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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
r
a
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√sNN=5.44 TeV arepresented.Comparing thesemeasurements tothosefromPb–Pb
collisions at √sNN=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 spatialanisotropiesininitialconditionsofthecollisionto momen-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 vncos[
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
nε
n,
(2)where
ε
n isthecorrespondingeccentricitycoefficient,whichgov-erns the shape of the initial state. The variable
κ
n encodes theresponseofthemedium,andinparticularissensitivetotheshear
E-mailaddress:alice -publications @cern .ch.
viscosity over entropydensity ratio(η
/
s)andthe lifetimeof the system. When valuesofη
/
s are finite,this inhibits the develop-mentofmomentumanisotropies.Ithasalsoreceivedabroader in-terest,asitslowerboundisdifferentforperturbativeQCD[8] and AdS/CFT [9].Experimental data fromboth the Relativistic Heavy-Ion Collider(RHIC) andthe LargeHadron Collider(LHC) [10–16], haveimpliedvaluesofη
/
s closetotheAdS/CFTminimumof1/
4π [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√
sNN
=
5.
44 TeV and Pb–Pb collisions at√
sNN=
5.
02 TeV havesimilar valuesof
ε
2 ata givencentrality[20,21].However, atthesamecentralitytheXe–XesystemsizeissmallerthanPb–Pb,and the impact of a finite
η
/
s suppressesκ
2 by 1/
R, where Rcor-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 thetransverse density 1
/
S dNch/dη (dNch/dη is thecharged particledensityandS isthetransversearea)acrossdifferentcollision en-ergies andsystems [17,22,23]. Both
ε
n and S are quantities thatareobtainedfromaninitialstatemodel.Aviolationofthescaling canbetheresultofincorrectmodelingofthedensity(S)orthe az-imuthalgeometry(εn).Thatbeingthecase,suchanexercisewhere
onecompares vn
/
ε
nasafunctionof1/
S dNch/dηforbothXe–Xe https://doi.org/10.1016/j.physletb.2018.06.0590370-2693/©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 theotherhand,anobservedviolationofthisscalingusing experimen-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 intheanalysisto 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.ThetrackfitusesanSPDhitifoneexistswithinthe tra-jectory,ifnot,they are constrainedto theprimary vertex.Such a configurationleads toarelativelyflatazimuthalacceptance.Track qualityisensuredbyrequiringtrackstohaveatleast70TPCspace pointsout ofa maximumof159withanaverageχ
2 perdegree-of-freedomforthetrackfitlowerthan2.Inaddition,thedistances ofclosestapproachtotheprimaryvertexinthexy planeandz
di-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 evaluatem particleflowcoefficientsvn
{
m}
.Thevn{
m}
coefficientscharacterizeflowfluctuations,andaresensitivetocorrelationsnot related to the common symmetry planes
n (“non-flow”), such
asthose due to resonances andjets. The contributionfrom flow fluctuationswasshowntodecrease vn
{
m≥
4}
andincrease vn{
2}
relativeto
vn[41]. Intheabsenceofflowfluctuationsand
non-flow,vn
{
m}
isindependentofm.BothmethodsfeaturecalculationsinvolvingtheQn-vectorwhichisdefinedas
Qn
=
M
i
einϕi
,
(3)where M is the numberof particles used tobuild the Qn-vector
ina single event, and
ϕ
i isthe azimuthalangle ofparticle i.Forthe Scalar Product method, the flow coefficients vn (denoted as
vn
{
2,
|
η
|
>
2}
)aremeasuredusing vn{
SP} =
un,kQ∗nQnQAn∗
QnQBn∗
QA nQBn∗
,
(4)where un,k
=
exp(
inϕk)
is the unit flow vector ofthe particle ofinterestk.Thebrackets
· · ·
denoteanaverageoverallevents,the doublebrackets· · ·
an averageover all particlesinall events, and∗ thecomplexconjugate.ThevectorQniscalculatedfromtheazimuthal distribution ofthe energy deposition measured in the V0A.Its x andy componentsaregivenby
Qn,x
=
j wjcos(nϕ
j),
Qn,y=
j wjsin(nϕ
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 istheamplitude measuredinchannel j.ThevectorsQAnandQBnare
determined from the azimuthal distribution ofthe energy depo-sitionmeasured intheV0C andthe azimuthaldistribution ofthe tracksreconstructedintheITSandTPC,respectively.Thelargegap in pseudo-rapidity (
|
η
|
>
2.
0) between thecharged particles in theTPCused todetermine vnandthose 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),andpreventstheirmeasurements.The flow coefficients vn
{
m}
from two- and multi-particlecu-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].Thisapproachprovidesacapabilityforthenecessary correc-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 Qn-vectors. The non-flowcon-tribution to vn
{
m≥
4}
in this framework is strongly suppressedby construction without the use of an
η
-gap. The newly devel-opedsub-eventmethods[44,45],provideadditionalmeansof sup-pressing any residual non-flow contributions for vn{
m≥
4}
. TheGeneric Framework isused for measurements of vn
{
2,
|
η
|
>
1}
and vn
{
m≥
4}
(including v2{
4,
3 sub-event}
) fromchargedtracksintheTPCacceptanceonly.
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 vn
{
m}
havethree sources:eventselection,tracktype/selection,andtheQn-vectorcorrection
proce-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.Onlystatisticaluncertaintiesare vis-ible(thinverticallines).Bottompanel:Ratiosofv2{4}/v2{2}comparedtosome
theoreticalpredictions.Thehydrodynamicpredictionsuseashearviscosityover en-tropyratioη/s=0.047 andinitialconditionsfromtheTRENTomodel[21,46].For v2{2},theALICEmeasurementsimplementa|η|>2.0 gapwhichisnotusedin
themodels.
ofTPCspacepoints),andcomparing anydifferencesbetween de-termining Qn or un,k from positive or negative only TPC tracks
(bothchargesignsareusedtobuildaflowvectorforthefinal re-sults).Finally,theuncertainties inQn-vector correctionprocedure
contributionareduetouncertaintiesinthepT dependent
efficien-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 TeVasafunctionofcentrality.Astrongerdependenceofv2 with
cen-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
andη
) are expected to be thelargest non-flow contribution,the similarities observed for vn{
2,
|
η
|
>
2}
and vn{
2,
|
η
|
>
1}
in-dicate non-flow is strongly suppressed by a gap of one unit of pseudorapidity. Theextractedvaluesof v2
{
m≥
4}
use Qn-vectorswithout any
η
gaps. The v2{
4,
3 sub-event}
results haveη
gapsbetweenthe Qn-vectorsto suppress non-flow.The sub-event
re-gionsare
−
0.
8<
η
≤ −
0.
4,−
0.
4<
η
≤
0.
4 and0.
4<
η
≤
0.
8.The equivalencewith v2{
4}
(noη
separation) demonstratesthat sucha gap is actually not required for these flow coefficients. Given
Fig. 2. Toppanel:Comparisonsofchargedparticlevn{2}integratedoverthe
trans-versemomentumrange0.2<pT<3.0 GeV/c asafunctionofcentralityfromXe–Xe
andPb–Pbcollisions.Middlepanel:Ratioofvn{2}(Xe–Xe/Pb–Pb)coefficients.
Bot-tompanel:Doubleratioofdataandtheory.Hydrodynamicalmodelpredictionsfrom EKRT[20] andV-USPHYDRO[21] areshown.Inallcases,onlystatistical uncertain-tiesarevisible(thinverticallines).
allthoseobservationsregardingnon-flow,onecaninterpret differ-encesbetween v2
{
2}
and v2{
4}
, v2{
6}
,v2{
8}
tobelargely drivenby 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 129Xeβ
2 deformation (
β
2=
0.
162), which ispre-dicted forthe 129Xe nucleus [47], but has never been measured directly.ItmodifiestheWoods–Saxondistributionasfollows[48]
ρ
(
r, θ )
=
ρ
01
+
e(r−R0−R0β2Y20(θ ))/a,
(6)where
ρ
0 is thedensityatthecenterof thenucleus, R0 thenu-clearradius,r isthedistanceawayfromthecenter,Y20isaBessel
functionofthesecondkind,anda istheskindepth.Accordingto Eq. (2),the ratioofflow coefficients v2
{
4}
/v2{
2}
should beiden-ticalto theratioof initialstate eccentricities
ε
2{
4}/
ε
2{
2}
.To testthis 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.Thehydrodynamiccalculationsgenerally pre-dictlowerratioscomparedtothedata,withthelargestdeviations beinginthesemi-centralregion(10–50%).
Fig. 3. Toppanel:Comparisonsofchargedparticlevn{2}integratedoverthe
trans-versemomentumrange 0.2<pT<3.0 GeV/c from Xe–XeandPb–Pb collisions
forfinercentrality binsincentral collisions.Statisticaland systematic uncertain-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 wherethe Xe–Xe values are
∼
35% higher. For the V-USPHYDRO and EKRTmodels [20,21] shown, both sets ofthe used initial condi-tion models demonstrateε
2{
2}
(Xe–Xe)/ε2{
2}
(Pb–Pb)∼
1 for thesemi-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 bethe 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,despiteusingdifferentvaluesofη
/
s,bothmodels pre-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 furthertheoreticalinvestigations.
Bothsetsofmodelpredictions(V-USPHYDROandEKRT) imple-menta129Xedeformationusing
β
2=
0.
162.Thevalueofβ
2iszeroforthe208Pbnucleus,asitis adoublemagicnucleus. The defor-mation fortheXe–XeV-USPHYDROpredictions contributes
∼
20% to the observed v2{
2}
for central collisions (compared with thecase whereno deformation is implemented), and hasno impact onv2
{
2}
forcentralitiesabove15%.Regardingv3{
2}
,itisgenerallylargerin Xe–Xe,whichreflectsthe factthat theinitial conditions fromboth models show
ε
3{
2}
(Xe–Xe)>
ε
3{
2}
(Pb–Pb) ata givencentrality forthe entirecentralityrange presented.The hydrody-namicpredictions for v3
{
2}
aresimilar forthe two models,withmaximumdeviations of
∼
5%fromthe data.Theβ
3 deformationforboth 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 foracentrality of
∼
15%. For 0–1% central collisions, where the over-lapgeometryisexpectedtoplayaminimalroleforbothsystems,v2
{
2}
is∼
60% larger for Xe–Xecollisions. In terms of theinitialstate,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 beenpreviously shown that
ε
n{
2}
decreases asthe number ofsourcesincreasesforasphericalsystem[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.Thesame lineof reasoning can explain why v3
{
2}
isobserved to belarger 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 inFig. 4. ThepT-differentialv2forchargedparticlesfromXe–Xecollisionsat√sNN=5.44 TeVandPb–Pbcollisionsat√sNN=5.02 TeVforvariouscentralityclasses.Statistical
Fig. 5. ThepT-differentialv3forchargedparticlesfromXe–Xecollisionsat√sNN=5.44 TeVandPb–Pbcollisionsat√sNN=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. Thecorresponding reduction in statisticaluncertainties is particularly usefulforthehigherpTmeasurements.Asexpected,thecentrality
dependenceof v2
{
2,
|
η
|
>
2}
fromXe–Xecollisions followsthatobserved 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 pT-differential
v3
{
2,
|
η
|
>
2}
coefficients. The Xe–Xe coefficients are typicallylargerthan 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}
ratiosasafunctionof1
/
S dNch/dηinXe–XeandPb–Pbcollisions,whereS andε
n{
2}
are obtained using various initial state models. The vn
{
2}/
ε
n{
2}
ratioprovides estimatesof
κ
n asperEq. (2).Asmentioned,whencomparing vn
/
ε
n from differentsystems, a violation of thescal-ing with 1
/
S dNch/dη (which increases with centrality), maybeindicativeofshortcomingsinthemodelingoftheinitialstate(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=
r ncos(nφ)
2
+
r nsin(nφ)
2 r n
,
(7) S=
4π σ
xσ
y,
(8)whichisdefinedsuch that thesources that contribute tothe ec-centricityandarea havetheproperty
x=
y=
0,wherex,
yand
ϕ
,
r arethecartesianandthepolarcoordinatesofthesource, respectively.Thequantitiesσ
x andσ
y representthestandardde-viations ofthe source distributions. The event averages used for Fig.6are
ε
n{
2}
=
ε
n2
+
σ
ε2n andS.Thenormalizationofthe
area is chosen such that for a Gaussian distribution the average densitycoincideswithNpart
/
S (Npart isthenumberofparticipat-ingnucleons),andwasusedinaprevious ALICEpublication[53]. Adeformation of
β
2=
0.
18±
0.
02 for the 129Xe nucleusisused[30,54].Thevalue wasobtainedfromextrapolatingmeasurements
of
β
2 fromnearbyisotopes(128Xeand130Xe),andtheoreticalcal-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 theTRENTo
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–Pbcollisions, 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 thescalingusingtheTRENToinitial 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 vn in Pb–Pb collisions at√
sNN=
2.
76 TeV [63]. TheIP-Glasma approachuses ColorGlass Condensatecalculationsto de-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}
.ThedropisalsoobservedintheMCGlaubernu-Fig. 6. Comparisonsofvn{2}/εn{2}integratedoverthetransversemomentumrange0.2<pT<3.0 GeV/c asafunctionof1/S dNch/dηinXe–XeandPb–Pbcollisions,where S andεn{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 dNch/dη.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 comparedtoq
=
3.Thesemodelimplementationsagainshowadropfor cen-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
/
SdNch/dη
∼
10 fm−2) are selected, and the pT-differential valuesof v2
{
2}/
ε
2{
2}
are shown. The pT-integratedvalues forthecon-stituentquark MC Glauber modelchosen (q
=
3) are observedto besimilarintheleftbottompanelofFig.6.Inthatfigure,theXe– Xecentralitybincorrespondstothefourthpointgoinglefttoright, whilethePb–Pbcentralitybincorrespondstothethirdpoint.The ratiointhebottompanelofFig.7usesaninterpolationofthePb– Pbdatapoints.Theratioisindependentoftheinitialstatemodel used,asallgivevery similarvaluesofε
2{
2}
(Xe–Xe)/ε2{
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:Ratiosofthescaled coef-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)andpT=
0.
716±
0.
004 GeV/c (Pb–Pb) for charged hadrons [64]. The ratio is close to 1 and shows no significant pT dependence. This indicates when such a
the pT-differentialmediumresponse (κ2
(
pT)
) iscontrolledbythetransverse 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 ALICEdetector 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–Xecolli-sions at
√
sNN=
5.
44 TeV compared with Pb–Pb collisions at√
sNN
=
5.
02 TeV atthe same centrality. The v3{
2}
coefficient islarger, consistent with expectations from hydrodynamical mod-els that reproduce the differences for both systems within
∼
5% (Figs.2and3).Thedifferencesforv2{
2}
arepredictedtobedrivenlargelybythehydrodynamicalresponseofthesystem. Forcentral collisions, v2
{
2}
is found to be larger inXe–Xe collisions, whichagreeswithpredictionsfromhydrodynamic models,butthe devi-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 ofthemodeling of the initial state via eccentricity scaling with trans-versedensity(Fig.6)havedemonstratedthatboththeMCGlauber (constituentquarks)andtheTRENTomodelsprovidethemost
sat-isfactorydescriptions.However,thedropobservedforv2
{
2}/
ε
2{
2}
incentralXe–XeandPb–Pbcollisionsisnotexpectedfrom hydro-dynamiccalculations. InthecaseoftheMC Glauber implementa-tions, the drop is more pronounced for nucleon and constituent quark(q
=
3)sources,andmayrequiresomeimprovementsinthe initialstatemodelingfortheregioninXe–XeandPb–Pbcollisions whereε
2{
2}
has the largest contribution from initial statefluc-tuations.Finally, fortwo Xe–XeandPb–Pb centralitybins witha similartransversedensityandsize,itisfoundthatthedouble ra-tio [v2
{
2}/
ε
2{
2}
(Xe–Xe)]/[v2{
2}/
ε
2{
2}
(Pb–Pb)] is largelyindepen-dentof pT (Fig. 7).Thismay indicatethe pT-differentialmedium
responseiscontrolledbythetransversedensityandsize, indepen-dentofthecollisionsystem.
Acknowledgements
The ALICE Collaboration would like to thank all its engineers andtechnicians fortheir invaluablecontributionstothe construc-tionoftheexperimentandtheCERNacceleratorteamsforthe out-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 of Sci-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)and Insti-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, Researchand Reli-gions,Greece;NationalResearch,DevelopmentandInnovation Of-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 StoricodellaFisicaeCentroStudieRicercheEnricoFermiand Isti-tutoNazionalediFisicaNucleare(INFN),Italy;Institutefor Innova-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;Nederlandse Organ-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 EducationandScienceoftheRussianFederationandNational Re-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;ScienceandTechnologyFacilities Coun-cil (STFC), United Kingdom; National Science Foundation of the United States ofAmerica (NSF) andUnited StatesDepartment of Energy,OfficeofNuclearPhysics(DOENP),UnitedStatesof Amer-ica.
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ALICECollaboration
