Centrality and pseudorapidity dependence of the charged-particle multiplicity density in Xe–Xe collisions at sNN=5.44TeV

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Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Centrality

and

pseudorapidity

dependence

of

the

charged-particle

multiplicity

density

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:

Received24May2018

Receivedinrevisedform23November2018 Accepted21December2018

Availableonline28December2018 Editor:L.Rolandi

InthisLetter,theALICECollaborationpresentstheﬁrstmeasurementsofthecharged-particlemultiplicity density,dNch/dη,and totalcharged-particle multiplicity, Ntot_ch,inXe–Xe collisions atacentre-of-mass

energypernucleon–nucleonpairof√sNN=5.44 TeV.The measurementsareperformedasafunction

of collision centralityover awide pseudorapidity range of−3.5<

η

<5. The values ofdNch/dη at

mid-rapidityandNtot

ch forcentralcollisions,normalisedtothenumberofnucleonsparticipatinginthe

collision(Npart)asafunctionof√sNN followthetrendsestablishedinpreviousheavy-ionmeasurements.

The samequantitiesare alsofoundtoincreaseas afunctionofNpart,and uptothe 5%mostcentral

collisionsthetrendsarethesameastheonesobservedinPb–Pb atasimilarenergy.Formorecentral collisions, the Xe–Xe scaled multiplicities exceed those in Pb–Pb fora similar Npart. The results are

compared to phenomenological models and theoretical calculations based on different mechanisms for particleproduction innuclear collisions.Allconsidered models describethe data reasonably well within 15%.

1. Introduction

Aplasma ofstrongly interacting quarksand gluonsis formed in the hot and dense nuclear matter created in ultra-relativistic heavy-ioncollisions [1,2].Themultiplicityofchargedparticles pro-duced in the collisions is a key observable to characterise the propertiesofthe mattercreatedinthesecollisions,astheoverall particleproductionis relatedto theinitial energydensity.Nuclei are extended objects and the degree of geometrical overlap be-tween them in the collision, expressed in terms of the impact parameter (b), varies. Since b is not directly measurable, an ex-perimentalproxyofcentralityis usedtocharacterise theamount ofnuclearoverlapinthecollisions.Typicalfeatures relatedtothe collisioncentralityarethenumberofnucleonsparticipatinginthe collision, Npart, andthenumber ofbinary nucleon–nucleon

colli-sions,Ncoll,amongtheparticipantnucleons.Collisionsofnucleiof

differentsizes leadtodifferent Npart and Ncoll forsimilarrelative

nuclearoverlap.The studyofthe productionof chargedparticles withdifferent collision systems andat various collision energies canhelp shed light on the role ofthe initial energydensity and theproductionmechanismofﬁnal-stateparticles.

Previous measurements of the system-size dependence of the charged-particle pseudorapidity density(dNch

/

d

η

) were

per-formedatRHIC,comparingAu–AuandCu–Cucollisions atvarious

_E-mail_address:_alice_{-publications}_@cern_.ch_.

centre-of-massenergies [3].TheALICE,ATLASandCMS Collabora-tions at the LHC have previously reported on dNch

/

d

η

inPb–Pb

collisions at

√

sNN

=

2

.

76 TeV [4–7] and 5.02 TeV [8,9]. The

de-pendenceofthecharged-particle densityaveragedatmid-rapidity (

|

η

|

<

0

.

5)

dNch

/

d

η

over the centre-of-mass energy shows a

steeper increase in central heavy-ion collisions than in proton– proton (pp) and proton–nucleus (pA) collisions. The values of

dNch

/

d

η

, normalised by the number of nucleon pairs

partici-patinginthecollision,increasefasterthanlinearlywithNpart.No

signiﬁcantdifferencesbetweentheshapesoftheNpartdependence

forthedifferentcollisionenergieswereobserved.

In this Letter, the ALICECollaboration presents the ﬁrst mea-surementoftheproductionofcharged,primaryparticlesinXe–Xe collisionsat

√

sNN

=

5

.

44 TeV.ThesizeoftheXe–Xe systemis

in-termediatebetweenpreviouslystudiedsystemsattheLHC,Pb–Pb [4,5,8,9] being the largestand p–Pb andpp [10,11] the smallest. Thecharged-particle pseudorapidity densityispresentedover the interval

−

3

.

5

<

η

<

5 andasafunctionofthecollisioncentrality. The mid-rapidity valuesnormalised by thenumber of participat-ing nucleon–nucleon pairs arealso reported.The results are also comparedwithmeasurementsatlowercollisionenergiesandwith theoreticalcalculations.

2. Experimentalsetup

ThedatawererecordedwiththeALICEapparatusin6hoursof stabledata-takingwith129Xebeams(16bunchesperbeam)

collid-https://doi.org/10.1016/j.physletb.2018.12.048

(2)

ingat

√

sNN

=

5

.

44 TeV in October2017. Thedatawere collected

withareducedmagneticﬁeldof0.2 T(ascomparedtothe nomi-nalvalueof0.5 T)intheALICEsolenoidmagnet.Theperformance anda detaileddescriptionofALICEcan be foundelsewhere [12]. Inthefollowing,thedetectorelementsrelevanttothisanalysisare brieﬂydescribed.

Theinnermost partofthetrackingsystemofALICEis the Sil-icon Pixel Detector (SPD) [13] which consists of two cylindrical layersofhybridsiliconpixelassemblies.Theinner andouter SPD layers are placed at radii of3.9 and7.6 cm fromthe interaction point and cover

|

η

|

<

2 and

|

η

|

<

1

.

4, respectively. The Forward MultiplicityDetector(FMD) [14,15] consistsofthreesetsofsilicon strip sensors,coveringthe pseudorapidities

−

3

.

5

<

η

<

−

1

.

8 and 1

.

8

<

η

<

5. The FMD records the energy deposited by charged particles impinging the detector.The V0detector [15,16] is used fortriggering andcentrality classiﬁcation.It consists oftwo sub-detectors, V0-A and V0-C, covering the pseudorapidity regions 2

.

8

<

η

<

5

.

1 and

−

3

.

7

<

η

<

−

1

.

7, respectively. The V0 has a timing resolutionbetter than 1 ns,allowing its fastsignalsto be combinedin a programmable logic toreject beam-induced back-groundevents while ensuring maximumeﬃciency forthe selec-tionofcollisionevents.TheZero-Degree Calorimeters(ZDCs) [17] are located at a distance of 112.5 m from the interaction point alongthebeamline,oneithersideoftheexperiment.They mea-suretheenergyofspectator(non-interacting)nucleons.TheZDCs are alsoused fortriggering andprovide timing informationused toselectcollisionsoccurringintheinteractionpointregion.

3. Datasampleandanalysismethod

ThehadronicinteractionrateinALICEwasabout150(80) Hzat thebeginning(end)ofthedata-taking.Themagneticfieldof0.2 T, reduced ascompared to normal Pb–Pb settings (0.5 T) increases the acceptance forlow-momentum particles, thus enhancing the acceptanceoftheV0systemforelectromagnetic(EM)interactions, which constitutea background forthis analysis. Inorder to sup-pressthissourceofcontamination, theminimumbiasinteraction trigger required a signal in each of the V0 sub-detectors in co-incidencewith a signal ineach ofthe two neutron ZDCs.It was verified by means ofa set ofcontrol triggers that such a trigger is fullyefficient forhadronicinteractions in the 0–90% centrality range.Inaddition,beam-backgroundinteractionsareremoved us-ingtheV0andtheZDCtiminginformation.The interaction prob-ability per bunch-crossing was sufficiently small that the chance oftwohadronicinteractionsoccurringwithintheintegrationtime ofthe involved detectors,so-calledpileup events,was negligible. A totalofabout1millionhadroniccollisionsareusedinthis anal-ysis.

The classiﬁcation of collisions into centrality classes uses the sumoftheamplitudesofthesignalsintheV0-A andV0-C detec-tors.Amodel ofparticleproduction,basedona Glauber descrip-tion [18,19], is ﬁtted to the V0 amplitude distribution [20]. The numberof particles inthe V0detector iscalculated witha two-componentmodelforthenumberofsourcesgivenby

Nsources

=

f

×

Npart

+ (

1

−

f

)

×

Ncoll

,

(1)

where f constrains the relative contributions of Npart and Ncoll,

coupled to a particle production model foreach source parame-terisedbythenegativebinomialdistribution(NBD).IntheGlauber calculation,thenucleardensityfor129XeisdescribedbyaWoods– Saxondistributionforadeformednucleus

ρ

(

r

, ϑ)

=

ρ

0

1

+

exp

r−R_a(ϑ )

.

(2)

Theparameter

ρ

0 isthenucleondensity,whichprovidesthe

over-allnormalisation.Thenuclearskinthicknessisa

=

0

.

59

±

0

.

07 fm [21]. The nuclear radius R is parametrised as a function of the polar angle

ϑ

by R

(ϑ)

=

R0

[

1

+ β

2Y20

(ϑ)

]

, where R0 is the

av-erage radius andthe Legendre polynomial Y20 describes the

nu-cleus deformation foran axially symmetric casewith no depen-dence on the azimuthal angle. For the average radius we used

R0

=

5

.

4

±

0

.

1 fm, scaling the results for 132Xe reported in [21]

bytheatomicmassnumber(A)dependenceoftheradius,namely

(

129

/

132

)

1/3 [19].Thedeformationparameter

β

2

=

0

.

18

±

0

.

02 is

obtainedby linearlyinterpolatingthe valuesmeasured fortheXe A-evenisotopesfrom124to136 [22].IntheGlaubermodel calcu-lation,theorientation ofthespheroid symmetryaxisisrandomly sampled. For

√

sNN

=

5

.

44 TeV collisions, an inelastic nucleon–

nucleon cross section of 68

.

4

±

0

.

5 mb, obtained by logarithmic interpolation of cross section measurements with respect to col-lision energies inpp collisions [23], isused. TheNBD-Glauber ﬁt provides a gooddescription oftheobserved V0amplitude in the region corresponding to the top 90% of the hadronic cross sec-tion,wheretheeffectsoftriggerineﬃciencyandcontaminationby EM processesare negligible.The averagenumbers ofparticipants

Npart

reportedinTable1areestimatedfromtheGlaubermodel

imposing thesame cutsappliedto the dataonthe simulatedV0 response. One should note that the centrality selection based on theV0amplitudeinduces abiasonthemeasured

dNch

/

d

η

.This

leadstoa

dNch

/

d

η

inthe70–80%(80–90%)centralityclassabout

3% (10%)lower thanthevalueonewouldobtainwithacentrality selectionbasedontheimpactparameter.

For all the collisions in the 0–90% centrality range the co-ordinates of the primary interaction point can be reconstructed withgoodaccuracybycorrelatinghitsinthetwo SPDlayers. The measurement ofthe charged-particle multiplicity densityat mid-rapidityusesinformationfromtheSPD.TheacceptanceoftheSPD for charged particles spans different pseudorapidity regions de-pending on the positionof the interactionpoint along the beam line, z.Forexample,forcollisions withthe vertexlocated within

|

z

| <

7 cm a maximum acceptance of

|

η

| <

1

.

5 can be reached, with approximately constant acceptance for

|

η

| <

0

.

5. To extend thepseudorapiditycoverageupto

|

η

| <

2,allcollisionswitha pri-maryvertexlocatedwithin

|

z

| <

20 cm havebeenconsidered.

Following the method developed earlier [4,5,8,9,24], tracklets (short track segments) are formed using the position ofthe pri-mary vertex and all possible combinations of hits between the two SPD layers. The primary charged-particle multiplicity den-sity dNch

/

d

η

isobtained fromthe numberof tracklets that pass

the quality selection criteria, after correcting for detector accep-tance,reconstruction andselectioneﬃciencies andcontamination from combinatorial background and secondary charged particles. This selection allows primary charged-particle detection down to a momentum of 30 MeV/c. The corrections are estimated using a detailedsimulation basedonevents generatedwiththe HIJING eventgenerator[25] withparticletransportinALICEperformedby GEANT3 [26]. Thedecayproducts oflong-liveddecaying particles like K0_S,

,

¯

and other strange hadrons are classiﬁed as sec-ondaryparticles[27] andthecontaminationfromtheseparticlesis subtracted fromdata.Itisknownthat HIJINGunderestimates the relativeproductionrateofstrange particlesinhigh-energy heavy-ioncollisions. Forthisreason, thesimulationhasbeenreweighed toreproducetherelativeparticleabundancesobservedinthedata which are about30% (50%) higher than HIJING inthe most cen-tral (peripheral) collisions. The reweighing factors have been de-rivedfroman estimateofK0

S,

and

¯

relativeproductioninthe

data,obtainedviainvariant massreconstructionandcomparedto HIJING.

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Table 1

ThedNch/dηandNtotch valuesfordifferentcentralityclasses,deﬁnedbyV0multiplicity.Theerrorsaretotaluncertainties,thestatisticalcontributionbeingnegligible.The

valuesofNpartobtainedwiththeGlaubermodelarealsoreported.TheerrorsareobtainedbyvaryingtheparametersoftheNBD-Glaubercalculation.

Centrality Npart dNch/dη Npart2 dNch/dη N

tot ch 2 NpartN tot ch 0–1% 246±2 1302±17 10.6±0.2 14700±300 119.5±2.6 1–2% 241±2 1223±25 10.1±0.2 13840±250 114.9±2.3 2–3% 236±3 1166±23 9.88±0.23 13250±280 112.3±2.8 3–4% 231±2 1113±20 9.64±0.19 12700±290 110.0±2.7 4–5% 225±3 1069±20 9.50±0.22 12180±260 108.3±2.7 0–2.5% 242±2 1238±25 10.2±0.2 14100±320 116.5±2.8 2.5–5.0% 229±2 1096±27 9.57±0.25 12440±280 108.6±2.6 5.0–7.5% 214±3 986±25 9.21±0.27 11230±330 105.0±3.4 7.5–10% 199±2 891±24 8.95±0.26 10300±300 103.5±3.2 0–5% 236±2 1167±26 9.89±0.24 13230±280 112.1±2.6 5–10% 207±3 939±24 9.07±0.27 10820±280 105.0±3.1 10–20% 165±3 706±17 8.56±0.26 8200±310 99.4±4.2 20–30% 118±4 478±11 8.10±0.33 5670±300 96.1±6.0 30–40% 82.2±3.9 315±8 7.66±0.41 3770±270 91.7±7.9 40–50% 54.6±3.6 198±5 7.25±0.51 2460±220 90.1±10 50–60% 34.1±3.0 118±3 6.92±0.63 1480±170 86.8±13 60–70% 19.7±2.1 64.7±2.0 6.57±0.73 828±44 84.1±10 70–80% 10.5±1.1 32.0±1.3 6.10±0.68 437±16 83.2±9.2 80–90% 5.13±0.46 13.3±0.9 5.19±0.58 181±7.0 70.6±6.9

The deposited energy signal in the FMD is used to measure thecharged-particlepseudorapiditydensityintheforwardregions (

−

3

.

5

<

η

<

−

1

.

8 and 1

.

8

<

η

<

5), following the method de-scribedelsewhere [5].Theenergylossismeasuredinthe51,200 Si stripsensors ofthedetectoranda statisticalapproachis usedto calculatethe inclusivenumberofchargedparticles.Adata-driven correctionderivedfrompreviousstudies [24] correctsforthe back-groundofsecondaryparticles,whichareabundant intheforward regions.

4. Systematicuncertainties

The systematicuncertainties on

Npart

are obtainedby

vary-ing the parameters of the Glauber model independently within their estimated uncertainties and repeating the NBD-Glauber ﬁt. The uncertaintydue to the centrality determination isestimated bychangingthevalueofV0amplitudethatcorrespondstothetop 90% ofthehadroniccrosssectionby

±

0

.

5%.Thisresultsinan un-certaintyon

dNch

/

d

η

of0.1% to4.8%fromcentral toperipheral

collisions.An additional 4% uncertaintyassignedto the most pe-ripheralclass,arising fromtheremaining contaminationfromEM processes,wasestimatedbystudyingtheenergydepositioninthe ZDCs [28].

Forthetrackletanalysisatmid-rapiditytherelativesystematic uncertaintyonthemeasurementofthecharged-particle multiplic-ityinperipheral(central)eventsarisesfromthefollowingsources: tracklet selection 0.1% (0.8%), calculated by varying the tracklet qualitycut up to4 timesthenominalvalue;combinatorial back-ground subtraction 0.5% (2.0%), estimated from simulations and cross-checked using an alternative method where artiﬁcial SPD clustersare addedto the data andthe numberof corresponding artiﬁcialreconstructedtracklets are usedforbackground subtrac-tion;particle composition 0.2%(0.2%),estimated bychanging the relative abundances ofprotons, pions andkaons by

±

30% inthe simulation;contamination by weak decays0.3% (0.3%),estimated by changing thereweighting factors; extrapolation to zero trans-versemomentum 0.6% (0.6%),obtained fromthe variation ofthe estimatedyieldofparticlesatlowtransversemomentumbya fac-toroftwointhesimulation;variationsindetectoracceptanceand eﬃciency1% (1%),evaluated by carrying out theanalysisfor dif-ferentslices of the z-position of theinteraction vertexandwith subsamples in azimuth. At forward rapidities, the uncertainties

Fig. 1. Charged-particlepseudorapiditydensityfor12centralityclassesoverabroad

ηrangeinXe–Xe collisionsat √sNN=5.44 TeV.Boxesaroundthe pointsreﬂect

thetotalsystematicuncertainties,whilethefilledsquaresontherightreflectthe normalisationuncertaintyfromthecentralitydetermination.Statisticalerrorsare negligible.Thereflection(opencircles)ofthe3.5<η<5 valuesaroundη=0 is alsoshown.Thelinescorrespondtofitstoagaussiandistributioninrapidity mul-tipliedbyaneffectiveJacobianoftransformationfromηtoy.

relatedtothemeasurement ofmultiplicity arisefromthe follow-ingsources:thedata-drivencorrection forsecondary particles [9] 6.1%; themerging algorithms ofsignalsfromSi stripstoa single particle 1%;variationin rejectionthresholdfor calculationof the charged-particle multiplicity per event +₋1%_2%; particle composition 2%,estimatedinthesamewayasinthetrackletanalysis.

Thesystematicuncertaintiesfromcentralityselectionand elec-tromagnetic interactions affect the overall normalisation of the results. The total systematic uncertainty, obtained by adding in quadrature all contributions,amounts to 6.4% (2%) forperipheral (central) in

|

η

|

<

2, to6.9% for

η

>

3

.

5 andto 6.4%elsewhere in theforwardregion,andispartiallycorrelatedover

η

andbetween differentcentralityclasses.

5. Results

Fig.1 presentsthe charged-particle multiplicity densitydNch

/

d

η

as a function of pseudorapidity for 12 centrality classes.The measurement is obtained from the SPD at mid-rapidity, FMD in forward-rapidities, and combined in regions of overlap (1

.

8

<

|

η

|

<

2) betweenthetwo detectors bytakingthe weighted

(4)

aver-age using the non-shared uncertainties asweights. The data are symmetrisedaround

η

=

0,averaging positiveandnegative

η

re-sultswherever possible,andextendedintothe non-measured re-gion

−

5

<

η

<

−

3

.

5 by reﬂecting the 3

.

5

<

η

<

5 valuesaround

η

=

0.Averagedvalues(leftandright)agreewithinthe uncertain-ties. Assumingthatthe charged-particlerapidity densitydNch

/

d y

hasGaussian shapeandusinganeffectiveJacobian,themeasured dNch

/

d

η

is ﬁtted withthisansatz anda width of

σ

=

4

.

4

±

0

.

1

isfound, consistentwiththe value obtainedinPb–Pb at

√

sNN

=

5

.

02 TeV [9].

The multiplicity density averaged over

|

η

|

<

0

.

5 in different centrality classes is shownin Table 1. The total charged-particle multiplicity Ntot_ch is determined from the data in the measured regionandfromextrapolations,up to

η

= ±

ybeam,inthe

unmea-suredregion.Threedifferentfunctionsareusedtoextrapolatethe datapoints:thedifferenceoftwoGaussiandistributionscentredat

η

=

0;aWoods–Saxon-likedistributioninrapidityasproposedby PHOBOS [29];andatrapezoidalform.Thetrapezoidansatz inthe forwardunmeasuredregionscorrespondstoalinearextrapolation upto

η

= ±

ybeamwiththestartingpointconstrainedbythe

mea-surements.AGaussiandNch

/

d y inrapidityresultsinadistribution

in pseudorapidity which is very similar to the difference of two Gaussianscentred at

η

=

0. Thecentral value inthe unmeasured regions(

−

8

.

6

<

η

<

−

3

.

5 and5

<

η

<

8

.

6)istakenastheaverage betweenthetrapezoidalfunction(whichgivesthelowestNtot

ch)and

theGaussian dNch

/

d y (which givesthehighest Ntot_ch).The

contri-butionfromthe extrapolatedregionislessthan 30%of Ntot ch.The

systematicuncertaintyoftheextrapolatedNtot_ch iscalculatedasthe quadraticsumofcontributionsfromthesystematicuncertaintyof the data and a conservative contribution obtained by comparing the results fromthe different ﬁt functions. It amounts to about 14% (4%)of Ntot

ch inperipheral(central) events.Inorderto

com-parebulkparticleproductionatdifferentenergiesandindifferent collisionsystems,theaveragecharged-particle multiplicitydensity

dNch

/

d

η

at mid-rapidity is divided by the average number of

participatingnucleonpairs,

Npart

/2. Thisallowsone to compare

nuclear collisions to pp andpp collisions. The

Npart

valuesare

calculatedwithintheGlaubermodel.

Fig.2(top) showsthemid-rapidity charged-particle multiplic-itynormalisedbythenumberofnucleonpairsparticipatinginthe collision, _N2

part

dNch

/

d

η

,inpp, pp,

¯

p(d)A andincentral heavy-ioncollisionsasafunctionofthecentre-of-massenergy.Thelines representﬁtstolowerenergyresults.TheXe–Xe resultisin agree-ment within the uncertainties with the trend established from previousheavy-ionmeasurements,whichshowsastrongerriseas a function of

√

sNN than for pp andp–Pb collisions. Fig. 2

(bot-tom)showsthetotal charged-particle multiplicity per participant nucleonpair _N2

partN

tot

ch,whichfollowsthetrendforcentral

heavy-ioncollisions.

Fig.3showsthecentralitydependenceofthemid-rapidityand the total multiplicities per participant nucleon pairs. The point-to-pointcentrality-dependent uncertainties areindicated by error bars whereas the shaded bands show the correlated uncertain-ties. The valuesof _N2

part

dNch

/

d

η

and

2

NpartN

tot

ch decrease by a

factor 2from the mostcentral to the mostperipheral collisions, where they agree with the values measured in minimum bias pp and p–Pb collisions [10,11]. The data are compared to lower energy results at

√

sNN

=

200 GeV [3] for the RHIC experiment,

√

sNN

=

2

.

76 TeV [4,5] and

√

sNN

=

5

.

02 TeV [8,9] forPb–Pb

colli-sionswherethelatterhasbeenre-analysedwiththesameanalysis techniqueinnarrowercentralityclasses,scaledtomatchtheXe–Xe dataat

√

sNN

=

5

.

44 TeV. The scalingfactors arecalculatedusing

theﬁtfunction ofFig.2 forthetop5% central collisions.Forthe 5% most central Xe–Xeand forthe 2% mostcentral Pb–Pb

colli-Fig. 2. Valuesof Npart2 dNch/dη(top)and

2 NpartN

tot

ch (bottom)forthe 5%most

centralXe–Xe collisionscomparedtopreviousmeasurementsinPb–Pb [4,6–9,30] and Au–Au [3,31–34] asafunctionof√sNN,aswellasfor inelasticpp,pp [10,

35,36] andnon-singlediffractivepAanddAcollisions[11,37].Thelinesarepower lawﬁtstothedata,excludingXe–Xe results.ThecentralPb–Pb measurementsfrom CMSandATLASat2.76 TeVhavebeenshiftedhorizontallyforclarity.

sions, the _N2

part

dNch

/

d

η

increasessteeply. A similar conclusion wasalsoreachedfortheRHICdata[3]:theCu–Cutrendresembles that ofAu–Au uptothemostcentralcollisionsandrisesabove it for the mostcentral collisions. The RHIC dataare alsoshown in Fig. 3 anda deviationfrom theLHC data for Npart

<

100 is

vis-ible, although withlargeuncertainties. The steeper risemight be duetomultiplicityfluctuationsinthetailoftheXe–XeV0 ampli-tude distribution [22]. Thefluctuationsoccurboth inthenumber ofcollisionsoverparticipantsandinthenumberofcharged parti-clesoverparticipants.Theriseisquantitativelyreproducedbythe NBD-Glauber fit.The total numberofcharged particles scaledby thenumberofparticipantpairsshowsaslightincreaseasa func-tion ofthe numberof participants in Fig. 3 (bottom),similar to thatofthemidrapidityresults,albeitwithlargerexperimental un-certainties.Fig.4showstheXe–XeandPb–Pbresultsasafunction of a differentscaling variable

(

Npart

−

2

)/(

2 A

)

,where A is the

atomic mass number of the colliding nucleus. The ﬁgure shows that _N2

part

dNch

/

d

η

and

2

NpartN

tot

ch have a similar dependence

on the numberof participants relative tothe possible maximum numberofparticipants,whichindicatesastrongerdependenceon geometricpropertiesofthecollisionzonethanonthecollision sys-temsizes.

The study of the centrality dependence of particle multiplic-ity for different collision systems provides a variable number of nucleon–nucleon collisions at equal number of participating nu-cleons and therefore may provide further information to clarify the measured deviation from Npart scaling. The scaling of the

charged-particle multiplicity by the number of participant nu-cleons was studied in detail and a deviation from Npart-scaling

was observed at RHIC energies [3,30,38–40]. The deviation from

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in-Fig. 3. The Npart2 dNch/dη(top)and

2 NpartN

tot

ch (bottom)forXe–Xe collisionsat

√

sNN=5.44 TeV as a functionofNpart. Theerror barsindicatethe

point-to-pointcentrality-dependentuncertaintieswhereastheshadedbandshowsthe cor-relatedcontributions. Alsoshownintheﬁgureistheresultfrominelasticppat

√

s=5.02 TeV aswellasnon-singlediffractivep–Pb collisions [11] andPb–Pb col-lisionsat √sNN=5.02 TeV [8,9].NotethatPb–Pb dataat√sNN=5.02 TeV were

re-analysedinnarrowercentrality classes.Data from lowerenergiesat √sNN=

2.76 TeV [4,5] and200 GeV[3] areshownforcomparison.

crease in hard processes in central collisions, but no conclusive evidencewasfoundtosupportthisinterpretation.Fig.5compares

2

Npart

dNch

/

d

η

inXe–Xe collisionsat

√

sNN

=

5

.

44 TeV with

dif-ferent parameterisations for particle production. Speciﬁcally, we used the two-component model in Eq. (1) and two power-law functions

dNch

/

d

η

∝

Nαpart and

dNch

/

d

η

∝

Nβ_coll.The functions

were ﬁtted to the Pb–Pb data at

√

sNN

=

5

.

02 TeV [8]. For the

Xe–Xe dataonlytheabsolutenormalisationwasadjusted.The val-uesofthe parameters are alsoconsistent withthose obtainedat SPSandRHICenergies[30,41].Whilenouniquephysicsconclusion canbe drawnfromsuch ﬁts,thissuggeststhatgeometrical argu-mentsmaybe suﬃcientto provideagood descriptionofparticle productionacrossdifferentcollidingsystemsandbeamenergies.

Describing particle production in relativistic heavy-ion colli-sionsasasuperpositionofemissionfromathermalcoreandhard scatteringsinacorona [42],onecanclassifytheparticipating nu-cleonsinto those that scatter only once (Ncorona

part ) and those that

scatter multiple times (N_partcore). The multiplicity can then be ﬁt-ted with the sum of those contributions,

dNch

/

d

η

ppNpartcorona

+

dNch

/

d

η

coreNcorepart, where

dNch

/

d

η

pp is the multiplicity

mea-suredininelasticpp collisions [10] and

dNch

/

d

η

core isthe

con-tributiontothecharged-particle multiplicity fromthecoreofthe ﬁreball,whichisﬁttedtothedata.Fig.5alsoshows

dNch

/

d

η

per

participantquark Nq-partcalculatedwithaGlaubermodelusing

ef-fectivewoundedconstituentquarks [44][43],asafunctionofNpart,

aswasdoneforPb–Pb collisionsat

√

sNN

=

5

.

02 TeV [45] thathave

beenre-analysed innarrowercentralityclasses.Inthe implemen-tationofthequark-Glaubermodelthepartonicdegreesoffreedom (3 or 5) are located around the nucleon centres [43]. The

effec-Fig. 4. The Npart2 dNch/dη(top)and

2 NpartN

tot

ch (bottom)forXe–Xe collisionsat

√

sNN=5.44 TeV asafunctionof(Npart−2)/(2 A).

Fig. 5. The 2

NpartdNch/dηfor Xe–Xe collisionsat

√_s

NN=5.44 TeV andPb–Pb

collisionsat√sNN=5.02 TeV [8],asafunctionofNpart.ThePb–Pb dataare

ﬁt-tedwithvariousparameterisationsofNpartand Ncoll,calculatedwiththeGlauber

model.Thesamefunctions,withthevaluesoftheparametersfromthePb–Pbﬁt, areusedfortheXe–Xe data.AlsoshownisdNch/dηperparticipantquark,Nq-part,

calculatedwiththeeffectivewoundedconstituentquarksmodel [43],asafunction ofNpart.ThenumberofparticipantquarksNq-part isnormalisedbytheaverage

numberofparticipantquarksinppcollisions,μ.

tive inelastic scattering cross section for collisions of constituent quarks is set to 20.38 mb and9.76 mb, for Nq

=

3 and Nq

=

5,

respectively, adjusted toreproduce the 68.4 mb nucleon–nucleon inelasticcrosssectionat5.44 TeV. Nq-part hasbeendividedbythe

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Fig. 6. The 2

NpartdNch/dηforXe–Xe collisionsat

√_s

NN=5.44 TeV asafunction

ofNpartcomparedtomodelpredictions[46,47,49–65].Thebottompanelshows

theratioofthemodelstothedata.Theshadedbandaroundthepointsreﬂectsthe correlatedsystematicuncertainties.

Nq

=

3 (Nq

=

5).Comparingthebehaviourof

dNch

/

d

η

interms

ofthedependenceonthenumberofnucleonorquarkparticipants in the collision, one concludes that Nq-part scaling describesthe

data better than Npart scaling as previously observed [40,45]

ex-ceptthe 0–10%centralityrangeinXe–Xecollisionswherea clear scalingviolationisobserved.

Fig. 6 shows a comparison of the Xe–Xe data to calculations fromtheoretical models at mid-rapidity. HIJING 2.1 [46,47] com-bines perturbative QCD processes with soft interactions, and in-cludes a strong impact parameter dependence of parton shad-owing [48]. For Xe–Xe data at

√

sNN

=

5

.

44 TeV it uses a large

gluon shadowing parameter of 0.28to limit the multiplicity per participant. With this choice, the same as in Pb–Pb collisions at

√

sNN

=

5

.

02 TeV, the multiplicities at mid-rapidity andthe

cen-tralitydependence inthe most central collisions are reproduced. AMPT [50,51] is amodelwhich implementshydrodynamical evo-lution of an initial state produced by HIJING. It includes spatial coalescence of quarks to hadrons, followed by hadronic scatter-ing.AMPT describesboth theshapeandtheoverall magnitudeof themid-rapiditydata.PYTHIA/Angantyr [52] extendsthenucleon– nucleonmodelofPYTHIA8.230 [53] tothecaseofheavy-ion colli-sions,essentiallyperformingindividualnucleon–nucleoncollisions atthepartonlevel,whiletheresultingLund-stringsarehadronised as an ensemble. It is interesting to note that this model agrees reasonably well with the data even though it was developed as an extension of a generator fornucleon–nucleon collisions. EPOS LHC [49] is a parton model based on the Gribov–Regge theory, designedforminimumbias hadronicinteractions,which incorpo-rates collective effects treatedvia a ﬂow parameterisation and a separationoftheinitialstate intocore-coronaparts.Theshapeof thecentrality dependenceis reproduced fairly well at intermedi-ate centralities, however, the model underestimates the absolute valuesof the multiplicity,as was the casein Pb–Pb collisions at

√

sNN

=

5

.

02 TeV [8]. The Dukeglobal calibratedmodel is based

on a Bayesian Statistics analysis using _TRENTo initial conditions for high-energy nuclear collisions [66,67]. The subsequent trans-portdynamicsisthensimulatedusingtheiEBE-VISHNU event-by-event simulations for relativistic heavy-ion collisions which uses ahybridapproachbasedon(2

+

1)-dimensionalviscous hydrody-namicscoupledtoahadroniccascademodel [68].TheDukeglobal calibratedmodelcanreproducetheshapeofthemid-rapidity dis-tribution,butoverestimatesslightlytheoverallmagnitude.

Saturation-inspired models (rcBK-MC [54,55], KLN [56–59], ASW[60],IP-Glasma[61,62] andEKRT[63–65])relyon perturba-tive QCD andan energy-dependent saturationscale, whichlimits thenumberofproducedpartons,andinturnthenumberof pro-duced particles. This results in a factorisation of the energyand centralitydependenceofparticleproductionor,inother words,in theinvarianceofthecentralitygrowth,asobservedinthe experi-mentaldata [69].ThercBK-MCmodellimitsthecentralitygrowth using the rc-BK equation. It provides a good description of the mid-rapidity data, both of the shape and the highest multiplic-ityreachedincentralcollisions.TheASWpredictionoverestimates thedata,whileitwas veryaccurateinPb–Pb at

√

sNN

=

5

.

02 TeV.

The KLN model doesnot describe the shape well and, although it agrees with the value measured for most central collisions, it is signiﬁcantly above the centrality dependence of the data. The IP-Glasma model naturally produces initial energy ﬂuctua-tions computed within the Color Glass Condensate framework combining an impact parameter dependent saturation model. It uses a gluon multiplicity scaled todescribe hadron multiplicities measured in Pb–Pb collisions at

√

sNN

=

5

.

02 TeV [8]. The

cen-tralitydependenceis strongerthanthat observed inmid-rapidity data over(under)-predicting the datain central (peripheral) colli-sions. The EKRT model forheavy-ion collisions uses perturbative QCD with a conjecture of gluon saturation to suppress soft par-tonproduction.Thesaturationscaleisalsodependentonthelocal productofthicknessfunctions,implyingageometricalscaling.The space–time evolution of the system is then described with vis-cous ﬂuid dynamics event-by-event. The normalisation is ﬁxed by exploitingthe 0–5%most centralmultiplicity measurement in Pb–Pb collisions at

√

sNN

=

2

.

76 TeV [70]. As forPb–Pb collisions

at

√

sNN

=

5

.

02 TeV,theEKRTmodelcan describeboththeshape

andtheoverallmagnitudeofmultiplicityoncentrality.Ingeneral, almost all models reproduce the steep rise versus

Npart

while

EPOS-LHC,ASWandKLNshowasaturationbehaviour.The predic-tionsshowasimilartrendasforthePb–Pbcase [8] andaltogether aﬂatterdistributionwithrespecttodata.

In Fig. 7, the models are compared to the pseudorapidity dependence of the dNch

/

d

η

for the top 5% central collisions.

HIJING 2.1 reproduces the pseudorapidity dependence at mid-rapidity well, butoverestimatesthe dataatforwardrapidity,due to the large value of the shadowing parameter used. AMPT and PYTHIA/Angantyrdescribe thedatafairlywell, witha slight over-estimate at forward rapidities. EPOS LHC reproduces the shape well, but under-predicts the multiplicity overall. The rcBK-MC is restrictedto

|

η

|

<

2

.

5 sinceitsformalism canonlybeusedfor ra-pidities far from the fragmentation regions. It shows a narrower distributionthanwhatisseenindata.KLNagreeswiththedataat mid-rapidity, butnot atforwardrapidity,whereitunder-predicts thedata.ForIP-Glasmatherapiditydependenceisprovidedbythe IP-Sat model [71] andit isconverted to pseudorapidity usingan effectivemassof0.2 GeV/c2.The shapeis widerthanthat ofthe data.Regardingthecaseofthepseudorapiditydependenceallthe models showsimilar trendsasforPb–Pb collisions [9] except HI-JING2.1whichdescribestheXe–Xemeasurementsbetterthanthe Pb–Pbdata.

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Fig. 7. ComparisonofdNch/dηasafunctionofηinthe0–5%centralclasstomodel

predictions.The bottompanelshowsthe ratioofthemodelstothe data.Boxes aroundthepointsreﬂectthetotaluncorrelatedsystematicuncertainties.

6. Conclusions

The measurements of the charged-particle multiplicity den-sityandits centrality dependencein Xe–Xe collisionsat

√

sNN

=

5

.

44 TeV have been presented over the pseudorapidity range

−

3

.

5

<

η

<

5 usingthe fullacceptanceofthe ALICEdetector. For the5% mostcentral collisions, theaveragecharged-particle pseu-dorapiditydensityatmid-rapidity(

|

η

|

<

0

.

5)is1167

±

26 andthe total number ofcharged particles is 13230

±

280.Scaled by the numberof participant pairs, theseare found to followthe same power-lawdependencewithenergyestablishedinprevious heavy-ionmeasurements.

The centrality dependences of _N2

part

dNch

/

d

η

and

2

NpartN

tot ch

arevery similartothose previouslymeasured inPb–Pb collisions atsimilarorlowerenergiesup tothe5%mostcentralXe–Xe col-lisions,wheretheXe–Xe resultsare largerthanthePb–Pb results ata similarnumberofparticipatingnucleons.Similar conclusions were drawn atRHIC fromthe comparisonof thedata forCu–Cu andAu–Aucollisions [72].Thesteeperrisemightbedueto multi-plicityﬂuctuationsinthetailoftheXe–XeV0amplitude.

While measurements of particle production in large and medium-sizedcollidingsystemssuch asXe–Xe areabundant and becomeevenmoreprecise,theunderlyingmechanismtodescribe theincrease withenergyandcentralityisstill notcompletely un-derstood.Deeperinsightofthesystemsizedependenceofparticle productionmaycomefromthestudyoflight-nucleicollisions,still notmuchexploredathighenergy,whichcouldbridgethegap be-tween the trends observed in pp andpA collisions andthose of themid-sizedXe–Xe andthelargePb–Pb systems.

Acknowledgements

TheALICECollaborationwouldliketothankN.Armesto, W.-T. Deng, A. Dumitru, K. Eskola, G. Levin, L. Lonnblad, S. Moreland,

H. Niemi,T.PierogandB.Schenkeforhelpfuldiscussionsontheir modelpredictions.

The ALICE Collaboration would like to thank all its engineers andtechniciansfortheir invaluablecontributions tothe construc-tionoftheexperimentandtheCERNacceleratorteamsforthe out-standingperformanceoftheLHCcomplex.TheALICECollaboration gratefully acknowledges the resources and support provided by all Gridcentres andtheWorldwide LHC ComputingGrid (WLCG) collaboration. The ALICE Collaboration acknowledges the follow-ingfundingagenciesfortheirsupportinbuildingandrunningthe ALICEdetector:A.I. AlikhanyanNationalScienceLaboratory (Yere-vanPhysicsInstitute) Foundation (ANSL),StateCommittee 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-nanciadora de Estudos e Projetos (Finep) and Fundação de Am-paroàPesquisa doEstadode SãoPaulo (FAPESP),Brazil; Ministry of Science & Technology of China (MSTC), National Natural Sci-ence Foundation of China (NSFC) and Ministry of Education of China (MOEC), China; Ministry of Science and Education, Croa-tia;MinistryofEducation,YouthandSportsoftheCzechRepublic, CzechRepublic;TheDanishCouncilforIndependentResearch Nat-ural Sciences, the CarlsbergFoundation and Danish National Re-search Foundation (DNRF), Denmark; HelsinkiInstitute of Physics (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 andTechnology, Ministryof Education,Research and Reli-gions,Greece;NationalResearch,DevelopmentandInnovation Of-fice,Hungary;DepartmentofAtomicEnergy, GovernmentofIndia (DAE),DepartmentofScienceandTechnology,GovernmentofIndia (DST), University Grants Commission,Government ofIndia (UGC) andCouncilofScientific andIndustrialResearch(CSIR),India; In-donesian Institute of Science, Indonesia; Centro Fermi – Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi and Instituto Nazionale di Fisica Nucleare (INFN), Italy; Institute for Innovative Science and Technology, Nagasaki Institute of Applied Science (IIST), Japan Society for the Promotion of Science (JSPS) KAKENHIandJapaneseMinistryofEducation,Culture, Sports, Sci-enceandTechnology (MEXT), Japan;Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Interna-cional enCienciay Tecnología(FONCICYT)andDirección General deAsuntosdelPersonalAcademico(DGAPA),Mexico;Nederlandse OrganisatievoorWetenschappelijkOnderzoek(NWO),Netherlands; TheResearchCouncilofNorway,Norway;CommissiononScience andTechnology forSustainable Developmentin theSouth (COM-SATS),Pakistan;PontificiaUniversidadCatólicadelPerú,Peru; Min-istry ofScience and Higher Education andNational Science Cen-tre, Poland; Korea Institute of Science and Technology Informa-tion and National Research Foundation of Korea (NRF), Republic ofKorea;MinistryofEducationandScientificResearch,Instituteof Atomic Physicsand Romanian NationalAgency forScience, Tech-nology and Innovation, Romania; Joint Institute for Nuclear Re-search (JINR), Ministry of Education and Science of the Russian FederationandNationalResearchCentre KurchatovInstitute, Rus-sia; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; NationalResearch Foundation of South Africa,South Africa;Centrode AplicacionesTecnológicasy Desar-rollo Nuclear (CEADEN), Cubaenergía, Cuba and Centro de

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Inves-tigacionesEnergéticas,MedioambientalesyTecnológicas(CIEMAT), Spain;SwedishResearchCouncil(VR)andKnut&AliceWallenberg Foundation(KAW),Sweden;EuropeanOrganizationforNuclear Re-search,Switzerland;NationalScienceandTechnologyDevelopment Agency(NSDTA),SuranareeUniversityofTechnology(SUT)and Of-ﬁce of the Higher Education Commission under NRU project of Thailand,Thailand;TurkishAtomicEnergyAgency(TAEK),Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and TechnologyFacilitiesCouncil(STFC),UnitedKingdom;National Sci-enceFoundationoftheUnitedStatesofAmerica(NSF)andUnited StatesDepartmentof Energy,Oﬃce ofNuclear Physics (DOE NP), UnitedStatesofAmerica.

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