothedependenceobservedforjetscomprisingbothchargedandneutralfragments,andcompatiblewith measurementsofthev2ofsinglechargedparticlesathigh pT.Goodagreementbetweenthedataand

predictions fromJEWEL,an event generatorsimulatingparton shower evolutioninthe presence ofa denseQCDmedium,isfoundinsemi-centralcollisions.

©2015CERNforthebenefitoftheALICECollaboration.PublishedbyElsevierB.V.Thisisanopen accessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.

1. Introduction

The aim of the heavy-ion program at the LHC is to study strongly interacting matter in ultra-relativistic nuclear collisions where the formation of a quark–gluon plasma (QGP), a decon-fined state of quarks and gluons, is expected [1]. Hard partons thatpropagatethroughthecollisionmediumloseenergyvia (mul-tiple) scattering and gluon radiation [2,3]. Jet measurements are usedtoexperimentally explorepartonenergylossinthehot and densemedium. StudiesattheLHCandRHIChaveshownthat jet andhigh-pT single particle productioninheavy-ioncollisions are

suppressed with respect to the expected production in a super-position of independent pp collisions [4–13]. This observation is consistent withenergy loss,which is further supported by mea-surementsofdijetenergy asymmetry anddi-hadronangular cor-relations[14–16].

Innon-centralPb–Pbcollisions,theinitialoverlapregionofthe collidingnucleiprojectedintotheplaneperpendiculartothebeam directionhas an approximately elliptic shape. Jetsemitted along theminoraxisoftheellipse(definedasthein-plane direction)on averagetraverselessmedium–andarethereforeexpectedtolose lessenergy–thanjetsthatareemittedalongthemajoraxisofthe

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

ellipse(theout-of-plane direction).Thedependenceofjet produc-tionontheanglerelativetothesecond-harmonicsymmetryplane



2 (thesymmetry planeangles



n define theorientationsofthe

symmetry axesoftheinitialnucleon distributionofthecollision) can be used to probe the path-length dependence of jet energy loss. This dependence is quantified by the parameter vch jet₂ , the coefficient of the second term ina Fourierexpansion ofthe az-imuthaldistributionofjetsrelativetosymmetryplanes



n,

dN d



ϕ

jet

− 

n

 ∝

1

+

∞



n=1 2vnjetcos



n



ϕ

jet

− 

n



,

(1)

where

ϕjet

denotestheazimuthalangleofthejet.

Incentralcollisions, theaveragedistancethata jetpropagates through the medium isapproximately equal in the in-plane and out-of-plane directions, therefore a small vch jet₂ is expected. In semi-central collisionsthe averagein-mediumdistanceis shorter, while the relative difference between the average distances in-plane and out-of-plane is larger, hence a non-zero vch jet₂ is ex-pected. Fluctuationsin the initial distributionof nucleons within the overlap region can lead to additionalcontributions to vch jet₂

andhigherharmoniccoefficientsintheFourierdecomposition. The path-length dependence of parton energy loss is of par-ticular interest because it is sensitive to the underlying energy-loss mechanism. For collisional (elastic) energyloss, the amount

http://dx.doi.org/10.1016/j.physletb.2015.12.047

0370-2693/©2015 CERN for the benefit of the ALICE Collaboration. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3_.

of lost energy depends linearly on path length, while for radia-tive (inelastic) energy loss, the dependence is quadratic due to interferenceeffects[17,18].Some strong-interactionmodelsbased on the AdS/CFT correspondence suggest an even stronger path-length dependence [19,20]. Earlier studies of the v2 of high-pT

single particles have already tested the path-length dependence of energy loss [21–25]. Comparisons of these results to theoret-ical calculations have shown that the v2 is sensitive to several

aspects of the medium evolution, including the effects of longi-tudinal andtransverseexpansion andthelife time ofthe system until freeze-out[26].It is thereforeimportant to measure multi-ple observablesthat are sensitive to the path-length dependence ofenergy loss,such asrecoil yields ofcharged particlesand jets [11,27,28].Jetsareexpectedtobetterrepresenttheoriginalparton kinematicsandprovidemoredetailedinformationonenergyloss. TheoreticalpredictionsfromJEWEL,whichcouplespartonshower evolutiontothepresenceofaQCDmediumwithadensityderived from Glauber simulations [29,30], have shown that a finite vjet₂

is expected for non-central collisions at the LHC. Similar results havebeen foundin vjet₂ studies inheavy-ioncollisions generated by the AMPT model [31,32]. A first measurement of vcalo jet₂ of jetscomprisingboth chargedandneutralfragmentshasbeen re-portedby the ATLAS Collaboration [33].The results presented in this paper extend the vch jet₂ measurement to a lower pT range

(pT

>

30 GeV

/

c forcentralcollisions andpT

>

20 GeV

/

c for

semi-centralcollisions).

Inthisarticle,measurements of vch jet₂ of R

=

0

.

2 chargedjets reconstructedwiththeanti-kT jetfinderalgorithminPb–Pb

colli-sionswith0–5%and30–50%collisioncentralityarepresented.The largest experimental challenge in jet analyses in heavy-ion colli-sions is the separation of the jet signal fromthe background of mostlylow-pT particlesfromtheunderlyingeventandfrom

unre-latedscatteringsthat takeplaceinthecollision.Thejet energyis correctedonajet-by-jetbasisusinganestimateofthebackground transversemomentumdensitywhichtakesintoaccountthe domi-nantflowharmonicsv2andv3 ofthebackgroundevent-by-event,

aswillbedescribed inSections2.1and2.2.Thecoefficient vch jet₂

isobtainedfrompT-differentialjetyieldsmeasuredwithrespectto

theexperimentally accessibleeventplane



EP,2,whichis

recon-structedatforwardrapidities(2

.

8

<

η

<

5

.

1 and

−

3

.

7

<

η

<

−

1

.

7, Sec. 2.1). The reported vch jet₂ hasbeen correctedback to the az-imuthalanisotropywithrespecttotheunderlyingsymmetryplane



2 by applying an event plane resolution correction (Sec. 2.4).

Jetsare reconstructedat mid-rapidity(

|

η

jet

|

<

0

.

7) using charged

constituenttrackswithmomenta0

.

15

<

pT

<

100 GeV

/

c,andare

required to contain a charged hadron with pT

≥

3 GeV

/

c. The

in-plane andout-of-plane jet spectraare unfolded independently to take into account detectoreffects and remaining azimuthally-dependent fluctuations in the underlying event transverse mo-mentum density (Sec.2.3). The jet spectra are corrected back to particle-leveljetsconsistingofonlyprimarychargedparticlesfrom thecollision.

2. Experimentalsetupanddataanalysis

ALICEisadedicatedheavy-ionexperimentattheLHCatCERN. A full overview of the detector layout and performance can be foundin [34,35].Thecentral barreldetectorsystem, coveringfull azimuth,ispositionedinasolenoidalmagnetwithafieldstrength of0.5 T.ItcomprisestheInnerTrackingSystem(ITS)builtfromsix layersofsilicondetectors(the SiliconPixel,Drift,andStrip Detec-tors:SPD,SDDandSSD)andaTimeProjectionChamber(TPC).The twoinnerlayersoftheITS,whichcomprisetheSPD,arelocatedat 3.9and7.2 cmradialdistancefromthebeamaxis.

The data presented in this paper were recorded in the Pb– Pb data taking periods in 2010 and 2011 at

√

sNN

=

2

.

76 TeV,

using aminimum-biastrigger (2010)oran onlinecentrality trig-ger for hadronic interactions (2011), which requires a minimum multiplicity in both the V0A and V0C detectors (discs of seg-mented scintillators coveringfull azimuth and2

.

8

<

η

<

5

.

1 and

−

3

.

7

<

η

<

−

1

.

7,respectively). The V0detectors areused to de-termine event centrality based on the energy deposition in the scintillator tiles[36]andtheeventplane orientation,seeSec.2.1. Centrality, determined fromthe sumoftheV0amplitudes,is ex-pressed as percentiles of the total hadronic cross section, with 0–5% referring to the most central (largest multiplicity) events [36].Thetriggerisfullyefficientinazimuthinthepresented cen-tralityranges.CentralityestimationusingtheV0systemdoesnot biasthe



EP,n determination[37].TimeinformationfromtheV0

detectors is used to reject beam-gas interactions fromthe event sampleandtheremainingcontributionofsuchinteractionsis neg-ligible.Onlyeventswithaprimaryvertexpositionwithin

±

10 cm alongthebeamdirectionfromthenominalinteractionpointwere usedintheanalysis.Atotalof6

.

8

×

106 _{eventswith0–5%}

central-ityand8

.

6

×

106 _{eventswith30–50%centrality,correspondingto}

integratedluminosities of18and5.6 μb−1,respectively,are used inthisanalysis.

ChargedparticletracksinthisanalysisaremeasuredbytheITS andTPCandareselectedinapseudorapidityrange

|

η

|

<

0

.

9 with transversemomenta0

.

15

<

pT

<

100 GeV

/

c.Toensureagood

mo-mentumresolution,trackswererequiredtohaveatleastthreehits per track inthe ITS. Since theSPD acceptanceis non-uniformin azimuthfor thedatasample used inthisanalysis, two classesof tracksareused.Thefirstclassrequiresatleastthreehitspertrack inthe ITS,withatleastonehit pertrackintheSPD. Thesecond class contains tracks without hits in the SPD, in which case the primary interaction vertexis used asan additionalconstraintfor themomentum determination.Foreachtrack, theexpected num-berofTPCspacepointsiscalculatedbasedonitstrajectory;tracks are acceptediftheyhaveatleast80%oftheexpectedTPC space-points, witha minimum of70 TPCpoints. Tracksproduced from interactions between particlesand thedetector,as well astracks originatingfromweakdecays(‘secondarytracks’)arerejected.The contribution ofsecondary tracks to thetrack sample isless than 10% fortracks with pT

<

1 GeV

/

c andnegligible fortracks with

highertransversemomentum.

2.1. Eventplanedetermination

The coefficient vch jet₂ quantifies azimuthalanisotropy with re-spect to



2. The azimuthal anisotropy of the underlying event

(‘backgroundflow’) isalsodescribed byaFourierserieswith har-monics vn

= 

cos

(

n

[

ϕ

− 

n

])

[38,39] where

ϕ

denotes thetrack

azimuthalangle.However,sincetheinitialdistributionofnucleons is not accessible experimentally,the eventplaneangles



EP,n,i.e.

the axes ofsymmetry of thedensity ofoutgoing particlesin the transverse plane,are usedinplace of



n when measuring vch jet2

and vn.

The event plane angles



EP,2 and



EP,3 in this study,

cor-responding to the two dominant Fourier harmonics, are recon-structed using the V0 detectors. Each V0 array consists of four ringsintheradial direction,witheach ringcomprisingeightcells withthesameazimuthalsize.Thecalibratedamplitudeofthe sig-nal in each cell, proportional to the multiplicity incident on the cell,isusedasaweight wcell intheconstructionoftheflow

vec-tors Qn [40]

Qn

=



cells

Inordertoaccountforanon-uniformdetectorresponsewhichcan generatea bias in the



EP,n azimuthal distribution, the

compo-nents ofthe Qn-vectorsare adjusted using a re-centering

proce-dure[41,42].TheV0AandV0Cdetectorscoverdifferent

η

regions inwhich multiplicity N andbackground flow vn maydiffer. The

totalV0 Q -vector istherefore constructedusingweights

χ

n [40]

thatare approximatelyproportionaltothe eventplane resolution ineachdetector,

Qn,V0

=

χ

n2,V0AQn,V0A

+

χ

n2,V0CQn,V0C

,

(3)

toachievetheoptimalcombinedeventplaneresolution.Theevent planesare reconstructedfromtherealandimaginarypartsof Qn

as



EP,n

=

arctan





[Qn]

[Qn]



/

n

.

(4)

The vch jet₂ itself is measured with respect tothe second har-monic event plane angle. It is corrected for the finite precision withwhichthetruesymmetryplaneismeasuredintheV0system byapplyinganeventplaneresolutioncorrection,seeSec.2.4.

2.2.Jetreconstructioninthepresenceofbackgroundflow

Jetfinding isperformedusingthe FastJet[43,44] implementa-tion of the infrared and collinear safe kT and anti-kT sequential

recombinationalgorithmsusingthepTrecombinationschemeand

takingmasslessjetconstituents.TheresolutionparameterR

=

0

.

2 determines the characteristic maximum distance of constituent trackstothejetaxisinthe

η

–

ϕ

plane.

In heavy-ion collisions, a large combinatorial background is presentfromparticles that arenot relatedto the hard scattering thatproducedagivenjet.Thisbackgroundissubtractedfromeach jet on an event-by-event basis. The anti-kT algorithm is used to

findsignaljets. Afiducialcut of

|

η

jet

|

<

0

.

7 is appliedon the

sig-naljets toensure that all jets are fullycontainedwithin theITS andTPCacceptances andedge effects are avoided.The contribu-tion of combinatorial (or ‘fake’) jets (clustered underlying event energy) to the measured jet spectrum is reduced by requiring thatreconstructed jetscontain atleastone chargedparticlewith

pT

>

3 GeV

/

c andhaveanarea ofatleast0.56

π

R2.These

selec-tioncriterialeavethehardpartofthejetspectrumunalteredwhile significantlyreducing thenumberofcombinatorialjetswhich sta-bilizestheunfoldingprocedure[4,5,45].

The kT-algorithm is used to estimate the average transverse

momentumdensityoftheunderlyingevent,



ρ

ch



,onan

event-by-eventbasis.Thequantity



ρ

ch



isthemedianofthedistributionof

praw_T,chjet

/

A (theratiooftransversemomentumtojetarea)of recon-structed R

=

0

.

2 kT-jets, excluding the leading two jetsfromthe

sampleasproposed in[46] andimplemented inearlierALICEjet studies[4,5,45].The kT jetsarerequired tolie within

|

η

jet

|

<

0

.

7

andhave anarea A

>

0

.

01.Thejet area A is determinedby em-bedding a fixed number of near zero-momentum ghostparticles

per event prior to jet finding; the number of ghost particles in eachreconstructedjetthengivesadirectmeasureofthejetarea. A ghostdensityof200particles perunitarea isused,sothat ap-proximately25ghostparticlesareclusteredintoajetwitharadius of 0.2.

Ineach event, theanisotropy ofthe underlyingeventis mod-eledusingthedominant[47]flowharmonicsv2andv3,

ρ

ch

(

ϕ

)

=

ρ

0



1

+

2

{

v2cos



2



ϕ

− EP

,2



+

v3cos



3



ϕ

− EP

,3



}



.

(5)

Fig. 1. Transverse

momentum density of charged tracks as a function of azimuthal

angle for a single event from the most central 0–5% event class. Data points (blue) are given with statistical uncertainties only. The red curve is the fit of Eq.(5)to the distribution, the green and gray curves, obtained from the fit of Eq.(5)as well, show the independent contributions of v2and v3to ρch(ϕ). The dashed magenta line is the normalization constant ρ0. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Here,

ρch

(

ϕ

)

istheazimuthaldistributionofsummedtrackpT for

tracks with 0

.

15

<

pT

<

5 GeV

/

c and

|

η

track

|

<

0

.

9. The

parame-ters

ρ0

and vn are determined event-by-event from a fit of the

right side of Eq. (5) to the data. The event plane angles



EP,n

are not fitted, but fixed to the V0 event plane angles. A single eventexampleofthisprocedureisillustrated inFig. 1,wherethe datapoints representthetransversemomentum density distribu-tioninasingle event,theredcurve representsthefull functional descriptionof

ρch

(

ϕ

)

(Eq.(5)),thegreenandgraycurvesgive the contributionsoftheseparateharmonicsv2andv3,andthedashed

magentalineisthenormalizationconstant

ρ0

.Toreduce thebias ofhard jets inthe estimatesof vn in Eq.(5) whileretaining

az-imuthal uniformity, the leading jet in each eventis removed by rejecting all tracksfor which

|

η

jet

−

η

track

|

<

R.The

η

separation

betweenthetracksandtheV0detectorsalsoremovesshortrange correlationsbetweentheeventplanesandtracks.

ThenumberofbinstowhichEq.(5)isfittedissetonan event-by-eventbasistothesquare rootofthenumberoftracks.Thefit maximizestheestimatedlikelihood[48],whichisbasedona Pois-son distribution for the bin content. Since the bin contents are not pure counts, butweighted by pT,the statisticaluncertainties

on each bin

σ

i are estimated as the sum of the squares of the

pT of the individual particles:

σ

i

=

σ

(

pT

)

= √

p2_T. A scaled

Poisson distribution P

(

xi

/

wi

|

mui

/

wi

)

is used as the probability

distributionforthedatapoints inthelikelihood calculation,with a scale factor wi

=

σ

_i2

/

yi where yi is the bin content and

μ

i

is theexpected signal fromthe fit function.The compatibility of each fit withthe data is tested by calculating the

χ

2 _and

eval-uating the probability of finding a test statistic at leastas large asthe observed one inthe

χ

2 _{distribution. When this}

probabil-ityis less than0.01, the average eventbackground density



ρ

ch



is usedinstead of

ρch

(

ϕ

)

; thisoccursin 3% (mostcentral) to7% (semi-central) ofevents.Theacceptance criterionis variedin the systematicstudies;thesensitivitytoitissmall.

Thecorrectedtransversemomentum pchjet_T ofajetofarea A is

calculatedfromthemeasuredrawjetmomentum,praw_T,chjet,as

pchjet_T

=

praw_T,chjet

−

ρ

ch localA (6)

where

ρch local

is obtained from integration of

ρch

(

ϕ

)

around

Fig. 2. TheδpTdistribution (Eq. (8)) from the random cone (RC) procedure as function of cone azimuthal angle ϕRCrelative to the event plane. In panel (a) the azimuthally-averaged background ρchhas been subtracted; in panel (b) the azimuthally dependent ρch(ϕ)from an event-by-event fit of the pT-density with Eq. (5). The solid black line represents the mean of the δpTdistribution.

ρ

ch local

=



ρ

ch 2R

ρ

0 ϕ

+R ϕ−R

ρ

ch

(

ϕ

)

dϕ

.

(7)

Thepre-factoroftheintegral, ρch

2Rρ0,ischosensuchthatintegration

over the full azimuth yields the average transverse momentum density



ρ

ch



.ThevalidityofEq.(5)asadescriptionofthe

contri-butionofbackgroundflowtotheunderlyingeventenergyistested byplacingconesofradius R

=

0

.

2 atrandompositions(excluding thelocation ofthe leading jet)inthe

η

–

φ

plane andsubtracting theexpected summed transversemomentum in acone fromthe measuredtransversemomentuminthecone,

δ

pT

=



ptracks_T

−

ρπ

R2

.

(8)

Here,

ρ

is theexpected transversemomentum density.This pro-cedure is repeatedmultiple timesper event, until the full phase spaceis covered, to obtain a distribution of

δ

pT values.The

δ

pT

distributionasafunctionoftheconeazimuthalangle

ϕRC

relative totheeventplane



EP,2 isshowninFig. 2.Inpanel(a)



ρ

ch



has

beenusedfortheestimationoftheunderlyingeventsummed pT

andinpanel(b)

ρch

(

ϕ

)

.Incorporatingazimuthal dependenceinto theunderlyingeventdescriptionleadstoasizablereductioninthe cosinemodulationofthe

δ

pTdistribution.

Theeffectivenessofthesubtractionofbackgroundflowis quan-tified by comparing the expected and measured widths of the

δ

pTdistributionintheabsence ofbackgroundflow,

σ

(δ

pTvn=0

)

(see

Fig. 2(b)) to the expected and measured widths of the

δ

pT

dis-tribution in thepresence of backgroundflow,

σ

(δ

pvn

T

)

(Fig. 2(a)).

Assumingindependentparticleemission andPoissonianstatistics, theexpectedwidthofthe

δ

pTdistributionintheabsenceof

back-groundflow(vn

=

0)isgivenby[45]

σ

(δ

pvn=0

T

)

=



NA

σ

2

(

pT

)

+

NA



pT2 (9)

whereNAistheaverageexpectednumberoftrackswithinacone,



pT



is the mean pT of a single particle spectrum and

σ

(

pT

)

is

the standard deviationof thisspectrum. This expectationcan be extendedtoincludecontributionsfrombackgroundflowby intro-ducing non-Poissonian density fluctuations (the background flow harmonics vn)[45],as

σ

(δ

pvn T

)

=



NA

σ

2

(

pT

)

+ (

NA

+

2N2_A

(

v2₂

+

v2₃

))



pT2

.

(10)

Fig. 3. Centrality

dependence of the measured and expected relative change in the

δpTdistribution width from using the azimuthally dependent ρch localinstead of the median ρch. The blue points give the expected reduction from simple assumptions about the behavior of charged particle spectra and flow harmonics vn (following Eqs.(9)and (10)). The red points use the measured widths from δpTdistributions directly. Statistical uncertainties are smaller than the marker size. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

The measured widths areobtained fromthe

δ

pT distributions

directly; thedistributions are constructedusingasthe transverse momentumdensity

ρ

inEq.(8)either



ρ

ch



toobtain

σ

(δ

pvTn

)

or

ρ

ch local for

σ

(δ

pvTn=0

)

.

Fig. 3 shows the expected and measured relative change in

the width of the

δ

pT distribution, quantified as

(

σ

(δ

p_Tvn

)

−

σ

(δ

pvn=0

T

))/

σ

(δ

p vn

T

)

, as function of collision centrality. The blue

points give the expected reduction from Eqs. (9) and (10). The red points use the measured widths from

δ

pT distributions. The

expectedchangeisingoodquantitativeagreementwiththe mea-sured changeover theentire centralityrange,indicating that the width of the

δ

pT distributions can be understood in terms of a

simpleindependentparticleemissionmodelwithbackgroundflow contributions.

The background subtraction, unfolding,and correction for the reactionplaneresolutionasdescribedinSections2.3and2.4were also validated using events consisting of PYTHIA jets embedded inheavy-ionbackgroundeventsandtoymodelevents.Inthefirst

study, full PYTHIA pp events were combined with reconstructed Pb–Pbcollisionstocreateeventswithacontrolledsignaland back-ground.ThesignaljetsfromPYTHIAhavenopreferredorientation,

vch jet₂

=

0,whiletheheavy-ioneventshavea non-zero v2 ofthe

softparticles. Jetsfound inthe events were matchedto the em-beddedPYTHIAjetsandtheanalysiswascarriedoutwithmatched jetsonly.Afterunfolding,thevch jet₂ wascompatiblewith0,as ex-pected. The other study was based on events generated using a simplethermalmodelforsoftparticleproductionanda distribu-tionofhigh-pT particlesthat resemblesthejetspectrum,as

sug-gestedin[49].Anon-zerov2

=

0

.

07 wasintroducedformomenta

pT

<

5 GeV

/

c tomodelthebackgroundflowandtwovariationsat

largepT

>

30 GeV

/

c: v2

=

0 or v2

=

0

.

05.Inbothcases,theinput

flowvalueswerecorrectlyreconstructedbytheanalysis.

2.3.Unfolding

Afterthesubtractionprocedurepresentedintheprevious sec-tion,themeasured jetspectrumisunfolded[50,51] tocorrectfor detectoreffectsandfluctuationsintheunderlyingeventtransverse momentumdensity.Mathematically,theunfoldedjetspectrumcan bederivedfromthemeasuredspectrumbysolving

M

(

prec_T,chjet

)

=

G

(

prec_T,chjet

,

pgen_T,chjet

)

T

(

p_Tgen_,chjet

)

ε

(

pgen_T,chjet

)

dpgen_T,chjet (11)

forT

(

pgen_T,chjet

)

,theunfoldedtruejetspectrum,whereM

(

prec_T,chjet

)

is themeasured jet spectrum, G

(

prec_T,chjet

,

pgen_T,chjet

)

is afunctional de-scription(responsefunction)ofdistortions duetobackground fluc-tuations and detector response, and

ε

(

pgen_T,chjet

)

is the jet finding efficiency.The coefficient vch jet₂ is not affected by the efficiency, hence

ε

(

pgen_T,chjet

)

willbeomittedfromhereon.Sincethemeasured jetspectrumisbinned, Eq.(11)isdiscretizedby replacingthe in-tegralbyamatrixmultiplication

Mm

=

Gm,t

·

Tt (12)

where T_t is the solution of the discretized equation (the prime indicates that T_t is not corrected for jet-finding efficiency). The combined response matrix Gm,t is the product of the response

matricesfromdetectoreffects andtransversemomentumdensity fluctuations,thelatterofwhichareconstructedindependentlyfor thein-planeandout-of-planespectrabyembeddingrandomcones atspecificrelativeazimuthwithrespecttotheeventplane(seethe textbelowEq.(13)forthedefinitionoftheintervals).

Thedetectorresponse matrix isobtainedby matching pp jets generatedbyPYTHIA[52](‘particle-level’jets)tothesame jets af-tertransportthroughthedetector(‘detector-level’jets)byGEANT3 [53], where the detector conditions are tuned to those of the Pb–Pbdata-takingperiods.Particle-leveljetscontainonlyprimary chargedparticlesproducedbytheeventgenerator,whichcomprise allprompt chargedparticles producedin thecollision,aswell as productsof strongandelectromagneticdecays,while productsof weakdecaysofstrangehadronsarerejected.Matchingisbasedon theshortestdistanceinthe

η

–

ϕ

planebetweendetectorleveland particleleveljetsandisbijective,meaningthat thereisa one-to-onecorrespondence betweendetectorandparticlelevel jets. The response matrix for background fluctuations is constructed from the

δ

pTdistributions,which,whennormalized,areprobability

dis-tributionsforthechange ofthejet energycausedbybackground fluctuations.

SolvingEq.(12)requiresinversion ofGm,t andgenerallyleads

to non-physical results which oscillate wildly due to the

statis-tical fluctuations of the measured jet yield. The unfolded solu-tion therefore needs to be regularized. In general this is done by introducing a penalty term for large local curvatures associ-atedwithoscillations.Variousalgorithmsforregularizedunfolding exist;the unfoldingmethodbased onthe SingularValue Decom-position(SVD unfolding)[54] isused inthisstudy.Acomparison totheunfoldedsolutionfrom

χ

2_{minimization[55]isusedinthe}

systematicstudies.

The measured jet spectrum is taken as input forthe unfold-ingroutineintherange30

<

pchjet_T

<

105 GeV

/

c for0–5%collision centralityand15

<

pchjet_T

<

90 GeV

/

c for30–50%collision central-ity. The lower bound corresponds to five times thewidth of the

δ

pT distribution,theupperboundistheedgeofthelastmeasured

binwhichcontainsatleast10counts.Thisconfigurationwasfound toleadtoreliableunfoldedsolutionsinMonte Carlostudies[4,49]. The unfolded jet spectrum starts at0 GeV

/

c toallow forfeed-in oftrue jetswithlow pchjet_T . Inaddition,combinatorial jetswhich are not rejected by the jet area and leading charged particle re-quirements are migrated to momenta lower than the minimum measured pchjet_T . The unfolded solution ranges up to 200 GeV

/

c

(0–5%) and170 GeV

/

c (30–50%) to allowformigration ofjetsto a pchjet_T higher than themaximum measured momentum. As the data points of the unfolded solution are strongly correlated for

pchjet_T outsidetheexperimentallymeasuredinterval, vch jet₂ willbe reportedonlywithinthelimitsofthemeasuredjetspectra.

2.4. Evaluationofvch jet₂

Thecoefficientvch jet₂ iscalculatedfromthedifferencebetween the unfolded pT-differential jet yields in-plane (Nin) and

out-of-plane (Nout) with respect to the second harmonic event plane,

correctedforeventplaneresolution,

vch jet₂

(

pchjet_T

)

=

π

4 1

R

2 Nin

(

pchjetT

)

−

Nout

(

p chjet T

)

Nin

(

pchjetT

)

+

Nout

(

p chjet T

)

.

(13)

Eq. (13) is derived by integrating Eq. (1) for n

=

2, over inter-vals



−

π₄

,

π₄



and



3₄π

,

5₄π

for Nin and



π 4

,

3π 4

and



5₄π

,

7₄π

for Nout,substituting



EP,2 for



2.Eq.(13)is sensitiveto

corre-lationsbetweeneven-orderharmonicsv2n and



EP,2.Asaresult

oftheintegrationlimitshowever,thefirstharmonicoftheFourier expansionthatcancontributetotheobservedvch jet₂ isvch jet₆ .The V0eventplane resolution

R

2 isintroducedto accountforthe

fi-niteprecisionwithwhichthetruesymmetryplane



2ismeasured

intheV0systemandisdefinedas

R

2

=



cos



2





_EPV0_,2

− 2

 

.

(14)

Measuring eventplanes inmultiple

η

regions (sub-events) allows fortheevaluationoftheresolutiondirectlyfromdata[56,57]. Us-ing the fullV0 detectorandnegative andpositive

η

sidesof the TPCassub-events,theresolutioninEq.(13)isevaluatedas

R

2

=

⎛

⎝



cos



2





_EPV0_,2

− 

_EPTPC_,,₂η>0

  

cos



2





_EPV0_,2

− 

_EPTPC_,,₂η<0

 



cos



2





_EPTPC_,,₂η>0

− 

_EPTPC_,,₂η<0

 

⎞

⎠

1/2

.

(15)

The eventplane resolution

R

2 is found tobe 0.47 in0–5%

cen-tralityand0.75in30–50%centralitywithnegligibleuncertainties. The



EP,2 anglesintheTPCareobtainedfollowingtheprocedure

of Eq. (4) on tracks with 0

.

15

<

pT

<

4 GeV

/

c, using unit track

weightsintheconstructionoftheflowvectorsQ2 (seeEq.(2)).

UsingtheV0detectorsforthereconstructionoftheeventplane guaranteesthatthejetaxisandeventplaneinformationare sepa-ratedinpseudorapidityby

|

η

|

>

1 andthus removes autocorre-lationbiasesbetweenthesignal jetsandeventplane orientation. The possiblenon-flow correlation betweenthe eventplane angle andjetsduetodi-jetswithonejetatmid-rapidityandonejetin theV0acceptancewas studiedusingthePYTHIAeventgenerator. The rateof such di-jetconfigurations was found to be negligible (lessthan 1 per milleof thetotal di-jetrateat mid-rapidity) for

pchjet_T

>

20 GeV.Possibleeffectsfromback-to-backjetpairswitha jetineachoftheV0detectorsareevensmaller.

2.5. Systematicuncertainties

Themeasuredvch jet₂ iscorrectedforexperimentaleffects,such asthefiniteeventplaneresolutionanddetectoreffectsonthejet energyscaleaswellastheeffectsoftheuncorrelatedbackground and its fluctuations using the corrections outlined in the Sec-tions2.1–2.4.Hydrodynamicflow ofthe backgroundistakeninto accountevent-by-eventintheunderlyingeventdescription, resid-ualeffects areremoved by azimuthally dependent unfolding.The remaininguncertaintiesinthesecorrectionproceduresaretreated assystematicuncertainties.Systematicuncertaintieson vch jet₂ are groupedinto twocategories, shape and correlated,basedon their point-to-point correlation. Shape uncertainties are anti-correlated betweenpartsoftheunfoldedspectrum:whentheyieldinpartof thespectrumincreases,itdecreaseselsewhereandviceversa. Cor-related uncertainties are correlated point-to-point. Both types of uncertaintieshoweverhavecontributionswhichleadtocorrelated changesofNin andNout.

Correlateduncertaintiesareestimatedforthein-planeand out-of-planejet spectraindependently. Twosourcesofcorrelated un-certainties are considered: tracking efficiency and the inclusion of combinatorial jets in the measured jet spectrum. The domi-nant correlated uncertainty (



10%) arises from tracking and is estimatedbyconstructingadetectorresponsematrixwitha track-ingefficiencyreducedby 4%(motivatedby studies[4]comparing reconstructed tracks to simulations of HIJING [58] events). The observed difference betweenthe nominaland modified unfolded solutionistakenasasymmetricuncertaintytoallowforan over-andunderestimation of the tracking efficiency. The sensitivityof theunfoldedresulttocombinatorialjetsistestedbychangingthe lower range of the unfolded solution from 0 to 5 GeV

/

c, which leads toan overall(correlated) increase oftheunfolded jetyield. Both correlated uncertainties are added in quadrature and prop-agatedto vch jet₂ assuming that variations are strongly correlated betweenthe in-plane andout-of-plane jet spectra, whilestill al-lowingforeffects fromazimuthally-dependentvariations in track occupancyandreconstructionefficiency,bysettingthesample cor-relationcoefficient

ρ

≡

σ

i,j

/(

σ

i

σ

j

)

to0.75.

Shape uncertainties fall into three categories: assumptions in the unfolding procedure, feed-in of combinatorial jets, and the sensitivityof the unfolded solution to the shape of the underly-ing event energy distribution. The dominant contribution to the unfolding uncertainty is related to the regularization of the un-foldedsolution.The SVDalgorithm[54] regularizestheunfolding byomittingcomponentsofthemeasured spectrumforwhichthe singular value is smallandwhich amplify statisticalnoise inthe result.Toexplorethesensitivityoftheresulttotheregularization strength, theeffective rankof thematrix equation that is solved isvariedbychanginganintegerregularizationparameterk by

±

1. The SVDunfolding algorithm uses aprior spectrumas the start-ingpointoftheunfolding;theresultoftheunfoldingistheratio

between the full spectrum and thisprior. The unfolded solution fromthe

χ

2 _{algorithm[55] isusedasprior (default)aswellasa}

PYTHIAspectrum.Thebiasfromthechoiceofunfoldingalgorithm itselfistestedbycomparingtheresultsoftheSVDunfoldingand the

χ

2 _algorithm.

Thesamenominalunfoldingapproachisusedforthein-plane and out-of-plane jet spectra and the

δ

pT distributions for the

in-plane andout-of-plane background fluctuations are similar in width; the unfolding uncertainty is therefore strongly correlated between the in-plane and out-of-plane jet spectra. These corre-lations are taken into account by applying the variations in the unfolding procedure to the in-plane andout-of-plane jet spectra atthesametimeandcalculatingtheresultingvariationsofvch jet₂ . Thetotaluncertaintyfromunfoldingisdeterminedbyconstructing a distributionofall unfoldedsolutions ineach pchjet_T intervaland assigningthewidthofthisdistributionasasystematicuncertainty. The other two components of the shape uncertainty are the sensitivityof theunfolded solutionto combinatorialjetsand un-certainties arising from the description of the underlying event; both are estimated on the in-plane andout-of-plane jet spectra independentlyandpropagatedtovch jet₂ asuncorrelated.A system-atic uncertainty is only assigned when the observed variation is found to bestatisticallyincompatible withthe nominal measure-ment.Theeffectofcombinatorialjetsistestedbyvaryingthe min-imumpchjet_T ofthemeasuredjetspectrumby

±

5 GeV

/

c,effectively increasingordecreasingthepossiblecontributionofcombinatorial jet yield atlow jetmomentum. Totest theassumptions madein the fittingofEq.(5) themaximum pT ofaccepted tracksis

low-eredto 4 GeV

/

c. Additionally, theminimum p-valuethat is used as a goodness offit criterion is changed from0.01 (the nominal value)to 0.1.Theminimumrequireddistanceoftrackstothe lead-ingjetaxisinpseudorapidityisenlargedto 0.3.

Table 1 gives an overview of the systematic uncertainties in terms of absolute uncertainties on vch jet₂ for all sources (where thetotaluncertaintyisthequadraticsumoftheseparate compo-nents).HighstatisticsMonte Carlotestinghasbeenusedtoverify thatuncertainties labeled‘



stat’areindeednegligiblecompared tootheruncertainties.

3. Resultsanddiscussion

The coefficients vch jet₂ as function of pchjet_T for 0–5% and 30–50%collisioncentralityarepresentedinFig. 4.Significant pos-itive vch jet₂ is observed insemi-central collisions andno (signifi-cant) pTdependenceisvisible.Theobservedbehaviorisindicative

ofpath-length-dependent in-medium partonenergy loss.The ob-served vch jet₂ in central collisions is of similar magnitude. The systematic uncertainties on themeasurement however are larger than thoseonthe semi-central vch jet₂ data,inparticular atlower

pchjet_T ,asaresultofthelargerrelativebackgroundcontributionto themeasuredjetenergy.

The significance of the results is assessed by calculating a

p-valueforthehypothesisthat vch jet₂

=

0 overthepresented mo-mentum range.The p-valueisevaluated startingfromamodified

χ

2 _{calculationthat takesintoaccount bothstatisticaland}

(corre-lated)systematicuncertainties,assuggestedin[59].Themodified

χ

2 _{forthehypothesisv}ch jet

2

=

μ

i iscalculatedbyminimizing

˜

χ

2

(

ε

corr

,

ε

shape

)

=



_n



i=1

(

v2,i

+

ε

corr

σ

corr,i

+

ε

shape

−

μ

i

)

2

σ

2 i



+

ε

_corr2

+

1 n n



i=1

ε

2 shape

σ

2 shape,i



(16)

Table 1

Systematic uncertainties on vch jet2 for various transverse momenta and centralities. Uncertainties in central and semi-central collisions are given in the same pTranges. The definitions of shape uncertainty and correlated uncertainty are explained in Sec.2.5. Fields with the value ‘stat’ indicate that no systematic effect can be resolved within the statistical limits of the analysis.

pchjetT (GeV/c) Uncertainty on v

ch jet 2

30–40 60–70 80–90 30–40 60–70 80–90

Centrality (%) 0–5 30–50

Shape Unfolding 0.017 0.012 0.016 0.016 0.011 0.015

pchjet_T -measured 0.013 stat stat 0.024 stat stat

ρch(ϕ)fit 0.015 stat 0.016 stat stat stat

Total 0.027 0.012 0.023 0.029 0.011 0.015

Correlated Tracking 0.009 0.009 0.009 0.007 0.007 0.007

pchjetT -unfolded stat stat stat stat stat stat

Total 0.009 0.009 0.009 0.007 0.007 0.007

Fig. 4. Second-order

harmonic coefficient

vch jet₂ as a function of pchjet_T for 0–5% (a) and 30–50% (b) collision centrality. The error bars on the points represent statistical uncertainties, the open and shaded boxes indicate the shape and correlated uncertainties (as explained in Sec.2.5).

withrespect tothesystematicshifts

εshape

,

εcorr

,where v2,i

rep-resentthemeasureddata(n points),

σ

iarestatisticaluncertainties

and

σshape

,i,

σcorr

,idenotethetwospecifictypesofsystematic

un-certainties.Theparameter

εcorr

isameasureofthefullycorrelated shifts;ashiftofalldatapointsbythecorrelateduncertainty

σcorr

,i

givesa totalcontributionto

χ

˜

2 _{ofone unit.Thesystematicshifts}

forthe shape uncertainty are taken to be of equal size for each point, since this gives the best agreement with the vch jet₂

=

0 hypothesis andthus provides a conservative estimate of the sig-nificance;the penalty factor is constructed such that an average shiftofalldatapointsby

σshape

addsoneunitto

χ

˜

2_.

The p-valueitself iscalculated usingthe

χ

2 _{distribution with}

n

−

2 degrees of freedom. For semi-central collisions a p-value

of0.0009isfound,indicating significantpositive vch jet₂ .Itshould be noted that the most significant data points are at pchjet_T

<

60 GeV

/

c; the results in the range 60

<

pchjet_T

<

100 GeV

/

c are

compatible with vch jet₂

=

0 (p-value 0.02). In central collisions, a p-value withrespect to thehypothesis of vch jet₂

=

0 of0.12is foundwhichindicatesthat vch jet₂ iscompatiblewith0withintwo standarddeviations. Followingthe sameapproach an upperlimit ofvch jet₂

=

0

.

088 isfoundwithinthesameconfidenceinterval.

3.1.Comparisontopreviousmeasurementsandmodelpredictions

Togeta betterqualitativeunderstandingoftheresults,the v2

of single charged particles vpart₂ [21,22] and the ATLAS vcalo jet₂

measurement [33] are shown together with the vch jet₂ measure-mentinFig. 5.TheATLASresultisforjetswithresolution param-eter R

=

0

.

2 within

|

η

|

<

2

.

1 comprising both chargedand neu-tralfragments.The eventplane angleismeasured bytheforward calorimetersystemat3

.

2

<

|

η

|

<

4

.

9.Jetsarereconstructedby ap-plyingtheanti-kT algorithmtocalorimetertowers,afterwhich,in

an iterativeprocedure,a flow-modulatedunderlying eventenergy issubtracted.Eachjetisrequiredtoliewithin



η

2

₊

_ϕ

2

_<

₀

_.

₂

ofeitheracalorimeterclusterofpT

>

9 GeV

/

c ora pT

>

10 GeV

/

c

trackjet withresolutionparameterR

=

0

.

4 builtfromconstituent tracks of pT

>

4 GeV

/

c (the full reconstruction procedurecan be

foundin[33,60]).

It is importantto realize that the energyscales ofthe ATLAS

vcalo jet₂ andALICEvch jet₂ measurementsaredifferent(astheALICE jetsdonotincludeneutralfragments)whichcomplicatesa direct comparisonbetweenthetwomeasurements.ThecentralATLAS re-sultsarealsoreportedin5–10%collisioncentrality.TheALICEand ATLASmeasurementsareinqualitativeagreement,bothindicating path-length-dependentpartonenergyloss.Giventheuncertainties, thedifferenceinthecentralvaluesofthemeasurementisnot sig-nificant.

Fig. 5alsoshowsthe v2 ofsinglechargedparticlesvpart₂ (from

[21,22]),whichisexpectedtobemostlycausedbyin-medium en-ergylossatintermediateandhighmomenta(pT



5 GeV

/

c).Even

thougha directquantitativecomparisonbetweenvch jet₂ andvpart₂

cannot be madeastheenergyscales forjetsandsingle particles aredifferent,themeasurementscanbecompared qualitatively,and

Fig. 5. Elliptic

flow coefficient

v2of charged particles [21,22](red, green) and R=0.2 full jets (comprising both charged and neutral fragments) measured within |η|<2.1

[33](blue) superimposed on the results from the current analysis of R=0.2 charged jets vch jet2 . In all measurements, statistical errors are represented by bars and systematic uncertainties by shaded or open boxes. Note that the same parton pTcorresponds to different single particle, full jet and charged jet pT. ATLAS vcalo jet2 and CMS v2from

[22,33]in 30–50% centrality are the weighted arithmetic means of measurements in 10% centrality intervals using the inverse square of statistical uncertainties as weights. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 6. vch jet₂ of R=0.2 charged jets obtained from the JEWEL Monte Carlo (red line) for central (a) and semi-central (b) collisions compared to data. JEWEL data points are

presented with only statistical uncertainties. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

itcanbeseenthat forcentralevents,thesingleparticle vpart₂ and

vch jet₂ areofsimilarmagnitudeandonlyweaklydependentonpT

over a large range of pT (

≈

20–50 GeV

/

c). For non-central

colli-sions (30–50%), the measurements of v2 for single particles and

jetsare also inqualitative agreement in the pT range wherethe

uncertaintiesallowforacomparison.

Fig. 6showsthevch jet₂ ofR

=

0

.

2 chargedjetsfromtheJEWEL Monte Carlo[29,30]comparedtothemeasured vch jet₂ .JEWEL sim-ulates parton shower evolution in the presence of a dense QCD medium by generating hard scatterings according to a collision geometryfromaGlauber[61]densityprofile.A1DBjorken expan-sionisused tosimulatethetime evolution ofthemedium. After radiativeandcollisionalenergyloss,PYTHIAis usedtohadronize thefragmentstofinalstateparticles.

TheanalysisontheJEWELeventsisperformedwiththe same jet definitionandacceptancecriteriathat are usedforthe vch jet₂

analysisindata,usingthesymmetryplane



2 fromthesimulated

initial geometry as



EP,2. The JEWEL Monte Carlo shows finite

significant vch jet₂ in semi-central collisions; in central collisions

vch jet₂ is compatiblewithzero.The JEWELresultforsemi-central 30–50%collisionsiscompatiblewiththemeasuredvalues(p-value 0.4 using Eq. (16) with the JEWEL results as hypothesis

μ

i and

the quadraticsumofthestatisticaluncertainties ofboth datasets as

σ

i inthe denominator ofthe firstsumof Eq.(16)). In central

JEWEL collisions vch jet₂ is consistent with zero, while the mea-sured values are compatible with the JEWEL vch jet₂ within two standard deviations.Itshould alsobe notedthat JEWELcurrently uses an optical Glauber modelfor the initial state andtherefore doesnotincludefluctuationsintheparticipantdistributiondueto the spatial configuration ofnuclei inthe nucleus. This simplified treatment ofthe overlapgeometrymayunderestimate the vch jet₂

[38,62]. Thiscomparisonofvch jet₂ inJEWELtoexperimental data complements earlierstudiesofthepath-length-dependent parton energylossandmodelpredictionsforthejet RAA [5].

4. Conclusion

The azimuthal anisotropy of R

=

0

.

2 charged jet production, quantified as vch jet₂ , has been presented in central and

semi-central collisions. Significant positive vch jet₂ is observed in semi-centralcollisions,whichindicates thatjet suppressionissensitive totheinitialgeometryofthe overlapregionofthecollision.This observationcanbeusedtoconstrainpredictionsofthepath-length dependenceofin-mediumpartonenergyloss.Incentralcollisions, thecentralvaluesofthemeasurementarepositive,butthe uncer-taintiesprecludedrawingastrongconclusiononthemagnitudeof

vch jet₂ .

Themeasured vch jet₂ forchargedjetsisalsocompared to sin-gleparticle v2 fromALICEandCMSand vcalo jet₂ fromATLAS.The

measurements cannot be directly compared quantitatively since theenergyscalesare different,butqualitatively, theresultsagree andindicate a positive v2 for both charged particles and jetsto

highpTincentralandsemi-centralcollisions.Thisobservation

in-dicatesthat partonenergylossislargeandthatthesensitivityto thecollisiongeometrypersistsuptohightransversemomenta.

TheJEWELMonte Carlopredictssizable vch jet₂ forsemi-central collisions and very small to zero vch jet₂ in central events. These predictionsareingoodagreementwiththesemi-central measure-ment. For central collisions, the JEWEL prediction is below the measurement,butmore datawouldbe neededtoreduce the un-certaintiesonthemeasurementsufficientlytoconstrainthemodel.

Acknowledgements

The ALICECollaboration wouldlike to thank all its engineers andtechniciansfortheirinvaluablecontributionstothe construc-tion of the experiment and the CERN accelerator teams for the outstandingperformance of the LHC complex. The ALICE Collab-oration gratefully acknowledges the resources and support pro-videdbyallGridcentresandtheWorldwideLHCComputingGrid (WLCG) collaboration. The ALICECollaboration acknowledges the followingfundingagenciesfortheir support inbuildingand run-ningthe ALICEdetector:State Committee ofScience, World Fed-eration of Scientists (WFS) and Swiss Fonds Kidagan, Armenia; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (FINEP),Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); National NaturalScienceFoundation ofChina(NSFC), theChineseMinistry of Education (CMOE) and the Ministry of Science and Technol-ogy of the People’s Republic of China (MSTC); Ministry of Edu-cation and Youth of the Czech Republic; Danish Natural Science Research Council, the Carlsberg Foundation and the Danish Na-tional Research Foundation; The European Research Council un-der the European Community’s Seventh Framework Programme; Helsinki Institute ofPhysics and theAcademy ofFinland; French CNRS–IN2P3, the ‘Region Pays de Loire’, ‘Region Alsace’, ‘Region Auvergne’ and CEA, France; German Bundesministerium fur Bil-dung, Wissenschaft, Forschung und Technologie (BMBF) and the HelmholtzAssociation;GeneralSecretariatforResearchand Tech-nology,Ministry of Development, Greece; National Research, De-velopmentandInnovationOffice(NKFIH),Hungary;Departmentof AtomicEnergy andDepartment ofScienceandTechnology ofthe GovernmentofIndia; IstitutoNazionale di Fisica Nucleare(INFN) and Centro Fermi – Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”, Italy; Japan Society for the Promotion of Science (JSPS) KAKENHI and MEXT, Japan; Joint Institute for Nuclear Research, Dubna; National ResearchFoundation of Korea (NRF);ConsejoNacionaldeCiencayTecnologia(CONACYT), Direc-cion General de Asuntos del Personal Academico (DGAPA), Méx-ico,AmeriqueLatineFormationacademique–EuropeanCommission (ALFA–EC) and the EPLANET Program (European Particle Physics LatinAmericanNetwork);StichtingvoorFundamenteelOnderzoek der Materie(FOM)andthe Nederlandse Organisatievoor

Weten-schappelijk Onderzoek (NWO), Netherlands; Research Council of Norway(NFR);NationalScienceCentreofPoland;Ministryof Na-tionalEducation/InstituteforAtomicPhysicsandNationalCouncil of Scientific Research in Higher Education (CNCSI-UEFISCDI), Ro-mania; Ministry of Education and Science of Russian Federation, Russian Academy of Sciences, Russian Federal Agency of Atomic Energy, Russian Federal Agency for Science and Innovations and The RussianFoundation forBasicResearch;Ministry ofEducation of Slovakia; Department of Science and Technology, Republic of South Africa; Centro de Investigaciones Energeticas, Medioambi-entales yTecnologicas (CIEMAT),E-Infrastructureshared between EuropeandLatin America(EELA),MinisteriodeEconomíay Com-petitividad (MINECO) of Spain, Xunta de Galicia (Consellería de Educación), Centro de Aplicaciones TecnológicasyDesarrollo Nu-clear(CEADEN),Cubaenergía,Cuba,andIAEA(InternationalAtomic EnergyAgency);SwedishResearch Council(VR)andKnut&Alice WallenbergFoundation (KAW);UkraineMinistryofEducationand Science;UnitedKingdomScienceandTechnologyFacilitiesCouncil (STFC);TheUnitedStatesDepartmentofEnergy,theUnitedStates NationalScience Foundation, the State of Texas, andthe State of Ohio; Ministry of Science, Education and Sports of Croatia and Unity throughKnowledge Fund, Croatia; Council ofScientific and IndustrialResearch(CSIR),NewDelhi,India;PontificiaUniversidad CatólicadelPerú.

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ALICECollaboration

J. Adam

40

,

D. Adamová

83

,

M.M. Aggarwal

87

,

G. Aglieri Rinella

36

,

M. Agnello

110

,

N. Agrawal

48

,

Z. Ahammed

132

,

S.U. Ahn

68

,

S. Aiola

136

,

A. Akindinov

58

,

S.N. Alam

132

,

D. Aleksandrov

99

,

B. Alessandro

110

,

D. Alexandre

101

,

R. Alfaro Molina

64

,

A. Alici

12

,

104

,

A. Alkin

3

,

J.R.M. Almaraz

119

,