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ALICE
Collaboration
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Article history:Received5October2015
Receivedinrevisedform3December2015 Accepted20December2015
Availableonline26January2016 Editor: L.Rolandi
Thecentralitydependenceofthecharged-particlepseudorapiditydensitymeasuredwithALICEinPb–Pb collisions at√sNN=2.76 TeV over abroadpseudorapidityrangeispresented.ThisLetterextendsthe
previousresultsreportedbyALICEtomoreperipheralcollisions.Nostrongchangeoftheoverallshapeof charged-particlepseudorapiditydensitydistributionswithcentralityisobserved,andwhennormalisedto thenumberofparticipatingnucleonsinthecollisions,theevolutionoverpseudorapiditywithcentrality islikewisesmall. Thebroadpseudorapidityrange(−3.5<
η
<5)allowspreciseestimatesofthetotal numberofproducedchargedparticleswhichwefindtorangefrom162±22(syst.) to17170±770(syst.) in 80–90% and 0–5% central collisions, respectively. The total charged-particle multiplicity is seen to approximatelyscalewiththenumberofparticipatingnucleonsinthecollision.Thissuggeststhathard contributionstothecharged-particlemultiplicityarelimited.Theresultsarecomparedtomodelswhich describedNch/dη
atmid-rapidityinthemostcentralPb–Pbcollisionsanditisfoundthatthesemodels donotcaptureallfeaturesofthedistributions.©2016CERNforthebenefitoftheALICECollaboration.PublishedbyElsevierB.V.Thisisanopen accessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
1. Introduction
The measurement of the charged-particle pseudorapidity (
η
) density distribution in heavy-ion collisions provides insight into thedominantparticleproductionmechanisms,suchasparton frag-mentation[1]andtheobservedphenomenonoflimiting fragmen-tation[2]. The unique capability of ALICE to perform such mea-surementsfromlargetosmalloverlapsofthecollidingnucleiover abroad pseudorapidity rangeallows forsignificant additional in-formationtobe extractede.g., thetotalnumberofcharged parti-clesandtheevolutionofthedistributionswithcentrality.The charged-particle pseudorapidity density (dNch
/
dη
) per sedoesnotprovideimmediateunderstandingoftheparticle produc-tionmechanism,butasabenchmarktoolforcomparingmodelsit isindispensable.Variousmodels
[3–5]
makedifferentassumptions onhowparticlesareproducedinheavy-ioncollisionsresultingin verydifferentcharged-particlepseudorapiditydensitydistributions —bothintermsofscaleandshape.Modelsmay,forexample, in-corporatedifferentschemesforthehadronisation oftheproduced quarks and gluons which leads to very different pseudorapidity distributionsofthechargedparticles.E-mail address:alice-publications@cern.ch.
TheALICECollaborationhaspreviously reportedresultsonthe charged-particlepseudorapiditydensityinthe0–30%mostcentral Pb–Pb collisions at
√
sNN=
2.
76 TeV overa wide pseudorapidityrange [6], andin the 80% mostcentral collisions atmid-rapidity (
η
≈
0) only [7]. The ATLAS Collaboration has reported on the charged-particle pseudorapidity density in the 80% most central eventsin a limitedpseudorapidityrange of|
η
|
<
2[8].Similarly, theCMSCollaborationhasreportedonthesamemeasurementsin the90%mostcentraleventsatη
≈
0,andforselectedcentralities upto|
η
|
<
2[9].In this Letter we present the primary charged-particle pseu-dorapidity densitydependenceonthe eventcentralityfrom mid-central (30–40%) to peripheral (80–90%) collisions over a broad pseudorapidity range to complement results previously reported byALICEinthe0–30%centralityrange.Unlikeprevious
[6]
,inthe forwardregions wherethesignalisdominatedby secondary par-ticlesproducedinthesurroundingmaterial,we usea data-driven correctiontoextracttheprimarycharged-particledensity.Primary chargedparticles are defined asprompt charged par-ticles produced in the collision, including their decay products, butexcludingproductsofweakdecaysofmuonsandlightflavour hadrons. Secondary charged particles are all other particles ob-servedintheexperimente.g.,particlesproducedthrough interac-tionswithmaterialandproductsofweakdecays.
http://dx.doi.org/10.1016/j.physletb.2015.12.082
0370-2693/©2016CERNforthebenefitoftheALICECollaboration.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
Inthefollowingsection,theexperimentalset-upwillbebriefly described. Section 3outlines analysis procedures anddescribesa data-drivenmethodtoisolatethenumberofprimarycharged par-ticles fromthe secondary particle backgroundat large pseudora-pidity.Systematicuncertainties arediscussedinSect.4.InSect.5, theresultantcharged-particlepseudorapiditydensitydistributions are presentedalong withtheir evolution withcentrality. Further-more we extract from the measured dNch
/
dη
distributions thetotalnumberofchargedparticles asafunction ofthenumberof participatingnucleons.Wefinallycomparethemeasured charged-particlepseudorapiditydensityto anumberofmodelpredictions beforeconcludinginSect.6.
2. Experimentalsetup
AdetaileddescriptionofALICEcanbefoundelsewhere[10,11]. Inthefollowingwe briefly describethedetectorsrelevantto this analysis.
The Silicon PixelDetector (SPD) is the inner-most detector of ALICE. The SPD consists of two cylindrical layers of 9
.
8×
106 silicon-pixels possessing binary read-out. It provides a measure-mentofchargedparticles over|
η
|
<
2 using so-calledtracklets —acombinationofhitsoneach ofthetwo layers(1and2) consis-tent with a trackoriginating fromthe interaction point. Possible combinationsofhitsnot consistentwithprimaryparticles canbe removed from the analysis, withonly a small (afew %) residual correction for secondary particles derived from simulations. The SPDalso provides a measurement,by combininghits on its two layers,oftheoffsetwithrespecttotheinteractionpoint,wherethe collisions occurred.IP
= (
0,
0,
0)
isatthecentreoftheALICE co-ordinatesystem,andIPz istheoffsetalongthebeamaxis.Finally,ahardware logicalor of hitsineach ofthetwolayers providesa triggerforALICE.
TheForwardMultiplicityDetector(FMD)isasiliconstrip detec-torwith51 200individualread-outchannelsrecordingtheenergy depositedby particles traversing thedetector.It consistsofthree sub-detectorsFMD1,2,and3,placedapproximately320 cm,79 cm and
−
69 cm along the beamline, respectively. FMD1consists of oneinner type ring(1i), whilebothFMD2and3consist ofinner (2i,3i) and outer type rings(2o, 3o). The ringshave almost full coverageinazimuth(ϕ
),andhighgranularityintheradial(η
) di-rection(seeTable 1
).TheV0isthemostforwardofthethreedetectorsusedinthis analysis.Itconsistsoftwosub-detectors:V0-A andV0-C placedat approximately333 cm and
−
90 cm alongthe beamline, respec-tively.Each of thesub-detectors are madeup of scintillator tiles withahightimingresolution.WhiletheV0providespulse-height measurements,theenergy-lossresolutionisnotfineenoughtodo an independent charged particle measurement.In previous mea-surements, using so-called satellite–main collisions (see Sect. 3), one could match the V0amplitude to the SPDmeasurements to obtainarelativemeasurementofthenumberofchargedparticles. However,forcollisions at|
IPz|
<
15 cm nosuch matchingispos-sible,andtheV0isthereforenot usedtoprovideameasurement ofthenumberofchargedparticlesinthisanalysis.Thedetectoris used,inan inclusivelogicalor with theSPD,fortriggering ALICE andtoprovideameasureoftheeventcentrality[7].
Details on the coverage, resolution, and segmentation of the threeuseddetectorsaregivenin
Table 1
.3. Datasampleandanalysismethod
TheresultspresentedinthispaperarebasedonPb–Pbcollision dataat
√
sNN=
2.
76 TeV taken by ALICEin2010. About 100 000Table 1
Overviewoftheresolution(δ),segmentation(),and coverageofthedetectors usedintheanalysis.The‘A’sidecorrespondsto
z
>0,whilethe‘C’sidecorresponds toz
<0.TheηrangeisspecifiedforcollisionswithIPz=0.Detector δrϕ δz ηrange SPD1 12 μm 100 μm −2.0 to 2.0 2 12 μm 100 μm −1.4 to 1.4 Detector ϕ r ηrange FMD1i 18◦ 254 μm 3.7 to 5.0 2i 18◦ 254 μm 2.3 to 3.7 2o 9◦ 508 μm 1.7 to 2.3 3o 9◦ 508 μm −2.3 to−1.7 3i 18◦ 254 μm −3.4 to−2.0 V0-A 45◦ 34 to 186 mm 2.8 to 5.1 -C 45◦ 26 to 127 mm −3.7 to−1.7
events with a minimum bias trigger requirement [7]were anal-ysedinthecentralityrangefrom0%to90%.Thedatawascollected over roughly 30 minutes where the experimental conditions did notchange.
The standardALICEeventselection [12]andcentrality estima-tor basedonthe V0-amplitudeare usedinthisanalysis[13].We includeherethe80–90%centralityclasswhichwasnotpresentin thepreviousresults[7].Asdiscussedelsewhere[13],the90–100% centrality class has substantial contributions fromQED processes andisthereforenotincludedinthisLetter.
Resultsinthemid-rapidityregion(
|
η
|
<
2)areobtainedfroma trackletanalysisusingthetwo layersoftheSPDasmentionedin Sect.2. Theanalysismethod anddatausedare identicalto what haspreviouslybeenpresented[6,7].Themeasurementsintheforwardregion(
|
η
|
>
2)areprovided bytheFMD.TheFMDrecordsthefullenergydepositionofcharged particles that impingeon thedetector.Since allcharged particles thathittheFMDareboostedinthelaboratoryframe,thedetection efficiencyiscloseto100%forallmomenta.Asreportedearlier[6], the mainchallenge inmeasuring thenumberofchargedprimary particlesinthisregion,isthelargebackgroundofsecondary parti-clesproducedinthesurroundingmaterial.Duetothecomplexity andthelimitedknowledgeofthematerialdistributionofsupport structures away fromthe central barrel, it hasnot been possible toadequately describe(onthefew%-level)thegenerationof sec-ondary particlesintheforwarddirections withintheprecision of thecurrentsimulationoftheALICEapparatus.Asuitablemeanstoextractthenumberofprimarycharged par-ticleswasfoundbyutilisingcollisionsbetweenso-called‘satellite’ bunchesandmainbunchesoffsetinintervalsof37.5 cmalongthe beam-line.Satellitebunchesarecausedbytheso-called debunch-ing effect[14]. Asmall fraction ofthe beam can be captured in unwanted RF buckets, due the way beams are injected into the accelerator, andcreate these satellite bunches spaced by 2.5 ns. Collisionsbetweensatelliteandmainbunchescancause instabili-tiesinthebeam,andtheLHChastakenstepstoreducethe num-ber ofthesekinds ofcollisions. ALICEhasthereforenot recorded collisions betweensatellite andmain bunchesbeforeor afterthe Pb–Pb runof2010. Insatellite–main collisions thebackgroundof secondaryparticleswasmuchsmallerandmuchbetterunderstood since significantlylessdetectormaterial shadowsthe forward de-tectors
[6]
.Astudyutilisingthesesatellite–maincollisionsledtothe publi-cationofthemeasurementofthecharged-particle pseudorapidity densityinthe30%mostcentraleventsover
|
η
|
<
5[6].Thestudy waslimitedincentralityreachbytheneedtousetheZero-Degree Calorimeter (ZDC) for the centrality estimation for collisions be-tween satellite and mainbunches. TheZDCmeasures theenergy ofspectator(non-interacting)nucleonswithtwocomponents:oneFig. 1. (Colouronline.)Comparisonofdata-driventosimulation-basedcorrectionsforsecondaryparticlesimpingingontheFMD.Differentmarkerscorrespondtodifferent collisionsystemsandenergies,andthecoloursindicatethefiveFMDrings.
S
(η)isshownfor0 cm<IPz<2 cm asanexample,whileE
(η)isindependentofIPz(seealsotext). Pythia wasusedforppcollisions,andthePb–PbpointsarefromsimulationwithaparameterisationwhichincludetheavailableALICEdataonparticlecomposition and
p
Tdistributions.BlackcirclescorrespondtoE
(η).measuresprotonsandtheothermeasures neutrons.TheZDCwas locatedatabout114 m fromtheinteraction pointon eitherside ofthe experiment[10],and was thereforeideally suitedfor that study.Thecentrality determinationcapabilityofthe ZDCis how-everlimitedtothe30%mostcentralcollisions[13].
Forcentralitieslargerthan30%theV0amplitudeisusedasthe centralityestimator,whichisavailableonlyforcollisionsat
|
IPz|
<
15 cm —theso-callednominalinteractionpointcorrespondingto main bunches of one beam colliding with main bunches of the otherbeam.
To extend the centrality reach of the dNch
/
dη
measurement,a data-driven correctionforthenumber ofsecondariesimpinging ontheFMDhasbeenimplemented.ForeachcentralityclassC ,we formtheratio
EC
(
η
)
=
dNch
/
dη
|C
,inclusive,nominal dNch/
dη
|C
,primary,satellite.
(1)Thatis,theratioofthemeasured inclusive charged-particledensity frommain–main collisions (
|
IPz|
<
10 cm) provided by the FMDtothe primary charged-particle densityfrom satellite–main colli-sions[6].Here,‘inclusive’denotesprimary and secondarycharged particles i.e., nocorrection was applied to account forsecondary particlesimpingingontheFMD.
Note,that thecorrection isformedbin-by-bin in pseudorapid-ity,sothatthepseudorapidityisthesameforboththenumerator anddenominator. However, the numeratorand denominator dif-fer in the offset along the beam line of origin of the measured particles:Forthenumeratortheoriginlieswithinthenominal in-teraction region,while forthedenominator theoriginwas offset bymultiplesof37.5 cm.
This ratio is obtained separately for all previously published centralityclasses:0–5%,5–10%,10–20%and20–30%.Thevariation of Ec fordifferent centralities is small (
<
1%, much smaller thantheprecisionofthemeasurements).Theweightedaverage
E
(
η
)
=
C
C EC(
η
)
CC
,
(2)is used as a global correction to obtain the primary charged-particlepseudorapiditydensity
dNch d
η
X,primary=
1 E(
η
)
dNch dη
X,inclusive,nominal,
(3)whereX standsforaneventselectione.g.,acentralityrange.
Thesimulation-basedcorrectionS
(
η
)
forsecondaryparticlesto the charged-particle pseudorapidity densityinthe forward direc-tionsisgivenbyS
(
η
)
=
Ninclusive,FMD(
η
)
Nprimary,generated(
η
)
,
(4)whereNinclusive,FMDisthenumberofprimaryand secondary
parti-clesimpingingontheFMD—asgivenbythetrackpropagationof the simulation, and Nprimary,generated is the number of generated
primary particles at a given pseudorapidity. Complete detector-simulation studies show that three effects can contribute to the generationofsecondaries,andhencethevalueofS
(
η
)
.Thesethree effectsare:materialinwhichsecondariesareproduced,the trans-versemomentum(pT)distributionandparticlecompositionofthegeneratedparticles, andlastly thetotal numberofproduced par-ticles. Of thesethree the material is by far the dominant effect, whilethepTandparticlecompositiononlyeffectsS
(
η
)
onthefewpercentlevel.Thetotalnumberofgeneratedparticleshasa negli-gibleeffectonS
(
η
)
.Thatis,thematerialsurroundingthedetectors amplifies the primary-particle signal through particle production byaconstantfactorthatfirstandforemostdependsontheamount ofmaterialitself,andonlysecondarilyonthepT andparticlecom-positionofthegeneratedprimaryparticles.
Toestimatehow much EC
(
η
)
itself wouldhavechanged ifan-other system or centrality range was used to calculate the cor-rection, S
(
η
)
is analysed from simulations with various collision systems and energies. We find that, even for large variations in particlecomposition and pT distributions, S(
η
)
only variesbyupto 5%. Reweighting the particle composition and pT distributions
fromthe various systemsto matchproduces consistent valuesof
S
(
η
)
ensuringthat the5%variations foundwereonlydueto par-ticlecompositionandpT distributionsdifferences.Thisuncertaintyis applied to E
(
η
)
to account for all reasonable variations ofthe particle composition and pT distributions,which cannot bemea-suredintheforwardregionsofALICE.
Fig. 1showsthecomparisonofthedatadrivencorrectionE
(
η
)
tothesimulation-basedcorrection S
(
η
)
from Pythia[15](pp)and a parameterisation of the available ALICE results [16,17] for Pb– Pbcollisions.Thesimulatedcollisionsarefortwodistinctsystems andspan over almost an order ofmagnitude in collisionenergy. Thetotal numberofproduced particlesinthesesimulations span fiveordersofmagnitude,andnodependenceof S(
η
)
on charged-particlemultiplicityisobserved.BycomparingE
(
η
)
to S(
η
)
fromsimulations,one findsagood correspondence between the two corrections except in regionswherethematerialdescriptioninthesimulations isknowntobe inadequate.This,togetherwiththefactthatthenumeratorand de-nominatorofEq.(1)measurethesamephysicalprocess,butdiffer foremost in the material traversed by the primary particles, and hence the number of secondary particles observed, implies that the correction E
(
η
)
is universal. Thatis, Eq.(3) is applicable forany eventselection X in anycollision system orat anycollision energy,wheretheproducedmultiplicity,pT distributions,and
par-ticle composition is close to the range ofthe simulated systems usedtostudyS
(
η
)
.Note, for the previously published results [6], which used satellite–main collisions, the simulation-based approach for cor-recting for secondary particles i.e., applying S
(
η
)
directly, was valid. As mentioned above, insatellite–main collisions, the parti-clesthatimpingeontheFMDtraversefarlessandbetterdescribed material in the simulation of the ALICE apparatus. The use of a simulation-based correction for secondary particles was in that analysiscross-checkedbycomparingtoandcombiningwith mea-surementsfromthe V0and SPD[6]. Despiteconcertedeffortsto improvethesimulationsbytheCollaborationithasnotbeen possi-bletoachievethesameaccuracyinS(
η
)
formain–maincollisions. Finally, the effect of variation of the location of the primary interactionpointonE(
η
)
wasstudied.Itwasfound,thattheeffect isnegligible,giventhatthedistributionofIPz aresimilarbetweenthenumeratorofEq.(1)andright-handsideofEq.(3),aswasthe caseinthisanalysis.
Themethodusedinthisanalysistoextracttheinclusive num-berofchargedparticlesfromtheFMDisthesameasforprevious publishedresults[6],except thatthedata-drivencorrectionE
(
η
)
— ratherthan asimulation-basedone S(
η
)
— isusedto correctfor secondaryparticles.4. Systematicuncertainties
Table 2summarises thesystematicuncertaintiesofthis analy-sis.Thecommonsystematicuncertaintyfromthecentrality selec-tioniscorrelatedacross
η
anddetailedelsewhere[13].FortheSPDmeasurements,thesystematicuncertaintiesarethe sameasforthepreviouslypublishedmid-rapidityresult[7],except foracontributionfromthecorrectionduetothelargeracceptance usedinthisanalysis. ThisuncertaintystemsfromtherangeofIPz
usedintheanalysis(here
|
IPz|
<
15 cm).AtlargerabsolutevaluesofIPz theacceptance correction fortheSPD trackletsgrows, and
the uncertaintywith it, beingtherefore
η
-dependent andlargest at|
η
|
≈
2.The various sources of systematic uncertainties for the FMD measurements are detailed elsewhere [6], but will be expanded uponinthefollowingsincesomevalueshavechangeddueto bet-terunderstandingofthedetectorresponse.
In the analysis, three
η
-dependent thresholds are used. The values for these thresholds are obtained by fitting a convoluted Landau–Gaussdistribution[18] tothe energyloss spectrum mea-suredbytheFMDinagivenη
range.Theuncertaintiesassociated withthesethresholdsaredetailedbelow.A charged particle traversing the FMD can deposit energy in more than one element i.e., strip, of the detector. Therefore it is necessaryto recombine two signalsto get thesingle charged-particleenergylossinthosecases.Thisrecombinationdependson alowerthresholdforacceptingasignal,andanupperthresholdto considera signal asisolated i.e.,all energyis depositedina sin-gle strip. Thesystematic uncertainties fromtherecombination of signalsarefoundbyvaryingthelowerandupperthresholdvalues withinboundsoftheenergylossfitsandbysimulationstudies.
Tocalculatetheinclusivenumberofchargedparticles,a statis-ticalapproachisused[6].Thestripsofthe FMDaredividedinto
Table 2
Summaryofsystematicuncertainties:thecommonsystematicuncertaintiesshared byboththeSPDandtheFMD,andtheuncertaintiesparticulartothedetectors.
Detector Source Uncertainty (%) Common Centrality 0.4–6.2 SPD Background subtraction 0.1 Particle composition 1 Weak decays 1 Extrapolation to pT=0 2 Event generator 2 Acceptance 0–2a FMD Recombination 1 Threshold +−12 Secondary particles 6.1 Particle composition & pT 2b a Pseudorapiditydependentuncertainty,largestat|η|=2. b Additionalcontributionin3.7<η<5.Seealsotext.
regions, andthe number ofempty strips is compared to the to-tal numberofstripsinagivenregion.Strips withasignal below agiventhresholdareconsideredempty.Thethresholdwasvaried within boundsofthe energyloss fitsandinvestigatedin simula-tionstudiestoobtainthesystematicuncertainty.
The data-driven correction for secondary particles defined in Eq. (2) is derived from the previously published results, and as such contains contributions from the systematic uncertainties of those results [6]. Factoring out common correlated uncertainties e.g., the contribution from the centrality determination, we find a contribution of 4.7% from the previously published results. By studying the variation of the numerator of Eq. (1) under differ-entexperimentalconditionse.g.,differentdata-takingperiods,and adding the variance in quadrature, the uncorrelated, total uncer-tainty on E
(
η
)
is found to be 6.1%. Systematic uncertainties can in generalnot becancelled betweenthenumerator and denomi-nator ofEq.(1),sincethesameη
regionsare probedbydifferent detectorelementsineach.Note, that the previously published result [6]used in Eq. (1)
alreadycarriesa2%systematicuncertaintyfromtheparticle com-positionand pT distribution
[6]
.Thiscontributioniscontainedinthe4.7%quotedabove,andispropagatedtothefinal6.1% system-aticuncertaintyon E
(
η
)
.Finally, it was found through simulations that the acceptance region of FMD1 is particularly affected by the variations in the number of secondary particles stemming from variations in the particlecompositionandpTdistribution,andgivesrisetoan
addi-tional2% systematicuncertainty, whichisaddedinquadratureto therestofthesystematicuncertainties,butonlyfor
η
>
3.
7. 5. ResultsFig. 2showsthecharged-particlepseudorapiditydensityfor dif-ferentcentralitiesfromeachdetectorseparately.
The combined distributions inFig. 3are calculated asthe av-erage of the individual measurements from the FMD and SPD, weighted by statisticalerrors and systematicuncertainties, omit-tingthosewhicharecommonsuchasthatfromthecentrality de-termination.Thedistributionsarethensymmetrisedaround
η
=
0 bytakingtheweightedaverageof±
η
points.Pointsat3.
5<
η
<
5 are reflected on to−
5<
η
<
−
3.
5 to provide the dNch/
dη
dis-tributions ina range comparableto the previously published re-sults[6].
Thelinesin
Fig. 3
arefitsoffGG
(
η
;
A1,
σ
1,
A2,
σ
2)
=
A1e −1 2 η2 σ12−
A 2e −1 2 η2 σ22,
(5)Fig. 2. (Colouronline.)MeasurementofdNch/dηpercentralityfromSPD(squares)andFMD(circles)separately.Errorbarsreflectthetotaluncorrelatedsystematicuncertainty
andstatisticalerroroneachpoint.ErrorbarsontheleftandrightreflectthecorrelatedsystematicuncertaintiesontheSPDandFMDpoints,respectively.Previouslypublished resultsfor0–30%overthefullpseudorapidityrange(diamonds)[6]andfor0–80%atmid-rapidity(stars)[7]arealsoshown.
Fig. 3. (Colouronline.)MeasurementofdNch/dηforallcentralitiesandabroadηrange.CombinedandsymmetriseddNch/dηover30–90%centralityfrombothSPDand
FMD(circles).Openboxesreflectthetotaluncorrelatedsystematicuncertaintiesandstatisticalerrors,whilethefilledboxesontherightreflectthecorrelatedsystematic uncertainty.Alsoshown,isthereflectionofthe3.5<η<5 valuesaroundη=0 (opencircles).Previouslypublishedresultsfor0–30%overthefullpseudorapidityrange (diamonds)[6]arealsoshown.ThelinescorrespondtofitsofEq.(5)tothedata.
tothe measured distributions. Thefunction fGG isthe difference
of two Gaussian distributions centred at
η
=
0 with amplitudesA1, A2, andwidths
σ
1,σ
2.The function describesthe data wellwithinthemeasuredregionwithareduced
χ
2smallerthan1.WefindvaluesofA2
/
A1 forallcentralities,from0.
20 to0.
31 butareconsistentwithinfituncertainties,withaconstantvalueof0
.
23±
0.
02.Likewisevaluesofσ
2/
σ
1forallcentralities,rangesfrom0.
28to0
.
36 andareconsistentwithaconstantvalueof0.
31±
0.
02. Qualitatively the shape ofthe charged-particle pseudorapidity densitydistributions broadens only slightlytoward more periph-eralevents,consistentwiththeaboveobservation.Indeed,the full-width half-maximum(FWHM) shown in Fig. 4 versus the num-berofparticipatingnucleons Npart—calculatedusinga Glaubermodel [13] — increase sharply only in the very most peripheral collisions. The dNch
/
dη
distributions doesnot extendfar enoughtocalculate reliable valuesfor FWHMdirectly fromthe data. In-stead fGG
(
η
)
−
max(
fGG)/
2=
0 was numericallysolved, andtheuncertaintiesevaluatedastheerrorof fGGattheroots,dividedby
theslope atthose roots. The widthofthe dNch
/
dη
distributionsfollows the same trend, in the region of 0–50%, as was seen in lowerenergyresults fromPHOBOSreproduced in
Fig. 4
for com-parison[2]
.Fig. 5presentsthecharged-particle pseudorapiditydensityper averagenumberofparticipatingnucleonpairs
Npart/
2 asafunc-tionoftheaveragenumberofparticipants
Npart.Althoughthereisaslightincreaseintheratiotothecentralpseudorapidity den-sitydistribution atlow
Npart(see lower partofFig. 5
), theun-certainties are large andno strongevolution of theshape of the pseudorapidity density distribution over pseudorapidity with re-spect to centrality is observed. The ratio at3
.
5<
|
η
|
<
4.
5 does deviate somewhat inperipheral collisions, which is attributed to thegeneralbroadeningofthepseudorapiditydensitydistributions inthosecollisions.To extract the total number of charged particles produced in Pb–Pbcollisions atvarious centralities,anumberoffunctions, in-cludingEq.(5),isfittedtothedNch
/
dη
distributions.AtrapezoidfT
(
η
;
ybeam,
M,
A)
=
A×
⎧
⎪
⎪
⎨
⎪
⎪
⎩
0|
η
| >
ybeam(
ybeam+
η
)
η
<
−
M(
ybeam−
M)
|
η
| <
M(
ybeam−
η
)
η
>
+
M,
(6)was successfully used by PHOBOS to describe limiting fragmen-tation [2]. Here,
[−
M,
M]
is the range in which the function is constant,andA istheamplitude.TheparameterisationfP
(
η
;
A,
α
, β,
a)
=
A1
−
1/
[α
cosh(
η
)
]21
+
e(|η|−β)/a,
(7)assuggestedbyPHOBOS,islikewisefittedtothedNch
/
dη
Fig. 4. (Colouronline.)Full-widthhalf-maximumofthecharged-particlepseudorapiditydistributionsversustheaveragenumberofparticipants.Theuncertaintiesonthe ALICEmeasurementsarefromthefitof fGGonlyandevaluatedat95%confidencelevel.AlsoshownarelowerenergyresultsfromPHOBOS[2].
Fig. 5. (Colouronline.)Thecharged-particlepseudorapiditydensitydistributionsscaledbytheaveragenumberofparticipantsinvariouspseudorapidityintervalsasafunction ofthenumberofparticipants.Thefourright-mostpoints(opensymbols)ineachηrange,aswellasthemid-rapiditypoints(circles)arefrompreviouslypublishedresults[6, 17].Theuncertaintieson NpartfromtheGlaubercalculationsareonlyincludedonthepointsatmid-rapidity.Thus,theuncertaintybandaroundthemid-rapiditypoints
reflectboththemeasurementuncertaintiesandtheuncertaintyon Npart,whileotherηrangesonlyshowthemeasurementuncertainties.Thelowerpartshowstheratio
ofeachdistributiontothepreviouslypublisheddistributionsfor|η|<0.5.
α
andβ
,andexpressesthewidthanddepthofthedipatη
≈
0, respectively. A is an overall scale parameter. Finally, to remedy someoftheobviousdefectsofthetrapezoidi.e.,anon-continuous firstderivativeatη
=
M,weuseaBjorken-inspiredfunction[6]fB
(
η
;
A,
μ
,
σ
)
=
A×
⎧
⎪
⎪
⎨
⎪
⎪
⎩
e− (η+μ)2 2σ2η
<
−
μ
e− (η−μ)2 2σ2η
>
+
μ
1|
η
| <
μ
,
(8)whichhasplateauat A for
|
η
|
<
μ
connectedtoGaussianfall-off beyond±
μ
.The fittedfunctionsare integratedoverη
up tothe beam rapidity±
ybeam= ±
7.
99. Although the dNch/
dη
distribu-tionsinprinciplecontinuetoinfinity,thereisnosignificantlossin generalityorprecisionbycuttingtheintegralat
η
= ±
ybeamsincethedistributionsrapidlyapproachzero.Noticethatallparameters ofthefunctionsareleftfreeinthefittingprocedure.Allfunctions give reasonable fits (with a reduced
χ
2 smaller than 1), thoughthetrapezoidandBjorken-inspiredansatzaretooflatatthe mid-rapidity.Thecalculationofthecentralvaluesanduncertaintiesare done as for previous results [6]: The central value is calculated fromtheintegralofthetrapezoidfittocomparedirectlyto
previ-ousresults;thespreadbetweentheintegralsandthecentralvalue isevaluatedtoobtaintheuncertaintyonthetotal Nch.
TheextrapolatedtotalNchversus
NpartisshowninFig. 6
,andcomparedtolowerenergyresultsfromPHOBOS[19].AtLHC ener-giestheparticleproductionasafunctionof
Npartshowsasimilarbehaviour tothelowerenergyresults,andthefactorisation[2]in centralityandenergyseemstohold(seefitin
Fig. 6
).In
Fig. 7
weshowcomparisonsofvariousmodelcalculationsto the measured charged-particle pseudorapidity density asa func-tionofcentrality.Thecentralityclassforagivenmodel-generated event was determined by sharp cuts in the impact parameter bandaGlaubercalculation
[13]
.The HIJING model [3] (version 1.383, with jet-quenching dis-abled, shadowing enabled, and a hard pT cut-off of 2.3 GeV) is
seentoovershootthedataforallcentralities.Inaddition,the dis-tributionsatallcentralitiesdecreasewithincreasing
|
η
|
fasterthan thedatawouldsuggest.AMPT[4]withoutstringmeltingreproducesthedatafairlywell atcentralpseudorapidityforthemostcentralevents—exactlyin the region it was tuned to, but it fails to describe the charged-particle pseudorapidity density for more peripheral events. Also, AMPT without string melting would suggest a wider central re-gion than supported by data, and similarly to HIJING decreases
Fig. 6. (Colouronline.)Extrapolationtothetotalnumberofchargedparticlesasafunctionofthenumberofparticipatingnucleons[13].Theuncertaintyontheextrapolation issmallerthanthesizeofthemarkers.Thefourright–mostpointsarethepreviouslypublishedresults[6].Afunctioninspiredbyfactorisation[2]isfittedtothedata,and thebestfityield
a
=35.8±4.2,b
=0.22±0.05 withareducedχ2of0.18.AlsoshownisthePHOBOSresultatlowerenergyresult[19]scaledtotheALICEtotalnumberofchargedparticlesperparticipantatNpart=180.
Fig. 7. (Colouronline.)ComparisonofdNch/dηpercentralityclassfromHIJING,AMPT(withandwithoutstringmelting),andEPOS-LHCmodelcalculationstothemeasured
distributions.
fasterthanthedata.AMPTwithstringmelting—whichessentially implementsquarkcoalescence,andthereforeamorepredominant partonphase—isseentobeveryflatatmid-rapidityand under-estimatestheyield,exceptforperipheralcollisions.
Finally,EPOS–LHC[5]reproduces theshapefairlywell, but un-derestimatesthedataby10to30%.
6. Conclusions
Thecharged-particlepseudorapiditydensityhasbeenmeasured in Pb–Pb collisions at
√
sNN=
2.
76 TeV over a broadpseudo-rapidity range, extending previous published results by ALICE to more peripheral collisions. In the mid-rapidity region the
well-established tracklet procedure was used. In the forward regions, a newdata-driven procedure tocorrect forthe large background dueto secondary particles was used. The results presented here areconsistentwiththebehaviourpreviously seeninmorecentral collisions andin a limited pseudorapidity range. No strong evo-lutionofthe overallshape ofthecharged-particle pseudorapidity density distributions as a function of collision centrality is ob-served.Whennormalisedtothenumberofparticipatingnucleons inthecollision,thecentralityevolutionissmallover the pseudo-rapidityrange.Sincethemeasurementwasperformedoveralarge pseudorapidityrange (
−
3.
5<
η
<
5), itallows foran estimate of the total number of charged particles produced in Pb–Pb colli-sions at√
sNN=
2.
76 TeV. The total charged-particle multiplicityisfound toscale approximatelywiththenumberof participating nucleons.This wouldsuggest that hardcontributions to thetotal charged-particle multiplicityare small.Fromperipheral tocentral collisions we observe an increase oftwo orders of magnitudein thenumberofproducedchargeparticles.Acomparisonofthedata tothedifferentavailablepredictionsfromHIJING,AMPT,and EPOS-LHCshowthatnoneofthesemodelscapturesboththeshapeand level of the measured distributions. AMPT however comes close in limited ranges of centrality. The exact centrality ranges that AMPTdescribesdependstronglyonwhetherstringmeltingisused inthe model ornot. EPOS-LHC —although systematically low — shows a reasonable agreement with the shape of the measured charged-particle pseudorapidity densitydistribution over a wider pseudorapidityrange.
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 Gridcentres andtheWorldwide LHCComputing Grid(WLCG) Collaboration. The ALICE Collaboration acknowledges the follow-ing funding agencies for their support in building and running theALICEdetector:StateCommitteeofScience,World Federation ofScientists (WFS) andSwiss Fonds Kidagan, Armenia; Conselho Nacionalde DesenvolvimentoCientífico e Tecnológico (CNPq), Fi-nanciadorade Estudose Projetos(FINEP),Fundação de Amparoà Pesquisa do Estado de São Paulo (FAPESP); National Natural Sci-enceFoundation ofChina (NSFC), theChinese Ministryof Educa-tion(CMOE)andtheMinistryofScienceandTechnologyofChina (MSTC); Ministry of Education andYouth of the Czech Republic; Danish Natural Science Research Council, the Carlsberg Founda-tionandthe DanishNationalResearchFoundation;The European ResearchCouncilundertheEuropeanCommunity’sSeventh Frame-work Programme; Helsinki Institute of Physics and the Academy of Finland; French CNRS-IN2P3, the ‘Region Pays de Loire’, ‘Re-gion Alsace’, ‘Region Auvergne’ and CEA, France; German Bun-desministerium fur Bildung, Wissenschaft, Forschung und Tech-nologie(BMBF)andtheHelmholtzAssociation;GeneralSecretariat forResearchandTechnology,MinistryofDevelopment,Greece; Na-tionalResearch,DevelopmentandInnovationOffice(NKFIH), Hun-gary; Department of Atomic Energy and Department of Science and Technology of the Government of India; Istituto Nazionale di Fisica Nucleare (INFN) and Centro Fermi–Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”, Italy; Japan So-ciety for the Promotion of Science (JSPS) KAKENHI and MEXT, Japan; Joint Institute for Nuclear Research, Dubna; National Re-search Foundation ofKorea (NRF); Consejo Nacional de Cienca y Tecnologia(CONACYT),DireccionGeneralde Asuntosdel Personal Academico (Dirección General Asuntos del Personal Académico,
UniversidadNacionalAutónomadeMéxico),México,Amerique La-tine Formationacademique–European Commission (ALFA-EC)and the EPLANET Program (European Particle Physics Latin Ameri-can Network); Stichting voor Fundamenteel Onderzoek der Ma-terie (FOM) and the Nederlandse Organisatie voor Wetenschap-pelijkOnderzoek(NWO),Netherlands;ResearchCouncilofNorway (NFR); National Science Centre, Poland; Ministry of National Ed-ucation/Institute for Atomic Physics and National Council of Sci-entific Research in Higher Education (CNCSI-UEFISCDI), Romania; Ministry ofEducation andScience of RussianFederation, Russian Academy of Sciences, Russian Federal Agency of Atomic Energy, Russian FederalAgencyforScience andInnovationsandThe Rus-sian Foundation forBasic Research; MinistryofEducation of Slo-vakia;DepartmentofScienceandTechnology,SouthAfrica;Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas (CIEMAT),E-InfrastructuresharedbetweenEuropeandLatin Amer-ica(EELA),Ministeriode EconomíayCompetitividad(MINECO)of Spain,XuntadeGalicia(ConselleríadeEducación),Centrode Apli-cacionesTecnológicasyDesarrolloNuclear(CEADEN),Cubaenergía, Cuba, and IAEA (International Atomic Energy Agency); Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW); Ukraine Ministry ofEducation and Science; United King-dom ScienceandTechnologyFacilities Council(STFC);The United States Department of Energy, the United States National Science Foundation, theState ofTexas,andtheStateofOhio; Ministryof Science,EducationandSportsofCroatiaandUnitythrough Knowl-edge Fund, Croatia; Council of Scientific and Industrial Research (CSIR),NewDelhi,India;PontificiaUniversidadCatólicadelPerú. References
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![Table 2 summarises the systematic uncertainties of this analy- analy-sis. The common systematic uncertainty from the centrality selec-tion is correlated across η and detailed elsewhere [13] .](https://thumb-eu.123doks.com/thumbv2/123dokorg/4912178.50895/4.918.463.855.155.345/summarises-systematic-uncertainties-systematic-uncertainty-centrality-correlated-detailed.webp)
![Fig. 6. (Colour online.) Extrapolation to the total number of charged particles as a function of the number of participating nucleons [13]](https://thumb-eu.123doks.com/thumbv2/123dokorg/4912178.50895/7.918.225.712.105.336/colour-online-extrapolation-charged-particles-function-participating-nucleons.webp)
