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

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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 ra c t

Articlehistory:

Received24May2018

Receivedinrevisedform23November2018 Accepted21December2018

Availableonline28December2018 Editor:L.Rolandi

InthisLetter,theALICECollaborationpresentsthefirstmeasurementsofthecharged-particlemultiplicity density,dNch/dη,and totalcharged-particle multiplicity, N^tot_ch,inXe–Xe collisions atacentre-of-mass energypernucleon–nucleonpairof√_s

NN=⁵.44 TeV.The measurementsareperformedasafunction of collision centralityover awide pseudorapidity range of−³.5<η<5. The values ofdNch/dη at mid-rapidityandN^tot_ch forcentralcollisions,normalisedtothenumberofnucleonsparticipatinginthe collision(Npart)asafunctionof√_s

NN 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%.

©^{2018PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

Aplasma ofstrongly interacting quarksand gluonsis formed in the hot and dense nuclear matter created in ultra-relativistic heavy-ioncollisions [1,2].Themultiplicityofchargedparticlespro- 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,N_coll,amongtheparticipantnucleons.Collisionsofnucleiof differentsizes leadtodifferent Npart and N_coll 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(dN_ch/d

η

) were per- formedatRHIC,comparingAu–AuandCu–Cucollisions atvarious

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

centre-of-massenergies [3].TheALICE,ATLASandCMSCollabora- tions at the LHC have previously reported on dN_ch/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 significantdifferencesbetweentheshapesoftheN_partdependence forthedifferentcollisionenergieswereobserved.

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

sNN=⁵.44 TeV.ThesizeoftheXe–Xe systemisin- 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 ofparticipat- 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

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

ingat√

sNN=⁵.44 TeV in October2017. Thedatawere collected withareducedmagneticfieldof0.2 T(ascomparedtothenomi- nalvalueof0.5 T)intheALICEsolenoidmagnet.Theperformance anda detaileddescriptionofALICEcan be foundelsewhere [12].

Inthefollowing,thedetectorelementsrelevanttothisanalysisare brieflydescribed.

Theinnermost partofthetrackingsystemofALICEis theSil- 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.Theymea- 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 interactionprob- ability per bunch-crossing was sufficiently small that the chance oftwohadronicinteractionsoccurringwithintheintegrationtime ofthe involved detectors,so-calledpileup events,was negligible.

A totalofabout1millionhadroniccollisionsareusedinthisanal- ysis.

The classification of collisions into centrality classes uses the sumoftheamplitudesofthesignalsintheV0-A andV0-C detec- tors.Amodel ofparticleproduction,basedona Glauberdescrip- 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 N_coll, coupled to a particle production model foreach source parame- terisedbythenegativebinomialdistribution(NBD).IntheGlauber calculation,thenucleardensityfor¹²⁹XeisdescribedbyaWoods–

Saxondistributionforadeformednucleus

ρ (

r

, ϑ) = ρ

0

1 1

+

^exp

r−R(ϑ ) a

.

(2)

Theparameter

ρ

0 isthenucleondensity,whichprovidestheover- 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+β2Y20(ϑ)]^{, where R}0 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].Thedeformationparameterβ2=⁰.18±⁰.02 is obtainedby linearlyinterpolatingthe valuesmeasured fortheXe A-evenisotopesfrom124to136 [22].IntheGlaubermodelcalcu- lation,theorientation ofthespheroid symmetryaxisisrandomly sampled. For √

s_NN=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 densityatmid- 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,allcollisionswithapri- 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-energyheavy- ioncollisions. Forthisreason, thesimulationhasbeenreweighed toreproducetherelativeparticleabundancesobservedinthedata which are about30% (50%) higher than HIJING inthe mostcen- tral (peripheral) collisions. The reweighing factors have beende- rivedfroman estimateofK⁰_S,and¯ relativeproductioninthe data,obtainedviainvariant massreconstructionandcomparedto HIJING.

Table 1

The^dNch/dηandN^tot_ch valuesfordifferentcentralityclasses,definedbyV0multiplicity.Theerrorsaretotaluncertainties,thestatisticalcontributionbeingnegligible.The valuesofNpartobtainedwiththeGlaubermodelarealsoreported.TheerrorsareobtainedbyvaryingtheparametersoftheNBD-Glaubercalculation.

Centrality Npart dNch/dη N_part² dNch/dη N_ch^tot _N²

partN^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] correctsfortheback- 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%.Thisresultsinanun- certaintyon ^dNch/d

η

^{of0.1% to4.8%fromcentral toperipheral} collisions.An additional 4% uncertaintyassignedto the mostpe- ripheralclass,arising fromtheremaining contaminationfromEM processes,wasestimatedbystudyingtheenergydepositioninthe ZDCs [28].

Forthetrackletanalysisatmid-rapiditytherelativesystematic uncertaintyonthemeasurementofthecharged-particlemultiplic- ityinperipheral(central)eventsarisesfromthefollowingsources:

tracklet selection 0.1% (0.8%), calculated by varying the tracklet qualitycut up to4 timesthenominalvalue;combinatorialback- 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 zerotrans- versemomentum 0.6% (0.6%),obtained fromthe variation ofthe estimatedyieldofparticlesatlowtransversemomentumbyafac- 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.Thelinescorrespondtofitstoagaussiandistributioninrapiditymul- tipliedbyaneffectiveJacobianoftransformationfromηtoy.

relatedtothemeasurement ofmultiplicity arisefromthefollow- 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.

Thesystematicuncertaintiesfromcentralityselectionandelec- 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 densitydN_ch/ 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 aver-

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

η

₌0,averaging positiveandnegative

η

re- sultswherever possible,andextendedintothe non-measuredre- gion −⁵<

η

<−³.5 by reflecting the 3.5<

η

<5 valuesaround

η

₌0.Averagedvalues(leftandright)agreewithintheuncertain- ties. Assumingthatthe charged-particlerapidity densitydNch/dy hasGaussian shapeandusinganeffectiveJacobian,themeasured dN_ch/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 N^tot_ch is determined from the data in the measured regionandfromextrapolations,up to

η

= ±^ybeam,intheunmea- suredregion.Threedifferentfunctionsareusedtoextrapolatethe datapoints:thedifferenceoftwoGaussiandistributionscentredat

η

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

η

= ±^ybeamwiththestartingpointconstrainedbythemea- surements.AGaussiandNch/dyinrapidityresultsinadistribution 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(whichgivesthelowestN^tot_ch)and theGaussian dNch/dy (which givesthehighest N^tot_ch).The contri- butionfromthe extrapolatedregionislessthan 30%of N^tot_ch.The systematicuncertaintyoftheextrapolatedN^tot_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 N^tot_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-particlemultiplic- itynormalisedbythenumberofnucleonpairsparticipatinginthe collision, _N²

part^dNch/d

η

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

s_NN than for pp andp–Pb collisions. Fig. 2 (bot- tom)showsthetotal charged-particle multiplicity per participant nucleonpair _N²

partN^tot_ch,whichfollowsthetrendforcentralheavy- 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 _Npart^{2 Ntot}_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–Pbcolli- 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 _N²

partdNch/dη(top)and _N²

partN^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–XeV0ampli- tude distribution [22]. Thefluctuationsoccurboth inthenumber ofcollisionsoverparticipantsandinthenumberofchargedparti- clesoverparticipants.Theriseisquantitativelyreproducedbythe NBD-Glauber fit.The total numberofcharged particles scaledby thenumberofparticipantpairsshowsaslightincreaseasafunc- tion ofthe numberof participants in Fig. 3 (bottom),similar to thatofthemidrapidityresults,albeitwithlargerexperimentalun- certainties.Fig.4showstheXe–XeandPb–Pbresultsasafunction of a differentscaling variable (^Npart−²)/(2A),where A is the atomic mass number of the colliding nucleus. The figure shows that _N²

part^dNch/d

η

and _N²

partN_ch^tot have a similar dependence on the numberof participants relative tothe possible maximum numberofparticipants,whichindicatesastrongerdependenceon geometricpropertiesofthecollisionzonethanonthecollisionsys- 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 N_part-scaling was observed at RHIC energies [3,30,38–40]. The deviation from N_part-scaling was initially thought to be due to a relative in-

Fig. 3.The _N²

partdNch/dη(top)and _N²

partN^tot_ch (bottom)forXe–Xe collisionsat

√sNN=5.44 TeV as a functionofNpart. Theerror barsindicatethe point-to- pointcentrality-dependentuncertaintieswhereastheshadedbandshowsthecor- 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 Npart2 ^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

_∝Nα

part and^dNch/d

η

_∝N^β_coll.The functions were fitted to the Pb–Pb data at √

sNN=⁵.02 TeV [8]. For the Xe–Xe dataonlytheabsolutenormalisationwasadjusted.Theval- uesofthe parameters are alsoconsistent withthose obtainedat SPSandRHICenergies[30,41].Whilenouniquephysicsconclusion canbe drawnfromsuch fits,thissuggeststhatgeometricalargu- mentsmaybe sufficientto provideagood descriptionofparticle productionacrossdifferentcollidingsystemsandbeamenergies.

Describing particle production in relativistic heavy-ion colli- sionsasasuperpositionofemissionfromathermalcoreandhard scatteringsinacorona [42],onecanclassifytheparticipatingnu- cleonsinto those that scatter only once (N_part^corona) and those that scatter multiple times (N_part^core). The multiplicity can then be fit- ted with the sum of those contributions, ^dNch/d

η

ppN_part^corona+ ^dNch/d

η

coreN^core_part, where ^dNch/d

η

pp is the multiplicity mea- suredininelasticpp collisions [10] and^dNch/d

η

core isthecon- tributiontothecharged-particle multiplicity fromthecoreofthe fireball,whichisfittedtothedata.Fig.5alsoshows^dNch/d

η

per participantquark Nq-partcalculatedwithaGlaubermodelusingef- fectivewoundedconstituentquarks [44][43],asafunctionofN_part, aswasdoneforPb–Pb collisionsat√

sNN=⁵.02 TeV [45] thathave beenre-analysed innarrowercentralityclasses.Intheimplemen- tationofthequark-Glaubermodelthepartonicdegreesoffreedom (3 or 5) are located around the nucleon centres [43]. The effec-

Fig. 4.The _N²

partdNch/dη(top)and _N²

partN^tot_ch (bottom)forXe–Xe collisionsat

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

Fig. 5.The _N²

part^dNch/dη^for Xe–Xe collisionsat √_s

NN=⁵.44 TeV andPb–Pb collisionsat√

sNN=⁵.02 TeV [8],asafunctionof^Npart^{.ThePb–Pb dataarefit-} tedwithvariousparameterisationsofNpartand Ncoll,calculatedwiththeGlauber model.Thesamefunctions,withthevaluesoftheparametersfromthePb–Pbfit, areusedfortheXe–Xe data.AlsoshownisdNch/dηperparticipantquark,Nq-part, calculatedwiththeeffectivewoundedconstituentquarksmodel [43],asafunction of^Npart^.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 N}q=^5, respectively, adjusted toreproduce the 68.4 mb nucleon–nucleon inelasticcrosssectionat5.44 TeV. Nq-part hasbeendividedbythe averagevalue inppcollisions

μ

= ^Nq-part^{,whichis 3.5(4.3) for}

Fig. 6.The _N²

part^dNch/dη^forXe–Xe collisionsat√_s

NN=⁵.44 TeV asafunction of^Npart^{comparedtomodel}predictions[46,47,49–65].Thebottompanelshows theratioofthemodelstothedata.Theshadedbandaroundthepointsreflectsthe correlatedsystematicuncertainties.

Nq=^{3 (N}q=^{5).ComparingthebehaviourofdN}ch/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 implementshydrodynamicalevo- 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-ioncolli- 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,whichincorpo- rates collective effects treatedvia a flow parameterisation and a separationoftheinitialstate intocore-coronaparts.Theshapeof thecentrality dependenceis reproduced fairly well atintermedi- 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-VISHNUevent-by- event simulations for relativistic heavy-ion collisions which uses ahybridapproachbasedon(2+1)-dimensionalviscoushydrody- namicscoupledtoahadroniccascademodel [68].TheDukeglobal calibratedmodelcanreproducetheshapeofthemid-rapiditydis- tribution,butoverestimatesslightlytheoverallmagnitude.

Saturation-inspired models (rcBK-MC [54,55], KLN [56–59], ASW[60],IP-Glasma[61,62] andEKRT[63–65])relyonperturba- tive QCD andan energy-dependent saturationscale, whichlimits thenumberofproducedpartons,andinturnthenumberofpro- duced particles. This results in a factorisation of the energyand centralitydependenceofparticleproductionor,inother words,in theinvarianceofthecentralitygrowth,asobservedintheexperi- 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 √

s_NN=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 softpar- 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.Thepredic- tionsshowasimilartrendasforthePb–Pbcase [8] andaltogether aflatterdistributionwithrespecttodata.

In Fig. 7, the models are compared to the pseudorapidity dependence of the dN_ch/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 slightover- 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 canonlybeusedforra- 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] exceptHI- JING2.1whichdescribestheXe–Xemeasurementsbetterthanthe Pb–Pbdata.

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-lawdependencewithenergyestablishedinpreviousheavy- ionmeasurements.

The centrality dependences of _N²

part^dNch/d

η

^and _Npart^{2 N}_ch^tot 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].Thesteeperrisemightbeduetomulti- plicityfluctuationsinthetailoftheXe–XeV0amplitude.

While measurements of particle production in large and medium-sizedcollidingsystemssuch asXe–Xe areabundant and becomeevenmoreprecise,theunderlyingmechanismtodescribe theincrease withenergyandcentralityisstill notcompletelyun- derstood.Deeperinsightofthesystemsizedependenceofparticle productionmaycomefromthestudyoflight-nucleicollisions,still notmuchexploredathighenergy,whichcouldbridgethegapbe- 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 totheconstruc- tionoftheexperimentandtheCERNacceleratorteamsfortheout- 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 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- 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;TheDanishCouncilforIndependentResearchNat- ural Sciences, the CarlsbergFoundation and Danish National Re- search Foundation (DNRF), Denmark; HelsinkiInstitute of Physics (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 andTechnology, Ministryof Education,Research andReli- gions,Greece;NationalResearch,DevelopmentandInnovationOf- 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 AplicacionesTecnológicasyDesar- rollo Nuclear (CEADEN), Cubaenergía, Cuba and Centro de Inves-