Measurement of the (anti-)3He elliptic flow in Pb–Pb collisions at sNN=5.02TeV

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Measurement

of

the

(anti-)

3

He

elliptic

flow

in

Pb–Pb

collisions

at

√

s

_NN

=

5

.

02 TeV

.

ALICE

Collaboration



a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Article history: Received16November2019

Receivedinrevisedform21March2020 Accepted3April2020

Availableonline8April2020 Editor: L.Rolandi

Theellipticflow(v2)of(anti-)3HeismeasuredinPb–Pbcollisionsat√sNN=5.02 TeV inthe transverse-momentum(pT) rangeof2–6GeV/c for thecentralityclasses 0–20%, 20–40%, and 40–60% usingthe event-plane method.Thismeasurementiscomparedtothat ofpions,kaons, andprotons atthe same center-of-mass energy. A clear mass ordering is observed at low pT, as expected from relativistic hydrodynamics. Theviolation ofthe scaling of v2 with thenumber of constituent quarks atlow pT, alreadyobservedforidentifiedhadronsanddeuteronsatLHCenergies,isconfirmedalsofor(anti-)3_He. Theellipticflowof(anti-)3HeisunderestimatedbytheBlast-Wavemodelandoverestimatedbyasimple coalescenceapproachbasedonnucleonscaling.Theellipticflowof(anti-)3_{Hemeasuredinthecentrality} classes0–20%and20–40%iswelldescribedbyamoresophisticatedcoalescencemodelwherethe phase-spacedistributions of protonsand neutrons are generated usingthe iEBE-VISHNUhybrid model with AMPTinitialconditions.

©2020EuropeanOrganizationforNuclearResearch.PublishedbyElsevierB.V.Thisisanopenaccess articleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

The primary goalof studying ultra-relativisticheavy-ion colli-sions isto investigate the propertiesof the Quark–Gluon Plasma (QGP),a phase ofmatter madeofdeconfined quarks andgluons, which is created under extreme conditions of high temperature andenergydensity.At the LargeHadron Collider(LHC), theQGP canbestudiedinaregionofthephasediagramwhereacross-over transitionfromthedeconfinedphasetoordinarynuclearmatteris expectedbasedon Quantum Chromodynamics(QCD) calculations onthelattice[1–3].

In ultra-relativisticheavy-ion collisions, light nuclei, hypernu-clei,andtheirantiparticlesareproducedinadditiontoother par-ticle species. The production mechanism of these loosely bound compositeobjects in heavy-ion collisions isnot clearand is still underdebate.Twophenomenologicalmodelsaretypicallyusedto describe the light (anti-)(hyper-)nuclei production: the statistical hadronizationmodel[4–9] andthecoalescenceapproach[10–13]. Intheformer,light nucleiareassumedtobeemitted byasource in local thermal and hadrochemical equilibrium and their abun-dancesarefixedatchemicalfreeze-out.Thismodelreproducesthe light-flavored hadronyields measured incentral nucleus–nucleus collisions, including those of (anti-)nuclei and (anti-)hypernuclei [4]. However, the detailedmechanism of hadron productionand theexplanationofthepropagationofloosely-boundstatesthrough thehadrongasphasewithoutasignificantreductionintheiryields

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

arenotaddressedbythismodel.Ithasbeenconjecturedthatsuch objectscouldbeproducedatthephasetransitionascompact col-orlessquarkclusterswhichareexpectedtointeractlittlewiththe surrounding matter [8]. In thecoalescence approach, light nuclei areassumedtobeformedbythecoalescenceofprotonsand neu-tronswhichare closeinphase-spaceatkinetic freeze-out[11].In thesimpleversionofthismodel,nucleonsaretreatedaspoint-like particlesandthecoalescenceprocess isassumedtohappenifthe differencebetweentheir momentaissmallerthanagiven thresh-old,typicallyoftheorderof100MeV/c,whichisafreeparameter of the model, while space coordinates are ignored. On the con-trary, in the state-of-the-art implementations of the coalescence approach,thequantum-mechanicalpropertiesofnucleonsand nu-cleiare takenintoaccount andthecoalescence probabilityis cal-culated from the overlapbetweenthe wave functionsofprotons andneutrons which are mapped ontothe Wigner densityof the nucleus.Thephase-spacedistributionsofprotonsandneutronsat thekineticfreeze-outaregeneratedfromparticleproduction mod-els,such asA Multi-PhaseTransportModel (AMPT)[14], orfrom hydrodynamicalsimulationscoupledtohadronictransportmodels [13]. The advanced coalescence model qualitatively describesthe deuteron-to-protonand3_{He-to-protonratiosmeasuredindifferent} collisionsystemsasafunctionofthecharged-particlemultiplicity [15], while the simple coalescence approach provides a descrip-tion of pT spectraof light (anti-)nuclei measured inhigh-energy hadroniccollisionsonlyinthelow-multiplicityregime[16].

A key observable to study the productionmechanism oflight (anti-)nuclei isthe elliptic flow, i.e.the second harmonic(v2) of the Fourier decomposition of their azimuthal production

distri-https://doi.org/10.1016/j.physletb.2020.135414

0370-2693/©2020EuropeanOrganizationforNuclearResearch.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

bution with respect to a collision symmetry plane. The latter is definedby theimpact parameter ofthe incomingnucleiandthe beamdirection[17].Theellipticflowoflightnucleiwasmeasured by PHENIX [18] andSTAR [19] at the RelativisticHeavy Ion Col-lider (RHIC). The centrality dependence of v2 for deuterons (d) andantideuterons(d)wasfoundtobequalitativelysimilartothat of identified hadrons [19]. An approximate atomic mass number ( A)scalingwasobservedfortheellipticflowoflightnucleiwhen comparedtotheprotonv2uptopT

/

A

=

1

.

5 GeV

/

c,withslight de-viationsforhigherpT

/

A [19].Theflowofidentifiedhadronsis of-tendescribedusingtheBlast-Wavemodel[20–22].Thisisamodel inspired by hydrodynamics, whichassumes that the system pro-ducedin heavy-ion collisions islocally thermalized and expands collectivelywithacommonvelocityfield.Thesystemundergoesa kineticfreeze-outatthetemperatureTkinandischaracterizedbya commontransverseradialflow velocity(

β

) atthefreeze-out sur-face.The Blast-Wavemodel,however, failsinreproducing the v2 oflight nuclei measured inAu–Au collisions at

√

sNN

=

200 GeV [19],which isinsteadwell describedby amore sophisticated co-alescencemodelwherethe phase-spacedistributions ofnucleons aregeneratedusingthestring-meltingversionofAMPT[14].

Theellipticflowofdandd wasmeasuredbytheALICE Collab-orationinPb–Pb collisionsat

√

sNN

=

2

.

76 TeV inthe transverse-momentum range 0

.

8

≤

pT

<

5 GeV

/

c for different centrality classes [23]. The scaling of v2 with the number of constituent quarks(nq)isviolated foridentified hadronsincludingdeuterons, withdeviationsupto20% [23].Predictionsfromsimultaneousfits of the pT spectra andthe v2 of charged pions, kaons, and pro-tonsusinga Blast-Wavemodelprovide agood descriptionofthe

v2ofdeuteronsinthemeasured pTrangeforallcentralities, con-sistent withcommonkinetic freeze-outconditions[23].A simple coalescencemodel,basedon the A-scaling ofv2 [24], failsin re-producingthe datafor all centralities andinthe entire pT range [23].Thedataarefairlywell describedbyacoalescenceapproach which uses as an input the phase-space distributions generated with the default AMPT settings [13]. However, this model does not describe the coalescence parameter B2, definedas the ratio betweentheinvariantyieldofdeuteronsandthesquareofthe in-variant yield ofprotons [23]. The predictions obtained usingthe string-melting version of AMPT, which described RHIC data, are notconsistentwiththeALICEmeasurement[23].

Thefirst measurementofthe(anti-)3Heellipticflow inPb–Pb collisionsat

√

sNN

=

5

.

02 TeV ispresentedinthispaper.This mea-surementcomplementsthepictureobtainedfromthatofthe pro-tonanddeuteronflowatLHCenergies.

2. Experimentalapparatusanddatasample

ALICEisone ofthefourbig experimentsattheLHC dedicated tothestudyofheavy-ioncollisionsatultra-relativisticenergies.A detailed description of the ALICEapparatus and its performance canbefoundinRefs. [25] and[26].

Trajectories of charged particles are reconstructed in the AL-ICE central barrelwith the Inner Tracking System (ITS) [25] and theTimeProjectionChamber(TPC) [27].Thesearelocatedwithin alarge solenoidal magnet,providing ahighly homogeneous mag-neticfieldof0.5Tparalleltothebeamline.TheITSconsistsofsix cylindrical layers of silicon detectors with a total pseudorapidity coverage

|

η

|

<

0

.

9 withrespecttothenominalinteractionregion. The ITS is used in the determination of primary and secondary vertices,andinthetrackreconstruction.TheTPCisthelargest de-tectorinthe ALICEcentral barrel,witha pseudorapiditycoverage

|

η

|

<

0

.

9. Itisusedfortrackreconstruction,charged-particle mo-mentummeasurementandforparticleidentificationviathe mea-surementofthespecificenergylossofparticlesintheTPCgas.The transverse-momentumresolutionrangesfromabout1%at1GeV/c

to about10% at50GeV/c inPb–Pb collisionsat

√

sNN

=

2

.

76 TeV [26] andat

√

sNN

=

5

.

02 TeV [28].The dE

/

dx resolutiondepends oncentralityandisintherange5–6.5%forminimumionizing par-ticles crossing the full volume of the TPC [26]. Collision events are triggeredby twoplastic scintillatorarrays, V0AandV0C [29], located onbothsidesofthe interactionpoint,covering the pseu-dorapidity regions

−

3

.

7

<

η

<

−

1

.

7 and 2.8

<

η

<

5.1. Each V0 array consistsoffourringsintheradial direction,witheach ring comprisingeightcellswiththesameazimuthalsize.TheV0 scin-tillators are used to determine the collision centrality from the measuredcharged-particlemultiplicity[30,31],andtomeasurethe orientationofthesymmetryplaneofthecollision.

The data usedfor thisanalysiswere collected in 2015during the LHC Pb–Pb runat

√

sNN

=

5

.

02 TeV. A minimum bias event trigger wasused,which requirescoincidentsignalsintheV0 de-tectorssynchronous withthe bunchcrossing timedefinedby the LHCclock.

3. Dataanalysis 3.1. Eventselection

In order to keep the conditions of the detectors as uniform as possible and reject background collisions, the coordinate of the primary vertexalong the beamaxis isrequired to be within 10 cmfromthe nominalinteraction point.Collisions with multi-ple primary verticesare taggedaspile-up eventsandrejected. A centrality-dependentnon-uniformityintheangulardistributionof thesymmetryplane,ofmaximum6% isfound.Inordertocorrect for thisnon-uniformity,the eventsare re-weighted basedon the collision centrality (C )andthe angleof thesymmetry plane



2. Theweight foragiventwo-dimensionalcell(C ,



2)isdefinedas theratiobetweentheaveragenumberofevents,forallC and



2, andtheactualnumberofeventsinthesametwo-dimensionalcell. ThecentralityclassesusedfortheanalysispresentedinthisLetter are0–20%,20–40%,and40–60%.Intotal,approximately20million eventsareselectedineachcentralityclass.

3.2. Trackselectionandparticleidentification

(Anti-)3He candidates are selected from the charged-particle tracks reconstructed in the ITS and TPC in the kinematic range

pT

/

|

z

|

>

1 GeV

/

c and

|

η

|

<

0

.

8, where z is the particle electric charge in units ofthe elementary charge. Tracks are required to havea minimumnumberofclustersinthe TPC, NTPC

cls ,ofatleast 70 out of a maximum of 159, and in the ITS, NITS_cls, of at least two with one cluster located in any of the two innermost ITS layers. The number of TPC clusters used in the dE

/

dx calcula-tion, NTPC_cls

(

dE

/

dx

)

isrequired to be larger than50. Good quality of the track fit is also required, expressed by

χ

2

_/

_NTPC

cls

<

4 and a ratio ofthe number ofTPC clustersattached to thetrack over the numberoffindable TPCclusters(accountingfor tracklength, location, andmomentum)larger than80%. Thecontributionfrom secondary tracksis reducedbyrequiring amaximumDistance of Closest Approach (DCA) to the primary vertex in the transverse plane(DCAxy

<

0

.

1 cm)andinthelongitudinaldirection(DCAz

<

1 cm).Theseselectioncriteriaensureahightrack-reconstruction ef-ficiency, whichis largerthan 80%, anda resolutioninthe dE

/

dx measured intheTPCofabout6% inthecentrality andpT ranges usedforthismeasurement.

TheexpectedaveragedE

/

dx for(anti-)3He,



dE

/

dx



3_He,isgiven by the Bethe formula and the standard deviation of the distri-bution of dE

/

dx

− 

dE

/

dx



3_He, denoted

σ

3_He

dE/dx, is theTPC dE

/

dx resolution measured for (anti-)3_{He. For the (anti-)}3_He identifica-tion, the dE

/

dx measured in the TPC is required to be within 3

σ

3He

Fig. 1. Distributions ofdE/dx− dE/dx3He



/σ3He

dE/dxmeasuredintheTPCforthetransverse-momentumranges2 ≤pT<3 GeV/c (left) and3≤pT<4 GeV/c (right). The verticalbarsrepresentthestatisticaluncertaintiesofthedata.Thebluedottedandthereddash-dottedlinesindicatethe3_Hand3_{Hecontributionswhiletheblacksolid} linesshowthesumofboth.Therangesusedforthesignalextractionareindicatedbytheverticalblack-dottedlines.

of



dE

/

dx

− 

dE

/

dx



3_He



/

σ

3He

dE/dx for the transverse-momentum ranges 2

≤

pT

<

3 GeV

/

c and 3

≤

pT

<

4 GeV

/

c are shownin Fig.1.Therangeused forthe (anti-)3He selectionisindicated by thevertical black-dotted lines.The contamination by (anti-)3_His estimated by fitting the measured



dE

/

dx

− 

dE

/

dx



3_He



/

σ

3He dE/dx distributioninagivenpT rangeusingtwoGaussianfunctions,one for(anti-)3_{Handtheother for(anti-)}3_{He.The(anti-)}3_H contribu-tion is subtracted fromthe distribution to extract the (anti-)3_He signal in the range within

±

3

σ

_dE3He_/dx. The contamination from (anti-)3_{Hisnegligiblefor p}

T

>

3 GeV

/

c (seerightpanel ofFig.1). The contamination from (anti-)4He is expected to be negligible over the full pT range considering that its production rate mea-suredinPb–Pb collisionsat

√

sNN

=

2

.

76 TeV issuppressed com-paredtothatof(anti-)3_Hebyafactor

_∼

_{300 [32].}

3.3.Secondary3_{Hefromspallationprocesses}

Themain backgroundfor thismeasurement isrepresented by secondary 3He produced by spallation reactions in the interac-tionsbetweenprimaryparticlesandnucleiinthedetectormaterial orinthe beampipe. Thisbackgroundsource isrelevant only for 3_{He,whilethiseffectisnegligibleforanti-}3_{He.Nuclearfragments} emittedin spallation processeshavealmost uniform angular dis-tributions withrespect to the directionof the incomingparticle, whileprimary 3_{He tracks originate fromthe primary vertex. The} contributionof secondary 3He produced by spallationcan be in-vestigatedfromthe DCAxy distribution,whichhas apeak around zero for primary 3He and is almost flat for secondary 3He. The DCAxydistributionsfor3Hecandidatesmeasuredinthe transverse-momentum ranges 2

≤

pT

<

3 GeV

/

c and 3

≤

pT

<

4 GeV

/

c areshown inFig. 2.The signof theDCAxy is positive ifthe pri-mary vertex is inside the track curvature and negative if it lies outside. Thesedistributions areobtained byselecting trackswith

|

DCAz

|

<

1cmandapplyingastricterrequirementfortheselection of 3_{He candidates, given by}

₋

₂

_≤



_dE

_/

_dx

_{− }

_dE

_/

_dx

_

3_He



/

σ

3He dE/dx

<

3. Thisasymmetric rangeis used toincrease thepurity ofthe 3_{He sample by suppressing the} 3_{H contamination. The} contribu-tion from secondary 3_{He produced by spallation is found to be} relevantin thisanalysisonly in thetransverse-momentum range 2

≤

pT

<

3 GeV

/

c.

ForthemeasurementpresentedinthisLetter,3He areusedfor 2

≤

pT

<

3 GeV

/

c, while the sum of 3He and 3He is used for higher pT wherethecontributionfromsecondary 3Hefrom spal-lation is negligible. This is possible because the elliptic flow of 3_{He and} 3_{He areconsistent within thestatisticaluncertainties in}

Fig. 2. DCAxy distributionsof3Hecandidates, selectedrequiring −2< (dE/dx−

dE/dx3He)/σ

3_He

dE/dx < 3, with |DCAz|<1 cm measured in the transverse-momentumintervals2≤pT<3 GeV/c (blue) and3≤pT<4 GeV/c (red). the pT range where these two measurements can be compared, i.e. pT

>

3 GeV

/

c, andin all centralityintervals. Avanishing dif-ference betweentheellipticflowof matterandantimatternuclei atLHCenergiesisalreadyobservedfor(anti-)protons [33,34] and (anti-)deuterons [23].This observationis consistent withthe de-creasingtrend ofthedifference betweenthe ellipticflow of pro-tons and antiprotons, deuterons and antideuterons with increas-ingcenter-of-mass energyatRHICgoing from

√

sNN

=

7

.

7 GeV to

√

sNN

=

200 GeV [35]. 3.4. Theevent-planemethod

Theinitial spatial anisotropyofthe hotanddensematter cre-ated in non-central nucleus–nucleus collisions results in an az-imuthal anisotropy ofparticle emission withrespectto the sym-metry plane. The azimuthal distribution of the emitted particles canbeexpressedasaFourierseries[36]

dN d

ϕ

∝

1

+

2



n≥1 vncos



n



ϕ

− 

n



,

(1)

where



n indicatestheorientationofthenth symmetryplane,

ϕ

istheazimuthalangleofaparticle,andtheFouriercoefficientsvn

arealsoreferredtoastheflowcoefficients.

Experimentally, the true symmetry plane can only be recon-structed approximately because of the finite detector resolution. Themeasured symmetryplane iscalled‘eventplane’.The elliptic

Fig. 3. Event-planeresolution

R

2 ofthesecondharmonicasafunctionofthe

col-lisioncentrality.

flowof(anti-)3_{HeismeasuredusingtheEvent-Plane(EP) method} [37].Thev2 of(anti-)3Heineach pT rangeisgiven by

v2

{

EP

,

|

η

| >

0

.

9

} (

pT

)

=

π

4R2 Nin-plane

(

pT

)

−

Nout-of-plane

(

pT

)

Nin-plane

(

pT

)

+

Nout-of-plane

(

pT

)

,

(2) where the

|

η

|

represents the minimal pseudorapidity gap be-tween the V0detectors andthe TPC, the R2 is the event-plane resolutionforthesecond harmonic,and Nin-plane and Nout-of-plane arethenumberof(anti-)3Hecandidatesin-planeandout-of-plane, respectively. Particles are regarded as ‘in-plane’ if the azimuthal difference

|

ϕ

|

= |

ϕ

− 

EP

2

|

<

45◦or

|

ϕ

|

= |

ϕ

− 

EP

2

|

>

135◦,and ‘out-of-plane’otherwise,where



EP₂ istheorientationoftheevent plane.The latterisreconstructed usingtheV0detectors.The cal-ibrated amplitude ofthe signal measured in each cell ofthe V0 arrays is used as a weight wcell in the construction of the flow vector Q2[37]

Q2

=

Ncell



j=1

wcell

·

exp

(

i2

ϕ

cell

)

(3)

whereNcell isthenumberofcells oftheV0detectorsand

ϕ

cell is theazimuthalangleofthegeometriccenterofeachcell.Inorder toaccountforanon-uniformdetectorresponsewhichcangenerate a bias in the



EP₂ distribution, the componentsof the Q2-vector are adjustedusing a re-centeringprocedure [38]. The orientation oftheeventplaneangleisobtainedusingtherealandimaginary partsof Q2



EP₂

=

1 2arctan



Im

(

Qn) Re

(

Qn)



(4) The event-plane resolution R2 is calculated using the three sub-eventcorrelationtechniquewithchargedparticles [37]

R2

=









cos



2





A₂

− 

B₂



 · 

cos



2





A₂

− 

C₂







cos



2





B₂

− 

C₂





,

(5)

whereA refers tothe eventplane measured usingtheV0 detec-tors,whileBandCrefertothoseobtainedinthepositive(

η

>

0) andnegative(

η

<

0)pseudorapidityregionsoftheTPC.Forthe lat-tertwomeasurements, asetofreconstructedchargedtrackswith 0

.

2

≤

pT

<

20 GeV

/

c and

|

η

|

<

0

.

8 isused.Minimal quality crite-riaareappliedtothesetracks,suchastherequirementofhavinga numberofTPCclusterslargerthan70anda

χ

2

_/

_NTPC

cls

<

4.The sec-ondharmonicevent-planeresolutionasafunctionofthecollision centralityisshowninFig.3.

Consideringthecentralitydependenceof R2,theellipticflow measurementsareperformedincentralityintervalsof5%widthfor therange0–40%,andof10%widthfortherange40–60%.The lat-tertwointervalsarelargerduetothelimitednumberof(anti-)3He candidates. The resolutions forthe centrality ranges 40–50% and 50–60%aregivenbytheweightedaveragesoftheresolutions cal-culatedincentralitybinsof5%width,withthenumberofcharged tracks inthe correspondingcentrality rangesasa weight.Finally, the elliptic flow measurements for the wider centrality classes usedinthisanalysisareobtainedasweightedaveragesofthe mea-surementsinthesmallercentrality ranges

v2

(

pT

)

=

ivi2

(

pT

)

·

N(ianti-)3_He

(

pT

)

iNi₍anti-)3_He

(

pT

)

,

(6) where vi

2

(

pT

)

is the elliptic flow measured in a given pT range and in the centrality interval i, and Ni

(anti-)3_He is the number of (anti-)3HecandidatesforthesamecentralityandpT range. 4. Systematicuncertainties

The mainsources ofsystematic uncertaintiesin this measure-ment are relatedtothe eventselection criteria, track reconstruc-tion, particleidentification, occupancyeffects intheTPC, andthe subtractionofthefeed-downcontributionfromweakdecaysof hy-pertritons.Exceptforthesystematicuncertaintyduetotheevent selection, allother contributionsareestimatedusingMonteCarlo (MC) simulations based on the HIJING generator [39]. Simulated eventsareenriched byaninjectedsample of(anti-)(hyper-)nuclei generatedwithaflatpTdistributioninthetransverse-momentum range 0

<

pT

<

10 GeV

/

c and a flat rapidity distribution in the range

−

1

<

y

<

1.Theinteractionsofthegeneratedparticleswith the experimental apparatus are modeled by GEANT 3 [40]. The input transverse-momentum distribution of injected (anti-)3_{He is} correctedusingcentralityandpT-dependentweightstoreproduce itsmeasuredshape,whichisdescribedbytheBlast-Wavefunction. The parameters are taken from the (anti-)3_{He measurement in} Pb–Pb collisionsat

√

sNN

=

2

.

76 TeV [41] assumingthesame spec-tralshapeinPb–Pb collisionsat

√

sNN

=

5

.

02 TeV.Thesystematic uncertainties estimatedusingtheMC simulationsarefoundtobe independent ontheinput parametrizationofthe (anti-)3_He spec-trum.Agoodmatchingbetweenthedistributionsofvariablesused fortrackselectionandparticleidentificationisfoundbetweendata andMCsimulations.Thisguaranteesthereliabilityofthedetector response descriptionandofthesystematicuncertaintiesobtained basedonMCsimulations.

4.1. Systematicuncertaintiesduetotheeventselectioncriteria

Theeffectofdifferenteventselectioncriteriaisstudiedby com-paring the v2 measurements obtained by varying the selection range of the z-coordinate of the primary vertex, using different centrality estimators, selecting events corresponding to opposite magnetic field orientations, using different pile-up rejection cri-teria, and selecting events with different interaction rates. The limited number of (anti-)3He candidates prevents the estimation of thissource ofsystematicuncertainties from datasince the v2 measurementsobtainedusingthesedifferentselectioncriteriaare consistent within theirstatisticaluncertainties, i.e.thesystematic uncertaintiesarecomparabletoorsmallerthanthestatisticalones. Thesystematicuncertaintyrelatedtoeventselectioncriteriais as-sumedtobeidenticaltothatoftheprotonv2 measuredinPb–Pb collisions at

√

sNN

=

5

.

02 TeV and itis takenfromRef. [34]. The totalsystematicuncertaintyduetotheeventselectionis2

.

7% and isobtainedbyaddingallcontributionsinquadrature.

4.2.Systematicuncertaintiesduetotrackingandparticleidentification

The systematic uncertainties due to track reconstruction and particleidentificationareestimatedusingMC simulations.Thisis doneto benefitfromthe largernumberof(anti-)3_{He inthe} sim-ulation ascompared to data to reduce the interference between statisticalfluctuationsandsystematicuncertainties. The same az-imuthal asymmetry as measured in data in each centrality and

pT rangeisartificiallycreatedfortheinjected(anti-)3He with re-spectto a randomlyoriented eventplane by rejecting a fraction ofthe out-of-plane (anti-)3_{He. This is done because the injected} (anti-)3He are produced with v2

=

0 by the MC generator. The v2 of the embedded (anti-)3He is then measured using the re-constructedtracksinthe simulation.Differenttrackselection cri-teria and signal extraction ranges are used to measure the v2, inwhich the analysis parameters are selected randomly inside a rangearound thedefaultvalue usingauniformprobability distri-bution. The different selection criteria are varied simultaneously in order to include the effects of their possible correlations. In eachcentralityclassandforeachtransverse-momentumrange,the measurements obtainedusingdifferent selectioncriteria followa Gaussiandistribution whosestandard deviationis verysimilar to thestatisticaluncertainty,indicatingaresidualcorrelationbetween systematicvariationsandstatisticalfluctuations.Assumingthatthe spreadofthedifferentmeasurementsisonlyduetostatistical fluc-tuations,themeanoftheGaussiandistributionisconsideredasthe bestestimate ofthereconstructed v2.Thedifferencebetweenthe injectedv2inthesimulationandthemeanoftheGaussianspread ofthe measurements is taken asthe systematic uncertainty due totracking andPID.This uncertaintyranges between1% and4%, depending on pT and centrality.An additional componentto the trackinguncertaintyoriginatesfromthedifferencebetweenthev2 measured usingthe positive andnegative pseudorapidity regions ofthe TPC. Thiscontributioncannot beestimated fromdatadue tothelimitednumberof(anti-)3_{Heandisassumedtobeidentical} tothatofthe protonv2 measurement,whichis2% [34]. The lat-teris addedinquadraturetothe systematicuncertaintiesrelated totrackingandparticleidentification.

4.3.SystematicuncertaintyduetooccupancyeffectsintheTPC

Different reconstruction efficiencies for in-plane and out-of-plane particles, due to occupancy effects in the TPC, can create a bias in the v2 measurement. This effect is studied using MC simulationsby comparing thereconstruction efficiencyfor differ-entcharged-particlemultiplicities.Thesametrackselectioncriteria usedindataare appliedtothe reconstructedtracksin the simu-lationfor the efficiency calculation. The maximum deviation be-tweenthe reconstructionefficiencies fordifferentmultiplicitiesis 0

.

5%, correspondingto aratiobetweenin-plane andout-of-plane efficiencies of r

=

0

.

995

±

0

.

001. The difference between the v2 measuredassumingr

=

1 andr

=

0

.

995 correspondstothe maxi-mumvariationrangeofv2.Thesystematicuncertaintyfrom occu-pancyisthengivenbythismaximumdifferencedividedby

√

12, assuming a uniformdistribution.This uncertaintydecreases with increasing pT andyields atmaximum2% forthecentralityrange 0–20%and0

.

5% forthecentralityranges20–40%and40–60%.

4.4.Systematicuncertaintyduetothefeed-downsubtraction

Thefeed-down systematicuncertaintyis dueto the unknown

v2 of(anti-)3He fromtheweak decayofthe(anti-)3H.The

frac-tionofsecondary(anti-)3He fromthe (anti-)3Hdecaysinthe re-constructedtracksample iscalculatedusingMC simulations.This fractionisabout 6% forthe centralityrange 0–20%and

∼

5% for thecentralityranges20–40%and40–60%,slightlyincreasingwith

Table 1

Summaryofsystematicuncertainties.Therangesrepresentthe minimumandmaximumuncertaintiesinthecasewherethe systematicuncertaintiesdependon

p

Tandcentrality.

Source of systematic uncertainty Value (%) Primary vertex selection 1 Centrality estimator 1.5 Magnetic field orientation 1 Pile-up rejection 1 Interaction rate 1.5 Tracking and particle identification 2−4.5 Occupancy in the TPC 0.5−2

Feed-down 2

Total 4−6

Fig. 4. Elliptic flow (v2)of(anti-)3He measured inPb–Pb collisionsat √sNN= 5.02 TeV forthecentralityclasses0–20%,20–40%,and40–60%.Thestatistical un-certaintiesareshownasverticalbars,systematicuncertaintiesasboxes.

pT.Therelativeabundancesof(anti-)3Hand(anti-)3Heinthe sim-ulationareadjustedtothemeasuredvaluesinPb–Pb collisionsat

√

sNN

=

2

.

76 TeV [42],assumingthattheyieldratiobetween (anti-)3Hand(anti-)3_{HedoesnotdiffersignificantlyfromthatinPb–Pb} collisions at

√

sNN

=

5

.

02 TeV,whichisnotpublished yet.The v2 of(anti-)3_{Hefromthe(anti-)}3

Hdecayisassumedtobewithinthe

rangeof

±

50% withrespectto the v2 ofthe inclusive(anti-)3He. Thisvariationisselectedtoprovideaconservativeestimateofthe feed-downuncertainty.Foreachoftheseextremes,thefeed-down contribution issubtracted. The systematicuncertainty dueto the feed-down subtraction is given by the difference between these twolimitsdividedby

√

12.Thisuncertaintyis

∼

2% inall central-ityranges,almostindependentofpT.

The different contributions to the systematic uncertainties of thismeasurementaresummarizedinTable1.

5. Results

5.1. Experimentalresults

Theelliptic flowof(anti-)3_{He measuredin Pb–Pb collisionsat}

√

sNN

=

5

.

02 TeV for the centrality classes 0–20%, 20–40% and 40–60%is showninFig.4asa functionof pT.Themeasurement inthetransverse-momentumrange2

<

pT

<

3 GeV

/

c isdone us-ing only 3_{He. An increasing elliptic flow is observed going from} central to semi-central collisions, as expected. This isdue to the increasing azimuthal asymmetryofthe overlapregionofthe col-lidingnucleiattheinitialcollisionstage,whichresultsinalarger azimuthal asymmetry ofthemomentaofthefinal-stateparticles. Ineach centralityclass, theellipticflow increaseswith pT in the measured pT range.

The(anti-)3_{Heellipticflowiscomparedtothatofpions,kaons,} and protons measured using the scalar-product method at the

Fig. 5. Comparison betweentheellipticflowof(anti-)3_{Hemeasuredusingtheevent-planemethodandthatofpions,kaons,andprotonsmeasuredusingthescalar-product} methodinPb–Pb collisionsat√sNN=5.02 TeV forthecentralityclasses0–20% (left),20–40% (middle)and40–60% (right).Seetextfordetails.Verticalbarsandboxes representthestatisticalandsystematicuncertainties,respectively.

Fig. 6. Comparison betweentheellipticflowofpions,kaons,protons,and(anti-)3_{Hedividedbythenumberofconstituentquarks(n}

q)asafunctionof

p

T/nq(upperpanels) andtransversekineticenergyperconstituentquark

E

kin

T /nq (lowerpanels)forthecentralityclasses0–20% (left),20–40% (middle)and40–60% (right).Seetextfordetails. Verticalbarsandboxesrepresentthestatisticalandsystematicuncertainties,respectively.

samecenter-of-mass energy[34] inFig. 5. Giventhegood event-planeresolutionshowninFig.3andthelargestatistical uncertain-tiesofthe(anti-)3Hev2measurements,thedifferencebetweenthe scalar-productandevent-planemethodtocalculatethe(anti-)3_He elliptic flow is negligible. The v2 of pions, kaons, and protons ismeasured in smallercentrality rangescompared tothose used in this analysis. The corresponding v2 for the centrality classes 0–20%,20–40%,and40–60%areobtainedasweightedaverages of the v2 measured in smallercentrality classesusingthe pT spec-tratakenfrom[43] asweights.Aclearmassorderingisobserved for pT

<

3 GeV

/

c, consistentwiththeexpectationsfrom relativis-tichydrodynamics[44]. The v2 of(anti-)3He showsaslowerrise with pT comparedtothat ofpions,kaons,andprotonsduetoits largermass.

The comparisons between the measurements of v2

/

nq of (anti-)3_{He,pions,kaons,andprotonsareshowninFig.6asa} func-tion of pT

/

nq (upper panels), and transverse kinetic energy per constituent quark Ekin_T

/

nq (lower panels). The transverse kinetic energyisdefinedasEkin

T

=



m2

₊

_p2

T

−

m,wherem isthemassof theparticle.Theviolationofnq scalingforthemeasuredrangeof pT

/

nq



0

.

7 GeV

/

c, alreadyestablished forthe ellipticflow mea-surementsofidentifiedhadronsattheLHC[23,34,45],isobserved alsofor(anti-)3_He.Then

q scalingatlarger pT

/

nqcannotbetested withthelimiteddatasampleusedforthisanalysis.

5.2. Modelcomparisons

The (anti-)3He v2 measurements are compared with the ex-pectations fromthe Blast-Wave model and a simple coalescence approachusingthesameprocedurefollowedin[23].

The Blast-Wave predictions are obtained froma simultaneous fit of the v2 and the pT spectra of pions, kaons, and protons measured inPb–Pb collisions at

√

sNN

=

5

.

02 TeV [34,43] in the transverse-momentum ranges 0

.

5

≤

pπ_T

<

1 GeV

/

c, 0

.

7

≤

pK

T

<

2 GeV

/

c, and0

.

7

≤

pp_T

<

2

.

5 GeV

/

c,respectively,andinthesame centralityclasses.ThefourparametersoftheBlast-Wavefits repre-sentthekineticfreeze-outtemperature(Tkin),themeantransverse expansion rapidity (

ρ

0), the amplitudeof its azimuthal variation (

ρ

a),andthevariationintheazimuthaldensityofthesource(s2), asdescribedin[21]. ThevaluesoftheBlast-Waveparameters ex-tracted from the fits are reported in Table 2 for each centrality interval. Theellipticflowof(anti-)3Heis calculatedusingthe pa-rametersobtainedfromthesimultaneousfitandthe3Hemass,i.e., assumingthesamekineticfreeze-outconditions.

The simplecoalescenceapproachusedinthiscontextisbased ontheassumptionthattheinvariantyieldof(anti-)3Hewith trans-versemomentum pTisproportionaltotheproductoftheinvariant yieldsofitsconstituentnucleonswithtransversemomentum pT

/

3 andonisospinsymmetry,forwhichtheprotonandneutronv2 are

Fig. 7. Elliptic flowof(anti-)3_{HeincomparisonwiththepredictionsfromtheBlast-Wavemodelandasimplecoalescenceapproachforthecentralityclasses0–20% (left),} 20–40% (middle),and40–60% (right).Thelowerpanelsshowthedifferencesbetweendataandmodelsforeachcentralityrange.Thestatisticaluncertaintiesofthedataand themodelareaddedinquadrature.Verticalbarsandboxesrepresentthestatisticalandsystematicuncertainties,respectively.

Table 2

Blast-Wave parametersextractedfromthe simultaneousfitsofthe pT spectraand

v

2ofpions,kaons,andprotons.Seetextfordetails.

Fit parameters Centrality classes

0–20% 20–40% 40–60%

Tkin(MeV) 106±1 110±1 117±1

ρ0×10−1 8.78±0.01 8.92±0.02 7.48±0.01

ρa×10−2 1.37±0.01 2.98±0.01 3.16±0.01

s2×10−2 4.06±0.01 9.02±0.01 1.29±0.01 identical.Consideringonlyellipticalanisotropiesoftheconstituent nucleons, i.e.neglecting higherorder harmonics, the coalescence predictionsareobtainedfromtheellipticflowofprotonsv2,p mea-suredinPb–Pb collisionsat

√

sNN

=

5

.

02 TeV [34] usingthescaling law[46] v_2,3_He

(

pT

)

=

3v2,p

(

pT

/

3

)

+

3v3_2,p

(

pT

/

3

)

1

+

6v2 2,p

(

pT

/

3

)

.

(7)

Fig. 7 shows the comparison of the (anti-)3He v2 measure-mentswiththepredictionsoftheBlast-Wavemodelandthe sim-ple coalescence approach. The differencesbetween the data and the model for each centrality interval are shown in the lower panels. These are calculated using the weighted averages of the modelsinthesamepTintervalsofthemeasurement.Forthe Blast-Wave model, the pT spectrum of (anti-)3He measured in Pb–Pb collisions at

√

sNN

=

2

.

76 TeV [41] is used as a weight. This is justifiedconsideringthatthe(anti-)3He pTspectruminPb–Pb col-lisions at

√

sNN

=

5

.

02 TeV is expected to be similar to that at

√

sNN

=

2

.

76 TeV,asobservedforlighterhadrons[43].Theproton spectrummeasured in Pb–Pb collisions at

√

sNN

=

5

.

02 TeV [43], withpT scaled by A

=

3,is usedasaweight forthecoalescence model.Thedataarelocatedbetweenthetwomodelpredictionsin allcentralityintervalsexceptformoreperipheralcollisions,where thecoalescenceexpectationsareclosertothedata.

The Blast-Wave model was found to be consistent with the (anti-)deuteron elliptic flow measured in Pb–Pb collisions at

√

sNN

=

2

.

76 TeV in the centrality intervals 0–10%, 10–20% and 20–40%,althoughthe(anti-)deuteronpTdistributionswereslightly underestimatedfor pT

<

2GeV/c inthe samecentralityintervals [23].Similarlytotheresultspresentedinthispaperfor(anti-)3He, thepredictionsfromthesimplecoalescence modeloverestimated the (anti-)deuteron v2 in all centrality intervals. In general, the measurementsof(anti-)deuteronand(anti-)3_{Heellipticflowatthe}

Fig. 8. Elliptic flow of(anti-)3_{He measured inthe centrality classes0–20% and} 20–40% in comparisonwith thepredictionsfromacoalescencemodelbased on phase-spacedistributionsofprotonsandneutronsgeneratedfromtheiEBE-VISHNU hybridmodelwithAMPTinitialconditions[13].Themodelpredictionsareshown aslinesandthebandsrepresenttheirstatisticaluncertainties.Thedifferences be-tweendataandmodelareshowninthelowerpanelforbothcentralityclasses.The statisticaluncertaintiesofthedataandthemodelareaddedinquadrature.Vertical barsandboxesrepresentthestatisticalandsystematicuncertainties,respectively. LHC consistently indicate that the simple coalescence and Blast-Wave models represent the upper and lower edges of a region where the data are typically located. The (anti-)deuteron elliptic flow measured in Pb–Pb collisionsat

√

sNN

=

2

.

76 TeV is simply closertothelowersideofthisregion.

The Blast-Wave model is a simplified parametrization of the systemexpansion which istypically used to describe thehadron

pT spectra and v2 withparameters tuned to data. However, this simple model cannot describe the full collective properties and dynamicsofthe system.Forthis, an approachbasedon relativis-tic viscous hydrodynamics coupled to an hadronicafterburner is needed.Thecomparisonofthemeasurementpresentedinthis pa-perwithanactualhydrodynamicalsimulationisunfortunatelynot possiblebecausetherearenopredictionsfor(anti-)3Heavailable.

The predictions from a more sophisticated coalescence model [13] are compared to the data in the centrality ranges 0–20% and20–40% inFig. 8. The lower panel showsthedifferences be-tween the data and the model forthese two centrality intervals calculated taking the weighted average of the model in each pT range,similarly towhat isdone for theBlast-Waveandthe

sim-plecoalescencepredictionsinFig.7.Inthismodel,thecoalescence probabilityisgivenby thesuperpositionofthewave functionsof the coalescingparticles, andthe Wigner function ofthe nucleus. The coalescence happens in a flowing medium, i.e., in the rest frame of the fluid cells. This introduces space-momentum corre-lationsabsentinthenaivecoalescenceapproach.Thephase-space distributionsofprotonsandneutronsaregeneratedfromthe iEBE-VISHNUhybridmodelwithAMPTinitialconditions[13].Although this model underestimates the yield of (anti-)3_{He measured in} Pb–Pb collisionsat

√

sNN

=

2

.

76 TeV inthetransverse-momentum rangeof 2

<

pT

<

7 GeV

/

c byalmost a factor oftwo [13], it is abletoreproducequantitativelytheellipticflowmeasurements in the centrality classes 0–20% and 20–40% presented here. More-over,thismodelprovidesagooddescriptionofthe pT spectraand pT-differentialellipticflow ofprotonsanddeuterons fordifferent centralityintervalsinAu–Au collisionsat

√

sNN

=

200 GeV andin Pb–Pb collisionsat

√

sNN

=

2

.

76 TeV [13].

6. Summary

Thefirst measurementofthe(anti-)3_{Heellipticflow inPb–Pb} collisions at

√

sNN

=

5

.

02 TeV is presented. An increasing trend of v2 with pT andone going fromcentralto semi-central Pb–Pb collisions is observed. This measurement is compared to that of pions, kaons, and protons at the same center-of-mass energy. A clearmassorderingatlow pTisobserved,asexpectedfrom rela-tivistichydrodynamics.Thescalingbehavior of v2 withthe num-ber of constituent quarks is violated for the measured range of

pT

/

nq



0

.

7 GeV

/

c also for(anti-)3He, asobserved forthe v2 of lighterparticlesmeasuredattheLHC.

The (anti-)3He elliptic flow measured in all centrality inter-valsliesbetweenthepredictions fromtheBlast-Wavemodeland a simple coalescence approach. This picture is consistent with that of the (anti-)deuteron v2 measured in Pb–Pb collisions at

√

sNN

=

2

.

76 TeV, which was also overestimated by the simple coalescencemodel,although itwas closerto theBlast-Wave pre-dictions.Theresultsonthe(anti-)deuteronand(anti-)3He elliptic flow measured at the LHC indicate that these two simple mod-elsrepresentupperandloweredgesofaregionwheretheelliptic flowoflight(anti-)nucleiaretypicallylocated.

A more sophisticated coalescence approach based on phase-spacedistributionsofprotonsandneutronsgeneratedbythe iEBE-VISHNU hybrid model with AMPT initial conditions provides a gooddescriptionofthedatainthetransverse-momentuminterval 2

≤

pT

<

6 GeV

/

c forthecentralityranges0–20%and20–40%.The samemodelalsoprovidesagooddescriptionofthe(anti-)deuteron

v2 measuredinPb–Pb collisionsat

√

sNN

=

2

.

76 TeV.Thismodel, however, fails in the description of the pT-dependent yield of (anti-)3HemeasuredinPb–Pb collisionsat

√

sNN

=

2

.

76 TeV. Declarationofcompetinginterest

Theauthorsdeclarethattheyhavenoknowncompeting finan-cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.

Acknowledgements

The ALICE Collaboration would like to thank all its engineers andtechnicians fortheir invaluablecontributionstothe construc-tion of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collab-oration gratefully acknowledges the resources and support pro-videdbyall GridcentresandtheWorldwide LHCComputingGrid (WLCG) collaboration. The ALICE Collaboration acknowledges the

following fundingagenciesfortheir supportin buildingand run-ningtheALICEdetector:A.I.AlikhanyanNationalScience Labora-tory(YerevanPhysicsInstitute)Foundation (ANSL),State Commit-teeofScienceandWorldFederationofScientists(WFS),Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung,Austria;MinistryofCommunicationsandHigh Tech-nologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico(CNPq), Fi-nanciadora de Estudose Projetos (Finep),Fundação de Amparo à Pesquisa do Estado de São Paulo(FAPESP) andUniversidade Fed-eraldoRioGrandedoSul(UFRGS),Brazil;MinistryofEducationof China (MOEC), MinistryofScience &Technology ofChina (MSTC) and NationalNatural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Founda-tion,Croatia;CentrodeAplicacionesTecnológicasyDesarrollo Nu-clear (CEADEN), Cubaenergía, Cuba;Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the Villum Fonden and Danish National Research Foundation (DNRF), Den-mark; HelsinkiInstitute ofPhysics(HIP), Finland;Commissariatà l’Énergie Atomique (CEA),Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre Nationalde la Recherche Scientifique (CNRS) and Région des Pays de la Loire, France; Bundesministerium für Bildung und Forschung (BMBF) andGSIHelmholtzzentrumfürSchwerionenforschungGmbH, Ger-many;GeneralSecretariatforResearchandTechnology,Ministryof Education, ResearchandReligions, Greece; NationalResearch De-velopmentandInnovationOffice,Hungary;DepartmentofAtomic Energy, Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Com-mission,GovernmentofIndia(UGC)andCouncil ofScientificand Industrial Research (CSIR), India; Indonesian Institute of Science, Indonesia;CentroFermi- MuseoStoricodellaFisicaeCentroStudi e Ricerche Enrico Fermi and Istituto Nazionale di Fisica Nucle-are (INFN), Italy; Institute for InnovativeScience andTechnology, Nagasaki Institute of Applied Science (IIST), Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and JapanSocietyforthePromotionofScience(JSPS)KAKENHI,Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through FondodeCooperaciónInternacionalenCienciayTecnología (FON-CICYT) andDirección Generalde AsuntosdelPersonal Academico (DGAPA), Mexico; NederlandseOrganisatie voorWetenschappelijk Onderzoek (NWO),Netherlands; TheResearch Council ofNorway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Uni-versidad Católica del Perú, Peru; Ministry of Science andHigher Education andNationalScienceCentre, Poland;Korea Institute of Science andTechnology InformationandNationalResearch Foun-dation of Korea (NRF), Republic of Korea; Ministry of Education andScientificResearch,InstituteofAtomicPhysicsandMinistryof ResearchandInnovationandInstituteofAtomicPhysics,Romania; Joint Institute for Nuclear Research (JINR), Ministry of Education and Science of the Russian Federation, National Research Centre KurchatovInstitute,RussianScienceFoundationandRussian Foun-dation forBasic Research, Russia; Ministryof Education, Science, Research andSport oftheSlovak Republic, Slovakia; National Re-searchFoundation ofSouthAfrica,SouthAfrica;SwedishResearch Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden;EuropeanOrganizationforNuclearResearch,Switzerland; Suranaree University of Technology (SUT), National Science and TechnologyDevelopmentAgency(NSDTA)andOfficeoftheHigher Education Commission under NRU project of Thailand, Thailand; Turkish Atomic Energy Agency(TAEK), Turkey;National Academy ofSciences ofUkraine, Ukraine; ScienceandTechnology Facilities Council (STFC), United Kingdom; National Science Foundation of

theUnitedStatesofAmerica(NSF)andUnitedStatesDepartment of Energy, Office of Nuclear Physics (DOE NP), United States of America.

References

[1]Y.Aoki,S.Borsanyi,S.Durr,Z.Fodor,S.D.Katz,S.Krieg,K.K.Szabo,TheQCD transitiontemperature:resultswithphysicalmassesinthecontinuumlimitII, J.HighEnergyPhys.06(2009)088,arXiv:0903.4155 [hep-lat].

[2]HotQCDCollaboration,T.Bhattacharya,etal.,QCDphasetransitionwithchiral quarksandphysicalquarkmasses,Phys.Rev.Lett.113(2014)082001,arXiv: 1402.5175 [hep-lat].

[3]HotQCDCollaboration,A.Bazavov,etal.,Equationofstatein(2+1)-flavorQCD, Phys.Rev.D90(2014)094503,arXiv:1407.6387 [hep-lat].

[4]J.Cleymans,S.Kabana,I.Kraus,H.Oeschler,K.Redlich,N.Sharma,Antimatter productioninproton-protonandheavy-ioncollisionsatultrarelativistic ener-gies,Phys.Rev.C84(2011)054916,arXiv:1105.3719 [hep-ph].

[5]A.Andronic,P.Braun-Munzinger,J.Stachel,H.Stöcker,Productionoflight nu-clei,hypernucleiandtheirantiparticlesinrelativisticnuclearcollisions,Phys. Lett.B697(2011)203–207,arXiv:1010.2995 [nucl-th].

[6]F.Becattini,E.Grossi,M.Bleicher,J.Steinheimer,R.Stock,Centrality depen-denceofhadronizationandchemicalfreeze-outconditionsinheavyion col-lisionsat√sN N=2.76 TeV,Phys.Rev.C90(2014)054907, arXiv:1405.0710

[nucl-th].

[7]V.Vovchenko,H.Stöcker,Examinationofthesensitivityofthethermalfitsto heavy-ionhadronyielddatatothemodelingoftheeigenvolumeinteractions, Phys.Rev.C95(2017)044904,arXiv:1606.06218 [hep-ph].

[8]A.Andronic, P.Braun-Munzinger, K.Redlich, J.Stachel,Decoding the phase structureofQCDviaparticle productionat highenergy,Nature561(2018) 321–330,arXiv:1710.09425 [nucl-th].

[9]N.Sharma,J.Cleymans,B.Hippolyte,M.Paradza,Acomparisonofp-p,p-Pb, Pb-Pbcollisionsinthethermalmodel:multiplicitydependenceofthermal pa-rameters,Phys.Rev.C99(2019)044914,arXiv:1811.00399 [hep-ph]. [10]S.T.Butler,C.A.Pearson,Deuteronsfromhigh-energyprotonbombardmentof

matter,Phys.Rev.129(1963)836–842.

[11] J.I.Kapusta,Mechanismsfor deuteronproduction inrelativisticnuclear col-lisions, Phys. Rev. C 21 (1980) 1301–1310, https://link.aps.org/doi/10.1103/ PhysRevC.21.1301.

[12]R.Scheibl,U.W.Heinz,Coalescenceandflowinultrarelativisticheavyion col-lisions,Phys.Rev.C59(1999)1585–1602,arXiv:nucl-th/9809092 [nucl-th]. [13]W.Zhao,L.Zhu,H.Zheng,C.M.Ko,H.Song,Spectraandflowoflightnuclei

inrelativisticheavyioncollisionsatenergiesavailableattheBNLRelativistic HeavyIonCollider andat the CERNLargeHadronCollider,Phys. Rev.C98 (2018)054905,arXiv:1807.02813 [nucl-th].

[14]Z.-W.Lin,C.M.Ko,B.-A.Li,B.Zhang,S.Pal,Amulti-phasetransportmodelfor relativisticheavyioncollisions,Phys.Rev.C72(2005)064901,arXiv:nucl-th/ 0411110 [nucl-th].

[15]K.-J.Sun,C.M.Ko,B.Dönigus,Suppressionoflightnucleiproductionin colli-sionsofsmallsystemsattheLargeHadronCollider,Phys.Lett.B792(2019) 132–137,arXiv:1812.05175 [nucl-th].

[16]ALICECollaboration,S.Acharya,etal.,Multiplicitydependenceoflight (anti-)nucleiproduction inp-Pbcollisionsat √sNN=5.02 TeV,arXiv:1906.03136

[nucl-ex].

[17]J.-Y.Ollitrault,Anisotropyasasignatureoftransversecollectiveflow,Phys.Rev. D46(1992)229–245.

[18]PHENIX Collaboration,S. Afanasiev, et al.,Ellipticflow for phi mesonsand (anti)deuteronsinAu+Aucollisionsat √sNN=200 GeV,Phys.Rev.Lett.99

(2007)052301,arXiv:nucl-ex/0703024 [NUCL-EX].

[19]STARCollaboration,L.Adamczyk,etal.,Measurementofellipticflowoflight nucleiat √sN N=200,62.4,39,27,19.6,11.5,and7.7 GeVat theBNL

Rel-ativisticHeavyIonCollider,Phys.Rev.C94(2016)034908,arXiv:1601.07052 [nucl-ex].

[20]E.Schnedermann,J.Sollfrank,U.W.Heinz,Thermalphenomenologyofhadrons from200-A/GeVS+Scollisions,Phys.Rev.C48(1993)2462–2475,arXiv:nucl -th/9307020 [nucl-th].

[21]STARCollaboration,C.Adler,etal.,IdentifiedparticleellipticflowinAu+Au collisionsat√sNN=130 GeV,Phys.Rev.Lett.87(2001)182301,arXiv:nucl-ex/

0107003 [nucl-ex].

[22] P.J.Siemens,J.O.Rasmussen,Evidenceforablastwavefromcompressed nu-clear matter, Phys. Rev.Lett. 42(1979) 880–883,https://link.aps.org/doi/10. 1103/PhysRevLett.42.880.

[23]ALICECollaboration,S.Acharya,etal.,Measurementofdeuteronspectraand ellipticflowinPb-Pbcollisionsat√sNN=2.76 TeV attheLHC,Eur.Phys.J.C

77(2017)658,arXiv:1707.07304 [nucl-ex].

[24]D.Molnar,S.A.Voloshin,Ellipticflowatlargetransversemomentafromquark coalescence,Phys.Rev.Lett.91(2003)092301,arXiv:nucl-th/0302014 [nucl-th]. [25]ALICECollaboration,K.Aamodt,etal.,TheALICEexperimentattheCERNLHC,

J.Instrum.3(2008)S08002.

[26]ALICECollaboration,B.Abelev,etal.,PerformanceoftheALICEExperimentat theCERNLHC,Int.J.Mod.Phys.A29(2014)1430044,arXiv:1402.4476 [nucl -ex].

[27]J.Alme,etal.,TheALICETPC,alarge3-dimensionaltrackingdevicewithfast readoutforultra-highmultiplicityevents,Nucl.Instrum.MethodsA622(2010) 316–367,arXiv:1001.1950 [physics.ins-det].

[28]ALICECollaboration,S.Acharya,etal.,Transversemomentumspectraand nu-clearmodificationfactorsofchargedparticlesinpp,p-PbandPb-Pbcollisions attheLHC,J.HighEnergyPhys.11(2018)013,arXiv:1802.09145 [nucl-ex]. [29]ALICECollaboration,E.Abbas,etal.,PerformanceoftheALICEVZEROsystem,

J.Instrum.8(2013)P10016,arXiv:1306.3130 [nucl-ex].

[30]ALICECollaboration,B.Abelev,etal.,CentralitydeterminationofPb-Pb colli-sionsat√sN N=2.76 TeV withALICE,Phys.Rev.C88(2013)044909,arXiv:

1301.4361 [nucl-ex].

[31] ALICECollaboration,S.Acharya, etal.,Centralitydeterminationinheavyion collisions,https://cds.cern.ch/record/2636623.

[32]ALICE Collaboration,S.Acharya, etal., Productionof4_{He and}4_{He inPb-Pb}

collisionsat√sNN=2.76 TeV attheLHC,Nucl.Phys.A971(2018)1–20,arXiv:

1710.07531 [nucl-ex].

[33]ALICECollaboration,B.B.Abelev,etal.,Ellipticflowofidentifiedhadronsin Pb-Pbcollisionsat√sNN=2.76 TeV,J.HighEnergyPhys.06(2015)190,arXiv:

1405.4632 [nucl-ex].

[34]ALICECollaboration,S.Acharya,etal.,Anisotropicflowofidentifiedparticles inPb-Pbcollisionsat√sNN=5.02 TeV,J.HighEnergyPhys.09(2018)006,

arXiv:1805.04390 [nucl-ex].

[35]M.RihanHaque,C.Jena,B.Mohanty,Areviewofellipticflowoflightnuclei inheavy-ioncollisionsatRHICandLHCenergies,Adv.HighEnergyPhys.2017 (2017)1248563,arXiv:1707.09192 [nucl-ex].

[36]S. Voloshin,Y. Zhang,FlowstudyinrelativisticnuclearcollisionsbyFourier expansionofazimuthal particledistributions,Z.Phys. C70(1996)665–672, arXiv:hep-ph/9407282 [hep-ph].

[37] A.M.Poskanzer,S.A.Voloshin,Methodsforanalyzinganisotropicflowin rel-ativisticnuclearcollisions,Phys.Rev.C58(1998)1671–1678,https://link.aps. org/doi/10.1103/PhysRevC.58.1671.

[38] I.Selyuzhenkov,S.Voloshin,Effectsofnonuniformacceptanceinanisotropic flowmeasurements,Phys.Rev.C77(2008)034904,https://link.aps.org/doi/10. 1103/PhysRevC.77.034904.

[39] X.-N.Wang,M.Gyulassy,Hijing:aMonteCarlomodelformultiplejet produc-tioninpp,pA,andAA collisions,Phys.Rev.D44(1991)3501–3516,https:// link.aps.org/doi/10.1103/PhysRevD.44.3501.

[40] R.Brun,F.Bruyant,F.Carminati,S.Giani,M.Maire,A.McPherson,G.Patrick, L.Urban,GEANTdetectordescriptionandsimulationtool,programlibrarylong write-up,https://doi.org/10.17181/CERN.MUHF.DMJ1.

[41]ALICECollaboration,J.Adam,etal.,Productionoflightnucleiandanti-nucleiin ppandPb-PbcollisionsatenergiesavailableattheCERNLargeHadronCollider, Phys.Rev.C93 (2)(2016)024917,arXiv:1506.08951 [nucl-ex].

[42]ALICECollaboration,J.Adam,etal.,3

H and3¯H productioninPb-Pbcollisions

at√sNN=2.76TeV,Phys.Lett.B754(2016)360–372,arXiv:1506.08453 [nucl

-ex].

[43]ALICECollaboration,S.Acharya,etal.,Productionofchargedpions,kaonsand (anti-)protonsinPb-Pbandinelasticppcollisionsat√sNN=5.02 TeV,arXiv:

1910.07678 [nucl-ex].

[44]S.Jeon,U.Heinz,Introductiontohydrodynamics,Int.J.Mod.Phys.E24(2015) 1530010,arXiv:1503.03931 [hep-ph].

[45]ALICECollaboration,B.Abelev,etal.,Ellipticflowofidentifiedhadronsin Pb-Pbcollisionsat√sNN=2.76 TeV,J.HighEnergyPhys.06(2015)190,arXiv:

1405.4632 [nucl-ex].

[46]D.Molnar,S.A.Voloshin,Ellipticflowatlargetransversemomentafromquark coalescence,Phys.Rev.Lett.91(2003)092301,arXiv:nucl-th/0302014 [nucl-th].

ALICECollaboration

S. Acharya

141

,

D. Adamová

93

,

S.P. Adhya

141

,

A. Adler

73

,

J. Adolfsson

79

, M.M. Aggarwal

98

,

G. Aglieri Rinella

34

, M. Agnello

31

,

N. Agrawal

10

,

48

,

53

, Z. Ahammed

141

, S. Ahmad

17

,

S.U. Ahn

75

,

A. Akindinov

90

,

M. Al-Turany

105

,

S.N. Alam

141

,

D.S.D. Albuquerque

122

,

D. Aleksandrov

86

,

B. Alessandro

58

,

H.M. Alfanda

6

,

R. Alfaro Molina

71

,

B. Ali

17

,

Y. Ali

15

,

A. Alici

10

,

27

,

53

, A. Alkin

2

,

J. Alme

22

,

T. Alt

68

,

L. Altenkamper

22

, I. Altsybeev

112

,

M.N. Anaam

6

,

C. Andrei

47

,

D. Andreou

34

,

H.A. Andrews

109

,

A. Andronic

144

,

M. Angeletti

34

,

V. Anguelov

102

,

C. Anson

16

,

T. Antiˇci ´c

106

,

F. Antinori

56

,

P. Antonioli

53

,

R. Anwar

125

, N. Apadula

78

,

L. Aphecetche

114

,

H. Appelshäuser

68

,

S. Arcelli

27

,

R. Arnaldi

58

,

M. Arratia

78

, I.C. Arsene

21

, M. Arslandok

102

, A. Augustinus

34

, R. Averbeck

105

,

S. Aziz

61

,

M.D. Azmi

17

,

A. Badalà

55

,

Y.W. Baek

40

,

S. Bagnasco

58

,

X. Bai

105

, R. Bailhache

68

,

R. Bala

99

,

A. Baldisseri

137

,

M. Ball

42

,

S. Balouza

103

,

R.C. Baral

84

,

R. Barbera

28

, L. Barioglio

26

,

G.G. Barnaföldi

145

,

L.S. Barnby

92

,

V. Barret

134

,

P. Bartalini

6

,

K. Barth

34

,

E. Bartsch

68

, F. Baruffaldi

29

, N. Bastid

134

,

S. Basu

143

,

G. Batigne

114

,

B. Batyunya

74

, P.C. Batzing

21

,

D. Bauri

48

, J.L. Bazo Alba

110

,

I.G. Bearden

87

,

C. Bedda

63

,

N.K. Behera

60

,

I. Belikov

136

, F. Bellini

34

, R. Bellwied

125

, V. Belyaev

91

,

G. Bencedi

145

,

S. Beole

26

,

A. Bercuci

47

,

Y. Berdnikov

96

,

D. Berenyi

145

,

R.A. Bertens

130

,

D. Berzano

58

,

M.G. Besoiu

67

,

L. Betev

34

,

A. Bhasin

99

,

I.R. Bhat

99

,

M.A. Bhat

3

,

H. Bhatt

48

,

B. Bhattacharjee

41

, A. Bianchi

26

,

L. Bianchi

26

,

N. Bianchi

51

, J. Bielˇcík

37

, J. Bielˇcíková

93

,

A. Bilandzic

103

,

117

,

G. Biro

145

,

R. Biswas

3

,

S. Biswas

3

,

J.T. Blair

119

, D. Blau

86

, C. Blume

68

,

G. Boca

139

,

F. Bock

34

,

94

,

A. Bogdanov

91

,

L. Boldizsár

145

,

A. Bolozdynya

91

,

M. Bombara

38

, G. Bonomi

140

,

H. Borel

137

,

A. Borissov

91

,

144

,

M. Borri

127

,

H. Bossi

146

,

E. Botta

26

,

L. Bratrud

68

, P. Braun-Munzinger

105

, M. Bregant

121

,

T.A. Broker

68

,

M. Broz

37

, E.J. Brucken

43

,

E. Bruna

58

,

G.E. Bruno

33

,

104

,

M.D. Buckland

127

,

D. Budnikov

107

,

H. Buesching

68

,

S. Bufalino

31

,

O. Bugnon

114

,

P. Buhler

113

,

P. Buncic

34

, Z. Buthelezi

72

,

J.B. Butt

15

, J.T. Buxton

95

,

S.A. Bysiak

118

,

D. Caffarri

88

,

A. Caliva

105

,

E. Calvo Villar

110

,

R.S. Camacho

44

,

P. Camerini

25

, A.A. Capon

113

,

F. Carnesecchi

10

, J. Castillo Castellanos

137

,

A.J. Castro

130

, E.A.R. Casula

54

,

F. Catalano

31

,

C. Ceballos Sanchez

52

,

P. Chakraborty

48

,

S. Chandra

141

, B. Chang

126

,

W. Chang

6

,

S. Chapeland

34

,

M. Chartier

127

,

S. Chattopadhyay

141

, S. Chattopadhyay

108

, A. Chauvin

24

, C. Cheshkov

135

,

B. Cheynis

135

,

V. Chibante Barroso

34

,

D.D. Chinellato

122

, S. Cho

60

, P. Chochula

34

,

T. Chowdhury

134

,

P. Christakoglou

88

,

C.H. Christensen

87

, P. Christiansen

79

, T. Chujo

133

,

C. Cicalo

54

,

L. Cifarelli

10

,

27

, F. Cindolo

53

,

J. Cleymans

124

,

F. Colamaria

52

, D. Colella

52

,

A. Collu

78

, M. Colocci

27

,

M. Concas

58

,

ii

,

G. Conesa Balbastre

77

, Z. Conesa del Valle

61

,

G. Contin

59

,

127

,

J.G. Contreras

37

,

T.M. Cormier

94

,

Y. Corrales Morales

26

,

58

,

P. Cortese

32

,

M.R. Cosentino

123

, F. Costa

34

, S. Costanza

139

,

J. Crkovská

61

,

P. Crochet

134

,

E. Cuautle

69

,

L. Cunqueiro

94

,

D. Dabrowski

142

, T. Dahms

103

,

117

,

A. Dainese

56

,

F.P.A. Damas

114

,

137

,

S. Dani

65

,

M.C. Danisch

102

, A. Danu

67

, D. Das

108

,

I. Das

108

,

P. Das

3

,

S. Das

3

,

A. Dash

84

, S. Dash

48

,

A. Dashi

103

,

S. De

49

,

84

,

A. De Caro

30

,

G. de Cataldo

52

,

C. de Conti

121

,

J. de Cuveland

39

,

A. De Falco

24

, D. De Gruttola

10

, N. De Marco

58

,

S. De Pasquale

30

,

R.D. De Souza

122

,

S. Deb

49

,

H.F. Degenhardt

121

,

K.R. Deja

142

, A. Deloff

83

,

S. Delsanto

26

,

131

,

D. Devetak

105

,

P. Dhankher

48

,

D. Di Bari

33

,

A. Di Mauro

34

, R.A. Diaz

8

,

T. Dietel

124

,

P. Dillenseger

68

,

Y. Ding

6

,

R. Divià

34

,

Ø. Djuvsland

22

,

U. Dmitrieva

62

,

A. Dobrin

34

,

67

,

B. Dönigus

68

,

O. Dordic

21

,

A.K. Dubey

141

, A. Dubla

105

,

S. Dudi

98

,

M. Dukhishyam

84

,

P. Dupieux

134

, R.J. Ehlers

146

, D. Elia

52

,

H. Engel

73

, E. Epple

146

,

B. Erazmus

114

,

F. Erhardt

97

,

A. Erokhin

112

,

M.R. Ersdal

22

,

B. Espagnon

61

, G. Eulisse

34

,

J. Eum

18

,

D. Evans

109

,

S. Evdokimov

89

,

L. Fabbietti

103

,

117

, M. Faggin

29

,

J. Faivre

77

,

A. Fantoni

51

,

M. Fasel

94

,

P. Fecchio

31

, A. Feliciello

58

,

G. Feofilov

112

, A. Fernández Téllez

44

,

A. Ferrero

137

,

A. Ferretti

26

,

A. Festanti

34

,

V.J.G. Feuillard

102

,

J. Figiel

118

,

S. Filchagin

107

,

D. Finogeev

62

,

F.M. Fionda

22

,

G. Fiorenza

52

,

F. Flor

125

,

S. Foertsch

72

, P. Foka

105

,

S. Fokin

86

,

E. Fragiacomo

59

, U. Frankenfeld

105

,

G.G. Fronze

26

,

U. Fuchs

34

, C. Furget

77

,

A. Furs

62

,

M. Fusco Girard

30

,

J.J. Gaardhøje

87

, M. Gagliardi

26

,

A.M. Gago

110

,

A. Gal

136

, C.D. Galvan

120

, P. Ganoti

82

,

C. Garabatos

105

,

E. Garcia-Solis

11

,

K. Garg

28

,

C. Gargiulo

34

,

A. Garibli

85

, K. Garner

144

,

P. Gasik

103

,

117

,

E.F. Gauger

119

,

M.B. Gay Ducati

70

,

M. Germain

114

,

J. Ghosh

108

,

P. Ghosh

141

,

S.K. Ghosh

3

, P. Gianotti

51

, P. Giubellino

58

,

105

,

P. Giubilato

29

,

P. Glässel

102

,

D.M. Goméz Coral

71

,

A. Gomez Ramirez

73

,

V. Gonzalez

105

,

P. González-Zamora

44

,

S. Gorbunov

39

,

L. Görlich

118

,

S. Gotovac

35

,

V. Grabski

71

, L.K. Graczykowski

142

,

K.L. Graham

109

, L. Greiner

78

, A. Grelli

63

,

C. Grigoras

34

,

V. Grigoriev

91

,

A. Grigoryan

1

,

S. Grigoryan

74

, O.S. Groettvik

22

,

J.M. Gronefeld

105

,

F. Grosa

31

,

J.F. Grosse-Oetringhaus

34

,

R. Grosso

105

,

R. Guernane

77

, B. Guerzoni

27

, M. Guittiere

114

,

K. Gulbrandsen

87

,

T. Gunji

132

,

A. Gupta

99

, R. Gupta

99

,

I.B. Guzman

44

, R. Haake

146

,

M.K. Habib

105

,

C. Hadjidakis

61

, H. Hamagaki

80

,

G. Hamar

145

,

M. Hamid

6

,

R. Hannigan

119

,

M.R. Haque

63

,

A. Harlenderova

105

, J.W. Harris

146

,

A. Harton

11

,

J.A. Hasenbichler

34

,

H. Hassan

77

,

D. Hatzifotiadou

10

,

53

,

P. Hauer

42

,

S. Hayashi

132

,

A.D.L.B. Hechavarria

144

, S.T. Heckel

68

,

E. Hellbär

68

,

H. Helstrup

36

,