Anisotropic flow in Xe–Xe collisions at √sNN = 5.44 TeV

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Physics Letters B

www.elsevier.com/locate/physletb

Anisotropic flow in Xe–Xe collisions at √

s _NN = ⁵ . 44 TeV

.ALICE Collaboration

a r t i c l e i n f o a b s t ra c t

Articlehistory:

Received23May2018

Receivedinrevisedform14June2018 Accepted25June2018

Availableonline30June2018 Editor:L.Rolandi

The first measurements of anisotropic flow coefficients vn for mid-rapidity charged particlesin Xe–

Xecollisions at√_s

NN=⁵.44 TeV arepresented.Comparing thesemeasurements tothosefromPb–Pb collisions at √_s

NN=⁵.02 TeV, v2 is found to be suppressed for mid-central collisions at the same centrality, and enhancedfor central collisions.Thevalues ofv3 aregenerally largerinXe–Xe thanin Pb–Pb at a givencentrality. Theseobservations are consistent with expectations from hydrodynamic predictions. When both v2 and v3 are divided by their corresponding eccentricities for avariety of initial state models,they generally scale with transverse density whencomparing Xe–Xe and Pb–Pb, with somedeviations observed incentral Xe–Xe and Pb–Pbcollisions. Theseresults assist inplacing strong constraintson boththe initial state geometry and medium response for relativistic heavy-ion collisions.

©^2018EuropeanOrganizationforNuclearResearch.PublishedbyElsevierB.V.Thisisanopenaccess articleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

Relativisticheavy-ioncollisionsarebelievedtocreateaQuark–

Gluon Plasma (QGP), a state of matter consisting of deconfined colorcharges.Thepressure gradientsintheQGPmedium convert spatialanisotropiesininitialconditionsofthecollisiontomomen- tum anisotropies of produced particles via multiple interactions, a phenomenon referred to as anisotropicflow [1]. The magnitude of anisotropic flow can be characterized by the flow coefficients (vn),whichare obtainedfromaFourierexpansion ofthe angular distributionofproducedparticles[2]

dN d

ϕ ^∝

¹

⁺

²

∞

n=¹

v_ncos

[

ⁿ

( ϕ −

n

)],

⁽¹⁾

where

ϕ

istheazimuthalangleoftheproducedparticle,nisthe flowharmonic,andnis thecorresponding symmetryplane an- gle.Forthe secondandthird orderflowcoefficients(v₂ and v₃), various hydrodynamical calculations have demonstrated the ap- proximaterelation[3–7]

vn

≈ κ

n

ε

n

,

(2)

where

ε

n isthecorrespondingeccentricitycoefficient,whichgov- erns the shape of the initial state. The variable

κ

n encodes the responseofthemedium,andinparticularissensitivetotheshear

E-mailaddress:alice-publications@cern.ch.

viscosity over entropydensity ratio(

η

/s) andthe lifetimeof the system. When valuesof

η

/s are finite,this inhibits the develop- mentofmomentumanisotropies.Ithasalsoreceivedabroaderin- terest,asitslowerboundisdifferentforperturbativeQCD[8] and AdS/CFT [9].Experimental data fromboth the Relativistic Heavy- Ion Collider(RHIC) andthe LargeHadron Collider(LHC) [10–16], haveimpliedvaluesof

η

/sclosetotheAdS/CFTminimumof1/4

π

[9],suggestingthattheQGPbehavesasanearperfectfluid.How- ever, uncertainties in the modeling of the initial state have pre- ventedtheextractionofmorepreciseinformation[17–19].

The datasetfromtheLHCXe–Xerun completedin2017may provide an opportunity to further constrain

η

/s. For mid-central collisions, various initial state models predict Xe–Xe collisions at

√s_NN=⁵.44 TeV and Pb–Pb collisions at √

s_NN=⁵.02 TeV have similar valuesof

ε

2 ata givencentrality[20,21].However, atthe samecentralitytheXe–XesystemsizeissmallerthanPb–Pb,and the impact of a finite

η

/s suppresses

κ

2 by 1/R, where R cor- responds tothe transversesize ofthe system[21]. Therefore,ra- tios of Xe–Xe/Pb–Pb v2 coefficients in the mid-centrality range could bedirectlysensitiveto

η

/s,withtheinfluenceoftheinitial state largely canceling out.Furthermore, hydrodynamical calcula- tions have shown that vn/

ε

n increases monotonically with the transverse density 1/S dNch/d

η

(dNch/d

η

is thecharged particle densityandS isthetransversearea)acrossdifferentcollisionen- ergies andsystems [17,22,23]. Both

ε

n and S are quantities that areobtainedfromaninitialstatemodel.Aviolationofthescaling canbetheresultofincorrectmodelingofthedensity(S)ortheaz- imuthalgeometry(

ε

n).Thatbeingthecase,suchanexercisewhere onecompares vn/

ε

nasafunctionof1/SdNch/d

η

forbothXe–Xe https://doi.org/10.1016/j.physletb.2018.06.059

0370-2693/©^2018EuropeanOrganizationforNuclearResearch.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

andPb–Pbcollisionscanfurtherconstraintheinitialstate.Similar investigations using RHIC data from Cu–Cuand Au–Au collisions ledtoimportantrefinements inthisregard,suchastherelevance of initial state fluctuations [24–26] and realization of finite val- uesof

ε

n forhigher order odd values of n (n≥^{3) [27]. On the} otherhand,anobservedviolationofthisscalingusingexperimen- taldata (assuming theinitial state predictions are accurate)may reveal deficiencies in the aforementioned hydrodynamical mod- eling.Addressing how theinformation fromXe–Xe collisions can shedmorelightonboththemediumresponseandinitialstate,is thecentralgoalofthisLetter.

2. Analysisdetails

ThetwodatasetsanalyzedwererecordedbytheALICEdetector attheLHCduringtheXe–Xe(2017)andPb–Pb(2015)runsatthe centerofmassenergiesof√

sNN=⁵.44 TeVand√

sNN=⁵.02 TeV, respectively.AmoredetaileddescriptionoftheALICEdetectorand itsperformancecanbefoundelsewhere [28–30].Charged-particle tracksatmid-rapidityarereconstructedusingtheTimeProjection Chamber(TPC) [28,31],theprimary trackingdetector.Information fromthe Inner Tracking System (ITS) [28,32] is used to improve thespatialandmomentumresolutionoftheTPCtracks.Thishelps to reject the backgroundfrom secondaries,which originate from weak decays,conversions, secondary hadronicinteractions in the detector material, and pile-up. The two innermost layers of the ITS, the Silicon PixelDetector (SPD), are employed for triggering andevent selection. The two V0 counters [28,33], each contain- ing 32 scintillator tiles and covering 2.8<

η

<5.1 (V0A) and

−³.7<

η

<−¹.7 (V0C), provideinformation fortriggering, event selection,thedeterminationofcentralityandthesymmetryplane angle [34].The triggerconditions andtheeventselection criteria aredescribedelsewhere[29].Anofflineeventselectionisapplied to remove beam-induced background (i.e., beam-gas events) and pile-upevents,whicharerejectedusinginformationfromtheITS andV0detectors.Primaryvertexinformationisprovidedbytracks reconstructedintheITSandTPC.Onlyeventswithareconstructed primaryvertexwithin10 cmfromthecenterofthedetectoralong thebeamaxis (thatpositionis denotedby P Vz) are used inthe analysisto ensureauniformacceptancein

η

.The resultingevent sampleavailableforanalysisconsistedof∼¹.0MXe–Xeeventsin the0–70%centralityrange,and∼^{67MeventsforPb–Pbcollisions} inthesamecentralityinterval.

Thechargedtracksatmid-rapidityusedtodeterminetheflow coefficients have the kinematic values 0.2<pT<10 GeV/c and

|

η

_|<0.8.ThetrackfitusesanSPDhitifoneexistswithinthetra- jectory,ifnot,they are constrainedto theprimary vertex.Such a configurationleads toarelativelyflatazimuthalacceptance.Track qualityisensuredbyrequiringtrackstohaveatleast70TPCspace pointsout ofa maximumof159withanaverage

χ

² perdegree- of-freedomforthetrackfitlowerthan2.Inaddition,thedistances ofclosestapproachtotheprimaryvertexinthexyplaneandzdi- rectionarerequiredtobelessthan2.4cmand3.2cm,respectively.

The charged particle track reconstruction efficiency is estimated from HIJING simulations [35,36] combined with a GEANT3 [37]

transportmodel.

Inordertoextracttheflow coefficientsfromchargedparticles produced in either Xe–Xe or Pb–Pb collisions, the Scalar Prod- uct[38] andGenericFramework[39,40] methodsareused,which evaluatemparticleflowcoefficientsvn{m}.Thevn{m}coefficients characterizeflowfluctuations,andaresensitivetocorrelationsnot related to the common symmetry planes n (“non-flow”), such asthose due to resonances andjets. The contributionfrom flow fluctuationswasshowntodecrease v_n{^m≥⁴}^{andincrease v}n{²}

relativeto^vn [41]. Intheabsenceofflowfluctuationsandnon- flow,vn{^m}^isindependentofm.Bothmethodsfeaturecalculations involvingtheQ_n-vectorwhichisdefinedas

Qn

=

M

i

e^inϕi

,

(3)

where M isthe numberof particles used tobuild the Qn-vector ina single event, and

ϕ

i isthe azimuthalangle ofparticle i.For the Scalar Product method, the flow coefficients vn (denoted as vn{²,|

η

_|>2}^{)aremeasuredusing}

vn

{

SP

} =

un,kQ^∗_n

QnQ^A_n^∗ QnQ^B_n^∗

Q^A_nQ^B_n^∗

,

(4) where un,k=^exp(in

ϕ

k) is the unit flow vector ofthe particle of interestk.Thebrackets· · · ^{denoteanaverageoverallevents,the} doublebrackets · · · ^{an averageover all particlesinall events,} and^∗ thecomplexconjugate.ThevectorQniscalculatedfromthe azimuthal distribution ofthe energy deposition measured in the V0A.Its xandy componentsaregivenby

Q_n,x

=

j

w_jcos

(

n

ϕ

j

),

Q_n,y

=

j

w_jsin

(

n

ϕ

j

),

(5)

where the sum runs over all channels j of the V0A detector (j=¹−^32),

ϕ

j is the azimuthal angle of channel j, and wj is theamplitude measuredinchannel j.ThevectorsQ^A_nandQ^B_nare determined from the azimuthal distribution ofthe energydepo- sitionmeasured intheV0C andthe azimuthaldistribution ofthe tracksreconstructedintheITSandTPC,respectively.Thelargegap in pseudo-rapidity (|

η

_|>2.0) between thecharged particles in theTPCused todetermine v_nandthose intheV0A greatlysup- presses non-flow effects. The course

ϕ

segmentation of the V0 leads to a deterioration of resolution forhigher order flow coef- ficients(n≥^{4),andpreventstheir}measurements.

The flow coefficients v_n{^m} ^{from two- and} multi-particle cu- mulants can also be obtainedusing the Generic Framework. The calculations using the Qn-vector are generally much more com- plex than those shown in Eq. (4), and can be found elsewhere [40].Thisapproachprovidesacapabilityforthenecessarycorrec- tions ofsystematic biases fromnon-uniform detector acceptance and tracking inefficiencies, and it has been used in other mea- surements[16,42,43].Itcanalsobeusedtosuppressnon-flowby placing an

η

-gapbetweenvarious Q_n-vectors. The non-flow con- tribution to vn{^m≥⁴} ^{in this framework is strongly suppressed} by construction without the use of an

η

-gap. The newly devel- opedsub-eventmethods[44,45],provideadditionalmeansofsup- pressing any residual non-flow contributions for vn{^m≥⁴}^{. The} Generic Framework isused for measurements of vn{²,|

η

_|>1} and vn{^m≥⁴} ^{(including v}2{⁴,3 sub-event}^{) fromchargedtracks} intheTPCacceptanceonly.

When constructing Eq. (3) from charged particles to deter- mine vn{^m}^,particle-wiseweights areplacedtoaccount fornon- uniformities in the

ϕ

acceptance and pT dependent efficiencies.

The systematicuncertainties for v_n{^m} ^{havethree sources:event} selection,tracktype/selection,andtheQn-vectorcorrectionproce- dure.The eventselectioncontributions weredeterminedby vary- ingtheP Vzranges,notapplyingthepile-uprejectioncriteria,and usingadifferentdetectorsystem(ITS)forcentralitydetermination.

The tracktype/selection uncertainties were determined by using tracks with TPC information only or tracks that always have an ITShit(whichchangesthecontributionsfromsecondaryparticles), changing the track quality cuts (such as the minimum number

Fig. 1.Toppanel:Chargedparticle vn integratedoverthetransversemomentum range0.2<pT<3.0 GeV/c asafunctionofcentralityfromXe–Xecollisions.The varioustechniquesareexplainedinthetext.Onlystatisticaluncertaintiesarevis- ible(thinverticallines).Bottompanel:Ratiosofv2{⁴}^/v2{²}^{comparedtosome} theoreticalpredictions.Thehydrodynamicpredictionsuseashearviscosityoveren- tropyratioη/s=⁰.047 andinitialconditionsfromtheTRENTomodel[21,46].For v2{2},theALICEmeasurementsimplementa|η|>2.0 gapwhichisnotusedin themodels.

ofTPCspacepoints),andcomparing anydifferencesbetweende- termining Qn or un,k from positive or negative only TPC tracks (bothchargesignsareusedtobuildaflowvectorforthefinalre- sults).Finally,theuncertainties inQn-vector correctionprocedure contributionareduetouncertaintiesinthepT dependentefficien- cies.Theindividualsourcesofsystematicuncertaintyareassumed uncorrelated and are added in quadrature to obtain the overall estimated systematic uncertainties. For the pT-integrated vn{^m} coefficients, the total systematic uncertainties are typically 2–3%, andsmallerthanthemarkersizeinthecorrespondingfigures.The systematicuncertaintiesforthe pT-differentialcoefficientscanbe larger,andaredenotedbyboxesintherelevantfigures.

3. Results

Thetoppanel ofFig.1showstwo- andmulti-particle pT-inte- gratedvn{^m}^{coefficientsfromXe–Xecollisionsat}√

sNN=⁵.44 TeV asafunctionofcentrality.Astrongerdependenceofv2 withcen- tralitycomparedwithv3 orv4,alsoobserved inPb–Pbcollisions at LHC energies [13–16], is expected based on simple consider- ations of how the almond shaped overlap region changes with centrality for A–A collisions. Given that near-side non-flow cor- relations (where the particles involved have similar values of

ϕ

and

η

) are expected to be thelargest non-flow contribution,the similarities observed for v_n{²,|

η

|>2} ^{and v}n{²,|

η

|>1} ^in- dicate non-flow is strongly suppressed by a gap of one unit of pseudorapidity. Theextractedvaluesof v₂{^m≥⁴}^{use Q}n-vectors without any

η

gaps. The v2{⁴,3 sub-event} ^{results have}

η

gaps betweenthe Qn-vectorsto suppress non-flow.The sub-eventre- gionsare−⁰.8<

η

≤ −⁰.4,−⁰.4<

η

≤⁰.4 and0.4<

η

≤⁰.8.The equivalencewith v2{⁴} ^(no

η

separation) demonstratesthat such a gap is actually not required for these flow coefficients. Given

Fig. 2.Toppanel:Comparisonsofchargedparticlevn{2}integratedoverthetrans- versemomentumrange0.2<pT<3.0 GeV/casafunctionofcentralityfromXe–Xe andPb–Pbcollisions.Middlepanel:Ratioofvn{²}(Xe–Xe/Pb–Pb)coefficients.Bot- tompanel:Doubleratioofdataandtheory.Hydrodynamicalmodelpredictionsfrom EKRT[20] andV-USPHYDRO[21] areshown.Inallcases,onlystatisticaluncertain- tiesarevisible(thinverticallines).

allthoseobservationsregardingnon-flow,onecaninterpretdiffer- encesbetween v₂{²}^{and v}2{⁴}^{, v}2{⁶}^,v2{⁸} ^{tobelargely driven} by flow fluctuations [41]. To quantify these differences, in the bottom panel of Fig. 1,the ratio v2{⁴}^/v2{²,|

η

_|>2} ^isshown, which is found to decrease for central collisions. The resultsare comparedtoahydrodynamiccalculationinthesamepanel,which usesan

η

/s=⁰.047 tomodelthemediumresponse[21].Forthese hydrodynamiccalculations,theTRENToinitialconditionmodel[46]

is usedtodetermine theeccentricities. Thejustificationforusing p=^{0 is described later inthe Letter. Theinitial condition model} implements a ¹²⁹Xe β2 deformation (β2=⁰.162), which is pre- dicted forthe ¹²⁹Xe nucleus [47], but has never been measured directly.ItmodifiestheWoods–Saxondistributionasfollows[48]

ρ (

r

, θ ) = ρ

0

1

+

^{e(r−R0−R0β2Y20(θ ))/a}

,

(6)

where

ρ

0 is thedensityatthecenterof thenucleus, R₀ the nu- clearradius,risthedistanceawayfromthecenter,Y20isaBessel functionofthesecondkind,anda istheskindepth.Accordingto Eq. (2),the ratioofflow coefficients v2{⁴}^/v2{²}^{should be iden-} ticalto theratioof initialstate eccentricities

ε

2{4}/

ε

2{2}.To test this relation,the bottom panel ofFig. 1 alsoshows theflow co- efficient ratios andthe eccentricity ratios from the same model.

The difference between the two curves shows that Eq. (2) only holdsapproximately.Thehydrodynamiccalculationsgenerallypre- dictlowerratioscomparedtothedata,withthelargestdeviations beinginthesemi-centralregion(10–50%).

Fig. 3.Toppanel:Comparisonsofchargedparticlevn{²}^{integratedoverthetrans-} versemomentumrange 0.2<pT<3.0 GeV/c from Xe–XeandPb–Pb collisions forfinercentrality binsincentral collisions.Statisticaland systematicuncertain- tiesareshownaslinesandboxes,respectively.Bottompanel:Correspondingratio ofvn{2}(Xe–Xe/Pb–Pb)coefficients.

Fig.2 showscomparisons of two-particle pT-integrated vn{²} coefficients from Xe–Xe and Pb–Pb collisions as a function of centrality.The differencesbetween thetwo systems are typically within 10% except for v₂{²} ^{in central 0–5% collisions where} the Xe–Xe values are ∼^{35% higher. For the V-USPHYDRO and} EKRTmodels [20,21] shown, both sets ofthe used initial condi- tion models demonstrate

ε

2{²}^(Xe–Xe)/

ε

2{²}^(Pb–Pb) ∼^{1 for the} semi-central range 20–60% (not shown in the figure). However, v2{²}^(Xe–Xe)/v2{²}^(Pb–Pb) ∼^{0.9 from the data, which might be} the result of the viscous effects described in the Introduction.

When implementing the hydrodynamical response, both models

alsoshowasimilarsuppressionforthesmallerXe–Xesystem, al- beit withdifferencesofup to∼^{5% comparedtothedata.Onthe} otherhand,despiteusingdifferentvaluesof

η

/s,bothmodelspre- dict similar ratios in the semi-central range. Some assumptions used ineach ofthe models (suchasthe freeze-outtemperature) are different, and investigating the impact of those assumptions on v2{²}^(Xe–Xe)/v2{²}^{(Pb–Pb) ratio should be a topic of further} theoreticalinvestigations.

Bothsetsofmodelpredictions(V-USPHYDROandEKRT)imple- menta¹²⁹Xedeformationusingβ2=⁰.162.Thevalueofβ2iszero forthe²⁰⁸Pbnucleus,asitis adoublemagicnucleus. Thedefor- mation fortheXe–XeV-USPHYDROpredictions contributes∼^20%

to the observed v₂{²} ^{for central collisions (compared with the} case whereno deformation is implemented), and hasno impact onv2{²}^forcentralitiesabove15%.Regardingv3{²}^{,itisgenerally} largerin Xe–Xe,whichreflectsthe factthat theinitial conditions fromboth models show

ε

3{²}^(Xe–Xe) >

ε

3{²}^{(Pb–Pb) ata given} centrality forthe entirecentralityrange presented.The hydrody- namicpredictions for v₃{²} ^{aresimilar forthe two models,with} maximumdeviations of∼^{5%fromthe data.The} β3 deformation forboth theXe andPb nucleiiszero[47], withbothmodels as- sumingsuchavalue.

InFig.3,similarcomparisonsaremadeinfinercentralitybins ascomparedwithFig.2forcentralcollisions.Thetransitionwhere Xe–Xe v₂{²} ^{becomes larger than the Pb–Pb values occurs fora} centrality of ∼^{15%. For 0–1% central} collisions, where the over- lapgeometryisexpectedtoplayaminimalroleforbothsystems, v2{²} ^is∼^{60% larger for Xe–Xe}collisions. In terms of theinitial state,thisisexpectedfortwo reasons.Thefirstrelatestothefact that the ¹²⁹Xe nucleus is deformed while the ²⁰⁸Pb nucleus is not,andthesecond relatesto theroleofinitial statefluctuations and thenumber of sources that contribute to

ε

n{²}^{. It has been} previously shown that

ε

n{²} ^{decreases asthe number ofsources} increasesforasphericalsystem[49],andifthenumberofsources were infinite,then

ε

n{²} ^{would be zero in this centrality range.}

GiventhataverycentralPb–Pbcollisionisexpectedtohavemore sourcesthanavery centralXe–Xecollision,fluctuationswouldbe expected togive riseto larger values of

ε

2{²} ^{forthe latter.The} same lineof reasoning can explain why v3{²} ^{isobserved to be} larger inXe–Xe compared to Pb–Pb inthe samecentrality inter- val.

Fig. 4 shows comparisons of two-particle pT-differential v2{2,|

η

|>2} coefficients from Xe–Xe and Pb–Pb collisions in

Fig. 4.ThepT-differentialv2forchargedparticlesfromXe–Xecollisionsat√_s

NN=⁵.44 TeVandPb–Pbcollisionsat√_s

NN=⁵.02 TeVforvariouscentralityclasses.Statistical andsystematicuncertaintiesareshownaslinesandboxes,respectively.

Fig. 5.ThepT-differentialv3forchargedparticlesfromXe–Xecollisionsat√_s

NN=⁵.44 TeVandPb–Pbcollisionsat√_s

NN=⁵.02 TeVforvariouscentralityclasses.Statistical andsystematicuncertaintiesareshownaslinesandboxes,respectively.

various centrality bins. As mentioned, the larger |

η

| ^{gap mea-} surements use both the TPC andthe V0 detectors, which maxi- mizes the numberof particles used to build the Qn-vectors. The corresponding reduction in statisticaluncertainties is particularly usefulforthehigherpTmeasurements.Asexpected,thecentrality dependenceof v₂{²,|

η

|>2}^{fromXe–Xecollisions followsthat} observed in Fig.1. Comparedwith Pb–Pb collisions in the semi- centralbins,itappearsthedifferencesobservedinFig.2arelarger in the mid-pT region, and this will be investigated more quan- titatively. Fig. 5 shows the same comparison for p_T-differential v₃{²,|

η

|>2} coefficients. The Xe–Xe coefficients are typically largerthan fromPb–Pb collisionsat agivencentralityatlow pT, whereas the larger statistical uncertainties for the Xe–Xe coeffi- cientsathigherpTmakeitdifficulttoestablishwhetherthereare anydifferencesbetweenthetwosystems.

Fig.6showsthe pT-integratedvn{²}/

ε

n{²}^{ratiosasafunction} of1/S dNch/d

η

inXe–XeandPb–Pbcollisions,whereS and

ε

n{²} are obtained using various initial state models. The vn{²}/

ε

n{²} ratioprovides estimatesof

κ

n asperEq. (2).Asmentioned,when comparing vn/

ε

n from differentsystems, a violation of the scal- ing with 1/S dNch/d

η

(which increases with centrality), maybe indicativeofshortcomingsinthemodelingoftheinitialstate(and its fluctuations). Regarding the model parameters used for this exercise, in the transverse plane for a single event, both the ec- centricities andareas are calculated inthe center ofmass frame respectivelyaccordingto

ε

n

=

^rncos

(

n

φ

)

²

+

^rnsin

(

n

φ

)

²

^rn

,

(7)

S

=

⁴

π σ

_x

σ

_y

,

(8)

whichisdefinedsuch that thesources that contribute totheec- centricityandarea havetheproperty ^x = ^y =^0,wherex,y and

ϕ

,rarethecartesianandthepolarcoordinatesofthesource, respectively.Thequantities

σ

x and

σ

y representthestandardde- viations ofthe source distributions. The event averages used for Fig.6are

ε

n{²}=

ε

n2+

σ

_ε²_n and^{S .The}normalizationofthe area is chosen such that for a Gaussian distribution the average densitycoincideswithNpart/S(Npart isthenumberofparticipat- ingnucleons),andwasusedinaprevious ALICEpublication[53].

Adeformation of β2=⁰.18±⁰.02 for the ¹²⁹Xe nucleusisused [30,54].Thevalue wasobtainedfromextrapolatingmeasurements

ofβ2 fromnearbyisotopes(¹²⁸Xeand¹³⁰Xe),andtheoretical cal- culations [47,55,56], with the uncertainty reflecting the different values obtained from each approach. The box errors in the fig- urerepresentthecorrespondinguncertaintiesontheratio.Forthe Monte Carlo (MC) Glauber and KLN models, the values of

ε

n{²} and S fora given V0based centralityclass were extractedusing a method described in a previous publication [34]. The multi- plicity of charged particles in the acceptance of the V0 detector is generated accordingto a negative binomial distribution, based onthe numberofparticipantnucleonsandbinary collisionsfrom each initial state model. The parameters used for this approach can be found elsewhere [52,54], and were optimized todescribe the multiplicity distributionfromthedata.Regarding theT_RENTo model,followingother approaches[21,46],themultiplicity inthe acceptanceoftheV0detectorwasmodeledbyscalingtheentropy production, againto matchthe multiplicity distributionfrom the data.

Thetopleftpanelshowsaninvestigationofsuchascalingwith the MC Glauber model [57,58], which uses nucleon positions as the sources. In particular, for v₂{²} ^{in central Xe–Xe and Pb–Pb} collisions, this model does not provide a clear scaling, and was already observed for v2 from Au–Au and U–U collisions at RHIC usingthe samemodel[59].The scalingusingthe MCKLNmodel (version 32)[51,60],whichassumesgluonsourcesandusesaColor Glass Condensateapproach to determinethe gluon spatial distri- bution, is shown in the top middle panel. The MC KLN scaling appears to work well for v3{2},but failsfor v2{2} withthe Xe–

XepointsbeingabovePb–Pbformorecentralcollisions.Asudden rise isalsoobserved forcentral Pb–Pbcollisions. Thisbehavior is in contrast to the MC Glauber nucleon model, where the Xe–Xe points are belowPb–Pbforcentral collisions.The toprightpanel investigates thescalingusingtheT_RENToinitial state model[46].

In thismodel,the distributionofnuclearmatter withinthe colli- sionzoneofA–Acollisionsiscontrolledbythepparameter,with p=0 mimicking IP-Glasma initial conditions [61,62]. The choice of parameterwas determined using Bayesianstatistics froma si- multaneous fitofchargedhadron multiplicitydistributions, mean transverse momentum measurements, andintegratedflow coeffi- cients v_n in Pb–Pb collisions at √

s_NN=².76 TeV [63]. The IP- Glasma approachuses ColorGlass Condensatecalculationstode- termine thedistributionof gluonsintheinitial state. Thismodel provides a better scaling compared withthe previous two other models. However forcentral Pb–Pb collisions, a dropis observed for v₂{²}/

ε

2{²}^{.ThedropisalsoobservedintheMCGlauber nu-}

Fig. 6.Comparisonsofvn{²}/εn{²}^{integratedoverthetransversemomentumrange0}.2<pT<3.0 GeV/casafunctionof1/SdNch/dηinXe–XeandPb–Pbcollisions,where Sandεn{²}^{arefromvariousinitialstatemodels}[46,50,51].Themodelsareexplainedinthetext.The¹²⁹Xedeformationimplementedisβ2=⁰.18±⁰.02,withthebox errorsrepresentingtheuncertaintyinβ2.MeasurementsofdNch/dη(|η|<0.5)fromXe–XeandPb–Pbcollisionswereobtainedfromseparatestudies[30,52].

cleonmodel,andappearstobepresentforthecentralXe–Xedata.

Suchadropisunexpectedfromhydrodynamiccalculations[17,23], which show a continuous increase of v2/

ε

2 with 1/S dN_ch/d

η

. It may point to deficiencies in the initial state modeling of the regionsinXe–Xe andPb–Pb collisions whereinitialstate fluctua- tions play the largest role in generatingsecond order eccentrici- ties.

Thebottompanelsshowratiosderivedfromconstituentquark MCGlauber calculations,which usequarkscontainedinnucleons asthesources whichcontribute to the eccentricity[50]. The pa- rameterqreferstothenumberofconstituentquarkspernucleon.

All implementations ofquark sources (3, 5, or7) appearto give areasonable scaling for v₂ and v₃, howeversome deviationsare observedin central Xe–Xe andPb–Pb collisions. The value q=⁵ wasfoundtodescribethechargedparticleyieldsbetterthanq=³ atLHC energies (assumingthe yields should scale withthe total number of quarks) [50], and there are hints of a slightly better scalingwithq=5 forv2{2} incentral Xe–Xecollisions compared toq=^3.Thesemodelimplementationsagainshowadropforcen- tral Pb–Pb collisions, which is least pronounced for q=^{7. This} suggestsinitialstatemodelsneedahighernumberofsourcesper nucleoninorder toachieve a continuous increase of v2{²}/

ε

2{²} formorecentralPb–Pbcollisions,andatransversedensityscaling whencomparingXe–XetoPb–Pb.

Finally, in Fig. 7, an investigation of whether the transverse density scaling holds as a function of pT is shown. Two Xe–Xe andPb–Pb centrality bins with similar transverse densities (1/S dN_ch/d

η

_∼10 fm⁻²) are selected, and the pT-differential values of v2{²}/

ε

2{²} ^{are shown. The p}T-integratedvalues forthe con- stituentquark MC Glauber modelchosen (q=^{3) are observedto} besimilarintheleftbottompanelofFig.6.Inthatfigure,theXe–

Xecentralitybincorrespondstothefourthpointgoinglefttoright, whilethePb–Pbcentralitybincorrespondstothethirdpoint.The ratiointhebottompanelofFig.7usesaninterpolationofthePb–

Pbdatapoints.Theratioisindependentoftheinitialstatemodel used,asallgivevery similarvaluesof

ε

2{²}^(Xe–Xe)/

ε

2{²}^(Pb–Pb).

Additionally, the transverse sizes (R=√

S/

π

) are very similar, so the previously mentioned viscous corrections should cancel.

Fig. 7.Toppanel:ComparisonofpT-differentialv2{²}/ε2{²}^{fromXe–XeandPb–Pb} collisionsforaselectionofcentralitybins.Statisticalandsystematicuncertainties areshownaslinesandboxes,respectively.Bottompanel:Ratiosofthescaledcoef- ficientsfromthetoppanel.ThePb–Pbpointsareinterpolatedinordertodetermine theratio.ThecirclemarkersshowXe–Xe20–30%/Pb–Pb30–40%whilethesquare makersshowXe–Xe30–40%/Pb–Pb30–40%.

The influence of radial flow should be very similar as ^pT = 0.710±⁰.004 GeV/c(Xe–Xe)and^pT =⁰.716±⁰.004 GeV/c (Pb–

Pb) for charged hadrons [64]. The ratio is close to 1 and shows no significant p_T dependence. This indicates when such a scal- ingholds,itdoessooverthe p_T rangepresented.Thismayshow

the pT-differentialmediumresponse (

κ

2(pT)) iscontrolledbythe transverse densityand size, independent of the collision system.

A comparisonofthescaledpT-differentialcoefficientsforthesame 30–40% centrality bin from Xe–Xe and Pb–Pb collisions is also shown. Inthiscase, the eccentricitiesare similar (the differences arewithin1%),howeverthetransversesizeanddensityoftheXe–

Xe system is smaller. The ratio appears to mildly decrease with increasing pT.Whetherthisistheresultofviscous effectsrelated tothetransversesizeofthesysteminfluencingthemid-pTregion more, ora smaller radial flow in Xe–Xe, remains an open ques- tion.

4. Summary

The first measurements of anisotropic flow coefficients vn in Xe–Xe collisions at √

sNN =5.44 TeV collisions from the ALICE detector at the LHC have been presented. Hydrodynamical pre- dictionsreproduce measurements of v2{⁴}^/v2{²}^{ratios from Xe–}

Xe collisions to within ∼^{15% (Fig. 1). In} semi-central collisions, it is found that the v₂{²} ^{coefficient is lower in Xe–Xe colli-} sions at √

sNN =⁵.44 TeV compared with Pb–Pb collisions at

√sNN=⁵.02 TeV atthe same centrality. The v3{²} ^{coefficient is} larger, consistent with expectations from hydrodynamical mod- els that reproduce the differences for both systems within ∼^5%

(Figs.2and3).Thedifferencesforv2{²}^{arepredictedtobedriven} largelybythehydrodynamicalresponseofthesystem. Forcentral collisions, v2{²} ^{is found to be larger inXe–Xe} collisions, which agreeswithpredictionsfromhydrodynamic models,butthedevi- ationstend tobe larger than ∼^{5% with respectto thesemodels.}

The differencesbetweentwo-particle pT-differential v2{²} ^coeffi- cientsfrom Xe–Xe compared to Pb–Pb are found to be larger at mid-pT compared to low-pT, whereas no such trend isobserved for v₃{²} ^within uncertainties (Figs.4 and5). The studies ofthe modeling of the initial state via eccentricity scaling with trans- versedensity(Fig.6)havedemonstratedthatboththeMCGlauber (constituentquarks)andtheT_RENTomodelsprovidethemostsat- isfactorydescriptions.However,thedropobservedforv2{²}/

ε

2{²} incentralXe–XeandPb–Pbcollisionsisnotexpectedfromhydro- dynamiccalculations. InthecaseoftheMC Glauber implementa- tions, the drop is more pronounced for nucleon and constituent quark(q=^{3)sources,andmayrequiresome}improvementsinthe initialstatemodelingfortheregioninXe–XeandPb–Pbcollisions where

ε

2{²} ^{has the largest} contribution from initial state fluc- tuations.Finally, fortwo Xe–XeandPb–Pb centralitybins witha similartransversedensityandsize,itisfoundthatthedoublera- tio [v₂{²}/

ε

2{²}(Xe–Xe)]/[v₂{²}/

ε

2{²}^{(Pb–Pb)] is largely indepen-} dentof pT (Fig. 7).Thismay indicatethe pT-differentialmedium responseiscontrolledbythetransversedensityandsize,indepen- dentofthecollisionsystem.

Acknowledgements

The ALICE Collaboration would like to thank all its engineers andtechnicians fortheir invaluablecontributionstotheconstruc- tionoftheexperimentandtheCERNacceleratorteamsfortheout- standingperformanceoftheLHCcomplex.TheALICECollaboration gratefully acknowledges the resources and support provided by all Gridcenters and theWorldwide LHCComputing Grid(WLCG) collaboration. The ALICE Collaboration acknowledges the follow- ingfundingagenciesfortheirsupportinbuildingandrunningthe ALICEdetector:A.I.AlikhanyanNationalScienceLaboratory(Yere- vanPhysicsInstitute) Foundation(ANSL),State Committee ofSci- enceandWorldFederationofScientists(WFS),Armenia; Austrian AcademyofSciencesandNationalstiftungfürForschung,Technolo- gie und Entwicklung, Austria; Ministry of Communications and

High Technologies, National Nuclear Research Center, Azerbaijan;

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Universidade Federal do Rio Grande do Sul (UFRGS), Fi- nanciadoradeEstudoseProjetos(Finep)andFundaçãodeAmparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil; Ministry of Science & Technology of China (MSTC), National Natural Science Foundation of China (NSFC) and Ministry of Education of China (MOEC), China;Ministry of Science and Education, Croatia; Min- istryofEducation,Youth andSportsofthe CzechRepublic, Czech Republic; The Danish Council for Independent Research | Natu- ral Sciences, the Carlsberg Foundation and Danish National Re- search Foundation (DNRF), Denmark; Helsinki Institute ofPhysics (HIP),Finland;Commissariatàl’EnergieAtomique(CEA)andInsti- tut National de Physique Nucléaire et de Physique des Particules (IN2P3) andCentre Nationalde la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie (BMBF) and GSI Helmholtzzentrum für Schw- erionenforschung GmbH, Germany; General Secretariat for Re- search and Technology,Ministry ofEducation, ResearchandReli- gions,Greece;NationalResearch,DevelopmentandInnovationOf- fice, Hungary;DepartmentofAtomicEnergyGovernmentofIndia (DAE),DepartmentofScienceandTechnology,GovernmentofIndia (DST), University Grants Commission,Government ofIndia (UGC) andCouncil ofScientificandIndustrialResearch(CSIR), India;In- donesian Institute of Science, Indonesia; Centro Fermi – Museo StoricodellaFisicaeCentroStudieRicercheEnricoFermiandIsti- tutoNazionalediFisicaNucleare(INFN),Italy;InstituteforInnova- tive ScienceandTechnology,NagasakiInstituteofAppliedScience (IIST),Japan SocietyforthePromotion ofScience(JSPS)KAKENHI and Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan; Consejo Nacional de Ciencia (CONA- CYT)yTecnología,throughFondodeCooperaciónInternacionalen Ciencia yTecnología(FONCICYT) andDirección Generalde Asun- tos delPersonalAcademico(DGAPA),Mexico;NederlandseOrgan- isatie voorWetenschappelijkOnderzoek (NWO),Netherlands; The ResearchCouncilofNorway,Norway;CommissiononScienceand Technology forSustainableDevelopmentintheSouth(COMSATS), Pakistan;PontificiaUniversidadCatólicadelPerú,Peru;Ministryof ScienceandHigherEducationandNationalScienceCentre,Poland;

KoreaInstituteofScienceandTechnologyInformationandNational ResearchFoundationofKorea(NRF),RepublicofKorea;Ministryof Education andScientific Research,Institute ofAtomicPhysicsand RomanianNationalAgencyforScience,TechnologyandInnovation, Romania; Joint Institute for Nuclear Research (JINR), Ministry of EducationandScienceoftheRussianFederationandNationalRe- search Centre Kurchatov Institute, Russia; Ministry of Education, Science, ResearchandSportof theSlovak Republic, Slovakia; Na- tionalResearchFoundationofSouthAfrica,SouthAfrica;Centrode AplicacionesTecnológicasyDesarrolloNuclear (CEADEN),Cubaen- ergía,CubaandCentrodeInvestigacionesEnergéticas,Medioambi- entales yTecnológicas(CIEMAT),Spain;SwedishResearchCouncil (VR)andKnut&AliceWallenbergFoundation(KAW),Sweden;Eu- ropean Organization for Nuclear Research, Switzerland; National Science andTechnology Development Agency (NSDTA), Suranaree University of Technology (SUT) and Office of the Higher Educa- tionCommissionunderNRUprojectofThailand,Thailand;Turkish Atomic Energy Agency (TAEK), Turkey;National Academy of Sci- encesofUkraine,Ukraine;ScienceandTechnologyFacilitiesCoun- cil (STFC), United Kingdom; National Science Foundation of the United States ofAmerica (NSF) andUnited StatesDepartment of Energy,OfficeofNuclearPhysics(DOENP),UnitedStatesofAmer- ica.