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

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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 ra c t

Articlehistory:

Received16November2019

Receivedinrevisedform21March2020 Accepted3April2020

Availableonline8April2020 Editor: L.Rolandi

Theellipticflow(v2)of(anti-)³HeismeasuredinPb–Pbcollisionsat√_s

NN=⁵.02 TeV inthetransverse- momentum(pT) rangeof2–6GeV/cfor 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-)³He.

Theellipticflowof(anti-)³HeisunderestimatedbytheBlast-Wavemodelandoverestimatedbyasimple coalescenceapproachbasedonnucleonscaling.Theellipticflowof(anti-)³Hemeasuredinthecentrality classes0–20%and20–40%iswelldescribedbyamoresophisticatedcoalescencemodelwherethephase- 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,andtheirantiparticlesareproducedinadditiontootherpar- 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-mailaddress:alice-publications@cern.ch.

arenotaddressedbythismodel.Ithasbeenconjecturedthatsuch objectscouldbeproducedatthephasetransitionascompactcol- orlessquarkclusterswhichareexpectedtointeractlittlewiththe surrounding matter [8]. In thecoalescence approach, light nuclei areassumedtobeformedbythecoalescenceofprotonsandneu- tronswhichare closeinphase-spaceatkinetic freeze-out[11].In thesimpleversionofthismodel,nucleonsaretreatedaspoint-like particlesandthecoalescenceprocess isassumedtohappenifthe differencebetweentheir momentaissmallerthanagiventhresh- 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-mechanicalpropertiesofnucleonsandnu- cleiare takenintoaccount andthecoalescence probabilityiscal- culated from the overlapbetweenthe wave functionsofprotons andneutrons which are mapped ontothe Wigner densityof the nucleus.Thephase-spacedistributionsofprotonsandneutronsat thekineticfreeze-outaregeneratedfromparticleproductionmod- els,such asA Multi-PhaseTransportModel (AMPT)[14], orfrom hydrodynamicalsimulationscoupledtohadronictransportmodels [13]. The advanced coalescence model qualitatively describesthe deuteron-to-protonand³He-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,withslightde- viationsforhigherpT/A[19].Theflowofidentifiedhadronsisof- 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-outsur- face.The Blast-Wavemodel,however, failsinreproducing the v2 oflight nuclei measured inAu–Au collisions at√

sNN=^{200 GeV} [19],which isinsteadwell describedby amore sophisticatedco- alescencemodelwherethe phase-spacedistributions ofnucleons aregeneratedusingthestring-meltingversionofAMPT[14].

Theellipticflowofdandd wasmeasuredbytheALICECollab- orationinPb–Pb collisionsat√

sNN=².76 TeV inthetransverse- 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 p_T 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], failsinre- 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 betweentheinvariantyieldofdeuteronsandthesquareofthein- 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.Thismea- surementcomplementsthepictureobtainedfromthatofthepro- 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.TheTPCisthelargestde- tectorinthe ALICEcentral barrel,witha pseudorapiditycoverage

|

η

_|<0.9. Itisusedfortrackreconstruction,charged-particlemo- mentummeasurementandforparticleidentificationviathemea- 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/dxresolutiondepends oncentralityandisintherange5–6.5%forminimumionizingpar- ticles crossing the full volume of the TPC [26]. Collision events are triggeredby twoplastic scintillatorarrays, V0AandV0C [29], located onbothsidesofthe interactionpoint,covering thepseu- dorapidity regions −³.7<

η

<−¹.7 and 2.8<

η

<5.1. Each V0 array consistsoffourringsintheradial direction,witheach ring comprisingeightcellswiththesameazimuthalsize.TheV0scin- 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 requirescoincidentsignalsintheV0de- 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 withmulti- 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 and2, 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, N^TPC_cls ,ofatleast 70 out of a maximum of 159, and in the ITS, N^ITS_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, N^TPC_cls (dE/dx) isrequired to be larger than50. Good quality of the track fit is also required, expressed by

χ

²/N^TPC_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-reconstructionef- ficiency, whichis largerthan 80%, anda resolutioninthe dE/dx measured intheTPCofabout6% inthecentrality andpT ranges usedforthismeasurement.

TheexpectedaveragedE/dxfor(anti-)³He,dE/dx³He,isgiven by the Bethe formula and the standard deviation of the distri- bution of dE/dx− ^dE/dx³He, denoted

σ

_dE^3He_/dx, is theTPC dE/dx resolution measured for (anti-)³He. For the (anti-)³He identifica- tion, the dE/dx measured in the TPC is required to be within 3

σ

_dE^3He_/dx from the expected average for ³He. The distributions

Fig. 1.Distributions of

dE/dx− dE/dx³He

/σ_dE^3He_/dxmeasuredintheTPCforthetransverse-momentumranges2 ≤pT<3 GeV/c(left)and3≤pT<4 GeV/c(right).The verticalbarsrepresentthestatisticaluncertaintiesofthedata.Thebluedottedandthereddash-dottedlinesindicatethe³Hand³Hecontributionswhiletheblacksolid linesshowthesumofboth.Therangesusedforthesignalextractionareindicatedbytheverticalblack-dottedlines.

of

dE/dx− ^dE/dx³He

/

σ

_dE^3He_/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-)³His estimated by fitting the measured

dE/dx− ^dE/dx³He

/

σ

_dE^3He_/dx

distributioninagivenpT rangeusingtwoGaussianfunctions,one for(anti-)³Handtheother for(anti-)³He.The(anti-)³Hcontribu- tion is subtracted fromthe distribution to extract the (anti-)³He signal in the range within ±³

σ

_dE^3He_/dx. The contamination from (anti-)³Hisnegligiblefor pT>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-)³Hebyafactor∼^{300 [32].}

3.3.Secondary³Hefromspallationprocesses

Themain backgroundfor thismeasurement isrepresented by secondary ³He produced by spallation reactions in the interac- tionsbetweenprimaryparticlesandnucleiinthedetectormaterial orinthe beampipe. Thisbackgroundsource isrelevant only for 3He,whilethiseffectisnegligibleforanti-³He.Nuclearfragments emittedin spallation processeshavealmost uniform angulardis- tributions withrespect to the directionof the incomingparticle, whileprimary ³He tracks originate fromthe primary vertex. The contributionof secondary ³He produced by spallationcan be in- vestigatedfromthe DCA_xy distribution,whichhas apeak around zero for primary ³He and is almost flat for secondary ³He. The DCA_xydistributionsfor³Hecandidatesmeasuredinthetransverse- 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 ³He candidates, given by −²≤

dE/dx− ^dE/dx³He

/

σ

_dE^3He_/dx

<3. Thisasymmetric rangeis used toincrease thepurity ofthe 3He sample by suppressing the ³H contamination. The contribu- tion from secondary ³He 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 ³Hefromspal- lation is negligible. This is possible because the elliptic flow of 3He and ³He areconsistent within thestatisticaluncertainties in

Fig. 2.DCAxy distributionsof³Hecandidates, selectedrequiring −²< (dE/dx− dE/dx³He)/σ_dE^3He_/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. p_T>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 ofpro- tons and antiprotons, deuterons and antideuterons with increas- ingcenter-of-mass energyatRHICgoing from√

s_NN=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)

wheren 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-planeresolutionR2 ofthesecondharmonicasafunctionofthecol- lisioncentrality.

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

v₂

{

^EP

, | η | >

0

.

9

} (

p_T

) = π

4R₂

N_in-plane

(

pT

) −

^Nout-of-plane

(

pT

)

N_in-plane

(

p_T

) +

^Nout-of-plane

(

p_T

) ,

(2) where the |

η

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

ϕ

_{|= |}

ϕ

₋^EP₂ |<45^◦or|

ϕ

_{|= |}

ϕ

₋^EP₂ |>135^◦,and

‘out-of-plane’otherwise,where^EP₂ istheorientationoftheevent plane.The latterisreconstructed usingtheV0detectors.Thecal- ibrated amplitude ofthe signal measured in each cell ofthe V0 arrays is used as a weight w_cell in the construction of the flow vector Q2[37]

Q2

=

N_cell

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.Forthelat- tertwomeasurements, asetofreconstructedchargedtrackswith 0.2 ≤^pT<20 GeV/c and|

η

|<0.8 isused.Minimal qualitycrite- riaareappliedtothesetracks,suchastherequirementofhavinga numberofTPCclusterslargerthan70anda

χ

²/N_cls^TPC<4.Thesec- ondharmonicevent-planeresolutionasafunctionofthecollision centralityisshowninFig.3.

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

v₂

(

p_T

) =

ivⁱ₂

(

p_T

) ·

^N₍ⁱ_anti-)3He

(

p_T

)

iNⁱ

(anti-)³He

(

pT

) ,

(6)

where vⁱ₂(p_T) is the elliptic flow measured in a given p_T range and in the centrality interval i, and Nⁱ

(anti-)³He is the number of (anti-)³HecandidatesforthesamecentralityandpT range.

4. Systematicuncertainties

The mainsources ofsystematic uncertaintiesin thismeasure- ment are relatedtothe eventselection criteria, trackreconstruc- tion, particleidentification, occupancyeffects intheTPC, andthe subtractionofthefeed-downcontributionfromweakdecaysofhy- pertritons.Exceptforthesystematicuncertaintyduetotheevent selection, allother contributionsareestimatedusingMonteCarlo (MC) simulations based on the HIJING generator [39]. Simulated eventsareenriched byaninjectedsample of(anti-)(hyper-)nuclei generatedwithaflatpTdistributioninthetransverse-momentum range 0< p_T<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-)³He is correctedusingcentralityandpT-dependentweightstoreproduce itsmeasuredshape,whichisdescribedbytheBlast-Wavefunction.

The parameters are taken from the (anti-)³He measurement in Pb–Pb collisionsat√

sNN=².76 TeV [41] assumingthesamespec- tralshapeinPb–Pb collisionsat√

sNN=⁵.02 TeV.Thesystematic uncertainties estimatedusingtheMC simulationsarefoundtobe independent ontheinput parametrizationofthe (anti-)³He spec- trum.Agoodmatchingbetweenthedistributionsofvariablesused fortrackselectionandparticleidentificationisfoundbetweendata andMCsimulations.Thisguaranteesthereliabilityofthedetector response descriptionandofthesystematicuncertaintiesobtained basedonMCsimulations.

4.1. Systematicuncertaintiesduetotheeventselectioncriteria

Theeffectofdifferenteventselectioncriteriaisstudiedbycom- 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.

Thesystematicuncertaintyrelatedtoeventselectioncriteriaisas- 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-)³He inthesim- ulation ascompared to data to reduce the interference between statisticalfluctuationsandsystematicuncertainties. The sameaz- imuthal asymmetry as measured in data in each centrality and pT rangeisartificiallycreatedfortheinjected(anti-)³He withre- spectto a randomlyoriented eventplane by rejecting a fraction ofthe out-of-plane (anti-)³He. 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 usingauniformprobabilitydistri- 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 spreadofthedifferentmeasurementsisonlyduetostatisticalfluc- tuations,themeanoftheGaussiandistributionisconsideredasthe bestestimate ofthereconstructed v₂.Thedifferencebetweenthe injectedv2inthesimulationandthemeanoftheGaussianspread ofthe measurements is taken asthe systematic uncertainty due totracking andPID.This uncertaintyranges between1% and4%, depending on p_T and centrality.An additional componentto the trackinguncertaintyoriginatesfromthedifferencebetweenthev2 measured usingthe positive andnegative pseudorapidity regions ofthe TPC. Thiscontributioncannot beestimated fromdatadue tothelimitednumberof(anti-)³Heandisassumedtobeidentical tothatofthe protonv2 measurement,whichis2% [34]. Thelat- 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 efficiencyfordiffer- entcharged-particlemultiplicities.Thesametrackselectioncriteria usedindataare appliedtothe reconstructedtracksin thesimu- 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 correspondstothemaxi- mumvariationrangeofv2.Thesystematicuncertaintyfromoccu- 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-)³Hdecaysinthere- constructedtracksample iscalculatedusingMC simulations.This fractionisabout 6% forthe centralityrange 0–20%and ∼^{5% for} thecentralityranges20–40%and40–60%,slightlyincreasingwith

Table 1

Summaryofsystematicuncertainties.Therangesrepresentthe minimumandmaximumuncertaintiesinthecasewherethe systematicuncertaintiesdependonpTandcentrality.

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%.Thestatisticalun- certaintiesareshownasverticalbars,systematicuncertaintiesasboxes.

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

√s_NN=².76 TeV [42],assumingthattheyieldratiobetween(anti- )³Hand(anti-)³HedoesnotdiffersignificantlyfromthatinPb–Pb collisions at√

sNN=⁵.02 TeV,whichisnotpublished yet.The v2 of(anti-)³Hefromthe(anti-)³Hdecayisassumedtobewithinthe rangeof±^{50% withrespectto the v}2 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% inallcentral-} ityranges,almostindependentofp_T.

The different contributions to the systematic uncertainties of thismeasurementaresummarizedinTable1.

5. Results

5.1. Experimentalresults

Theelliptic flowof(anti-)³He 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<p_T<3 GeV/c isdoneus- ing only ³He. 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-)³Heellipticflowiscomparedtothatofpions,kaons, and protons measured using the scalar-product method at the

Fig. 5.Comparison betweentheellipticflowof(anti-)³Hemeasuredusingtheevent-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-)³Hedividedbythenumberofconstituentquarks(nq)asafunctionofpT/nq(upperpanels) andtransversekineticenergyperconstituentquarkE^kin_T /nq (lowerpanels)forthecentralityclasses0–20% (left),20–40% (middle)and40–60% (right).Seetextfordetails.

Verticalbarsandboxesrepresentthestatisticalandsystematicuncertainties,respectively.

samecenter-of-mass energy[34] inFig. 5. Giventhegoodevent- planeresolutionshowninFig.3andthelargestatisticaluncertain- tiesofthe(anti-)³Hev2measurements,thedifferencebetweenthe scalar-productandevent-planemethodtocalculatethe(anti-)³He 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 p_T spec- tratakenfrom[43] asweights.Aclearmassorderingisobserved for p_T<3 GeV/c,consistentwiththeexpectationsfromrelativis- 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-)³He,pions,kaons,andprotonsareshowninFig.6asafunc- tion of pT/nq (upper panels), and transverse kinetic energy per constituent quark E^kin_T /nq (lower panels). The transverse kinetic energyisdefinedasE^kin_T =

m²+^p2_T−^{m,wheremisthemassof} theparticle.Theviolationofnq scalingforthemeasuredrangeof p_T/n_q⁰.7 GeV/c, alreadyestablished forthe ellipticflow mea- surementsofidentifiedhadronsattheLHC[23,34,45],isobserved alsofor(anti-)³He.Then_q scalingatlarger p_T/n_qcannotbetested 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 √

s_NN=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≤^ppT<2.5 GeV/c,respectively,andinthesame centralityclasses.ThefourparametersoftheBlast-Wavefitsrepre- sentthekineticfreeze-outtemperature(T_kin),themeantransverse expansion rapidity (

ρ

0), the amplitudeof its azimuthal variation (

ρ

a),andthevariationintheazimuthaldensityofthesource(s2), asdescribedin[21]. ThevaluesoftheBlast-Waveparametersex- 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-)³Hewithtrans- versemomentum pTisproportionaltotheproductoftheinvariant yieldsofitsconstituentnucleonswithtransversemomentum p_T/3 andonisospinsymmetry,forwhichtheprotonandneutronv2 are

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

Table 2

Blast-Wave parametersextractedfromthe simultaneousfitsofthe pT spectraandv2ofpions,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√

s_NN=⁵.02 TeV [34] usingthescaling law[46]

v_2,3He

(

p_T

) =

^3v2,p

(

pT

/

3

) +

^3v3_2,p

(

pT

/

3

)

1

+

^6v2_2,p

(

p_T

/

3

) .

(7)

Fig. 7 shows the comparison of the (anti-)³He v2 measure- mentswiththepredictionsoftheBlast-Wavemodelandthesim- 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.FortheBlast- Wave model, the p_T 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

√s_NN=².76 TeV,asobservedforlighterhadrons[43].Theproton spectrummeasured in Pb–Pb collisions at√

s_NN=⁵.02 TeV [43], withpT scaled by A=^{3,is usedasaweight forthe}coalescence 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-)deuteronp_Tdistributionswereslightly underestimatedfor pT < 2GeV/cinthe samecentralityintervals [23].Similarlytotheresultspresentedinthispaperfor(anti-)³He, thepredictionsfromthesimplecoalescence modeloverestimated the (anti-)deuteron v₂ in all centrality intervals. In general, the measurementsof(anti-)deuteronand(anti-)³Heellipticflowatthe

Fig. 8. Elliptic flow of(anti-)³He measured inthe centrality classes0–20% and 20–40% in comparisonwith thepredictionsfromacoalescencemodelbased on phase-spacedistributionsofprotonsandneutronsgeneratedfromtheiEBE-VISHNU hybridmodelwithAMPTinitialconditions[13].Themodelpredictionsareshown aslinesandthebandsrepresenttheirstatisticaluncertainties.Thedifferencesbe- 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 p_T 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.Thecomparisonofthemeasurementpresentedinthispa- 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 showsthedifferencesbe- tween the data and the model forthese two centrality intervals calculated taking the weighted average of the model in each p_T 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 distributionsofprotonsandneutronsaregeneratedfromtheiEBE- VISHNUhybridmodelwithAMPTinitialconditions[13].Although this model underestimates the yield of (anti-)³He measured in Pb–Pb collisionsat√

sNN=².76 TeV inthetransverse-momentum rangeof 2 <pT<7 GeV/c by almost a factor oftwo [13], it is abletoreproducequantitativelytheellipticflowmeasurements in the centrality classes 0–20% and 20–40% presented here. More- over,thismodelprovidesagooddescriptionofthe p_T 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-)³Heellipticflow 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,asexpectedfromrela- tivistichydrodynamics.Thescalingbehavior of v2 withthenum- ber of constituent quarks is violated for the measured range of p_T/n_q⁰.7 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-Wavepre- 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- spacedistributionsofprotonsandneutronsgeneratedbytheiEBE- VISHNU hybrid model with AMPT initial conditions provides a gooddescriptionofthedatainthetransverse-momentuminterval 2≤^pT<6 GeV/cforthecentralityranges0–20%and20–40%.The samemodelalsoprovidesagooddescriptionofthe(anti-)deuteron v₂ measuredinPb–Pb collisionsat√

s_NN=².76 TeV.Thismodel, however, fails in the description of the pT-dependent yield of (anti-)³HemeasuredinPb–Pb collisionsat√

sNN=².76 TeV.

Declarationofcompetinginterest

Theauthorsdeclarethattheyhavenoknowncompetingfinan- cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.

Acknowledgements

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

following fundingagenciesfortheir supportin buildingandrun- ningtheALICEdetector:A.I.AlikhanyanNationalScienceLabora- 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;MinistryofCommunicationsandHighTech- 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) andUniversidadeFed- 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;CentrodeAplicacionesTecnológicasyDesarrolloNu- 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; NationalResearchDe- 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,RussianScienceFoundationandRussianFoun- dation forBasic Research, Russia; Ministryof Education, Science, Research andSport oftheSlovak Republic, Slovakia; NationalRe- 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