Longitudinal asymmetry and its effect on pseudorapidity distributions in Pb–Pb collisions at √sNN = 2.76 TeV

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Physics Letters B

www.elsevier.com/locate/physletb

Longitudinal asymmetry and its effect on pseudorapidity distributions in Pb–Pb collisions at √

s _NN = ² . 76 TeV

.ALICE Collaboration

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

Articlehistory:

Received30October2017

Receivedinrevisedform9March2018 Accepted15March2018

Availableonline22March2018 Editor:L.Rolandi

FirstresultsonthelongitudinalasymmetryanditseffectonthepseudorapiditydistributionsinPb–Pb collisions at√_s

NN =^{2.76 TeVattheLargeHadronColliderareobtainedwiththe ALICEdetector.The} longitudinal asymmetry arises becauseofanunequal number ofparticipatingnucleons fromthe two collidingnuclei,andisestimatedforeacheventbymeasuringtheenergyintheforwardneutron-Zero- Degree-Calorimeters(ZNs).Theeffectofthelongitudinalasymmetryismeasuredonthepseudorapidity distributionsofchargedparticlesintheregions|η_|<0.9,2.8<η<5.1 and−³.7<η<−¹.7 bytaking theratioofthepseudorapiditydistributionsfromeventscorrespondingtodifferentregionsofasymmetry.

Thecoefficientsofapolynomialfittotheratiocharacterisetheeffectoftheasymmetry.AMonteCarlo simulationusingaGlaubermodelforthecollidingnucleiistunedtoreproducethespectrumintheZNs andprovidesarelationbetweenthemeasurablelongitudinalasymmetryandtheshiftintherapidity(y0) oftheparticipantzoneformedbytheunequalnumberofparticipatingnucleons.Thedependenceofthe coefficientofthelinearterminthepolynomialexpansion,c1,onthemeanvalueofy0isinvestigated.

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

1. Introduction

Ina heavy-ion collision,the numberof nucleons participating fromeach ofthe two collidingnuclei isfinite, andwillfluctuate event-by-event. The kinematic centre of mass of the participant zone,definedastheoverlapregionofthecollidingnuclei,ingen- eralhasafinitemomentuminthenucleon–nucleoncentreofmass frame because of the unequal number of nucleons participating fromthetwonuclei.Thismomentumcausesalongitudinalasym- metry in the collision and corresponds to a shift of rapidity of the participantzone withrespect to the nucleon–nucleon centre ofmass (CM) rapidity,termed therapidity-shift y0. The value of y₀isindicativeofthemagnitudeofthelongitudinalasymmetryof thecollision [1,2].Assumingthenumberofnucleonsparticipating fromeachofthetwonucleiis A andB,thelongitudinalasymme- tryinparticipantsisdefinedas

α

part= ^A_A⁻₊^B_B ^andtherapidity-shift canbeapproximatedasy₀∼=¹2ln^A_B atLHCenergies [2].

The shift in the CM frame of the participant zone, which evolvesintoastateofdensenuclearmatter,needstobeexplored in heavy-ion collision models. Comparison of model predictions with the observed -polarisation, possibly due to vorticity from the initial state angular momentum surviving the evolution, re- quiresaprecisedetermination ofinitial conditionsandhencethe

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

shiftintheCMframe [3–5].Such ashiftmayalsoaffectobserva- tions on correlationsamongst particles,which eventually provide informationaboutthestate ofthematterthroughmodelcompar- isons.Further,theresultantdecreaseintheCMenergymayaffect various observables includingthe particle multiplicity.The trans- verse spectraareknowntobe affectedby theinitialgeometryof the events, as estimated through techniques of event shape en- gineering, indicating an interplay between radial and transverse flow [6].Themeasurementoflongitudinalasymmetrywillprovide anewparametertowardseventshapeengineering,affectingmany otherobservables.

The simplest of all possible investigations into the effect of longitudinal asymmetry is a search for modification ofthe kine- maticdistributionoftheparticles.Thepseudorapiditydistribution (dN/d

η

)ofsoftparticles,averagedoveralargenumberofevents, is symmetric in collisions of identical nuclei. These distributions were observed to be asymmetric in collisions of unequal nuclei such as d–Au [7] and p–Pb [8–10] and have been explained in termsoftherapidity-shiftoftheparticipantzone [11].Inaheavy- ioncollision,theeffectoftherapidity-shiftoftheparticipantzone shouldbediscernibleinthedistributionofproducedparticles.This smalleffectcan beestimatedby takingtheratioofpseudorapid- ity distributions inevents corresponding todifferent longitudinal asymmetries [2].

It was suggested that the rapidity distribution of an event, scaled by the average rapidity distribution, can be expanded in termsofChebyshevpolynomials, wherethecoefficientsofexpan- https://doi.org/10.1016/j.physletb.2018.03.051

0370-2693/©^{2018TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

sionaremeasuresofthestrengthoflongitudinalfluctuationsand canbedeterminedbymeasuringthetwoparticlecorrelationfunc- tion [12]. Usingthe samemethodology,the event-by-eventpseu- dorapidity distributions are also expanded in terms of Legendre polynomials [13].TheATLASCollaborationexpandedthepseudora- piditydistributionsintermsofLegendrepolynomialsandobtained thecoefficientsbystudyingpseudorapiditycorrelations [14].

Inthepresentwork,theeventsare classifiedaccordingtothe asymmetrydeterminedfromthemeasurementofenergiesofneu- tron spectators on both sides of the collision [2]. The effect of asymmetryisinvestigatedbytakingtheratioofthemeasuredraw dN/d

η

distributionsforeventsfromdifferentregionsofthedistri- butionofmeasuredasymmetry.Amajoradvantageofstudyingthis ratioisthecancellationof(i)systematicuncertainties and(ii)the effectsofshortrange correlations. Thefirst measurements ofthe effectofasymmetry ontherawdN/d

η

distributionsarereported here.

Thepaperisorganisedasfollows:Sect.2providesanintroduc- tion to the experimental setup andthe details of the data sam- ple.Section3discusses thecharacterisation ofthechangeinraw dN/d

η

distributions for events classified in different asymmetry regions.Section 4 describesthe simulationsemployed to provide arelationbetweenthemeasuredasymmetryandtherapidity-shift y0 of the participant zone. The relation between the parameter characterisingthechangeinrawdN/d

η

distributionsisshownfor differentcentralities inSect.5,along withits relationto theesti- matedvaluesof y0.

2. Experimentaldetailsanddatasample

TheanalysisusesdatafromPb–Pb collisioneventsat√ sNN = 2.76TeV, recordedintheALICEexperimentin2010,withamin- imumbias trigger [15,16]. The data used inthe presentanalysis isrecordedintheneutronZeroDegreeCalorimeters (ZNs),theV0 detectors,theTimeProjectionChamber(TPC)andtheInnerTrack- ingSystem(ITS).Both ZNsandV0detectorsare oneithersideof theinteractionvertex,thoseinthedirectionofpositivepseudora- pidityaxisarereferredasV0AandZNAandthoseintheopposite directionarereferredasV0CandZNC.Adetaileddescriptionofthe ALICEdetectorsandtheirperformancecanbefoundelsewhere [17, 18].

Theeventasymmetryis estimatedusing theenergymeasured inthetwoZNssituated114metresawayfromthenominalinter- actionpoint(IP)oneitherside.TheZNsdetectonlyspectatorneu- tronsthatarenotboundinnuclearfragments,sincethelatterare bentawaybythemagneticfieldoftheLHCseparationdipole.The ZNdetectionprobability forneutrons is 97.0% ± ^0.2%(stat) ±^3%

(syst) [19]. The relative energyresolution of the1n peak at 1.38 TeVis21%fortheZNAand20% fortheZNC [19].Theproduction ofnuclearfragmentsincreaseswithcollisionimpactparameterde- grading the resolution on the number of participating nucleons.

TheenergyintheZNsisagoodmeasureofthenumberofspecta- torneutronsonlyforthemorecentralcollisions [18].Theanalysis islimited tothe top 35% mostcentral sample andemploys data from∼².7 millionevents.

The raw dN/d

η

distributions in the region |

η

|<0.9 are ob- tainedbyreconstructingthechargedparticletracksusingtheTPC and ITS. The requirements on the reconstructed tracks obtained using the measurements in these detectors are the same as in other earlieranalyses [15]. The measured amplitudes inthe V0A (+².8<

η

<+⁵.1) andV0C (−³.7<

η

<−¹.7) are used to es- timate the raw dN/d

η

distributions of charged particles in the forwardregions. Both V0AandV0Care scintillatorcounters,each withfour segments in pseudorapidity andeight segments in az- imuth.Therawdistributions measuredare termedasdN/d

η

dis-

tributionsthroughoutthemanuscript.Inordertoensureauniform detectorperformance,thepresentanalysisuseseventswithz po- sition (along the beam direction) of the interaction vertex, Vz, within ± ^{5 cm of the IP in ALICE. The centrality of Pb–Pb col-} lisionswas estimatedby twoindependentmethods.Oneestimate wasbasedonthechargedparticlemultiplicityreconstructedinthe TPCandtheother wasbasedon theamplitudesintheV0detec- tors[20].

3. Analysisandsystematicuncertainties

Inthepresentanalysis,changesintherawpseudorapiditydis- tribution ofchargedparticles areinvestigated fordifferentvalues ofmeasuredasymmetryoftheevent.Themethodofmeasurement oftheasymmetryandtheparameterscharacterisingthechangein dN/d

η

distributionsarediscussedinthissection.

3.1. Analysis

Anyeventasymmetryduetounequalnumberofnucleonsfrom the two participatingnucleimaymanifest itself inthe longitudi- naldistributions,i.e.dN/dy (or dN/d

η

)oftheproducedparticles because of a shift in the effectiveCM. Assuming that the rapid- itydistributions can bedescribed by a symmetricfunction about a mean y₀ (y₀=⁰.0 for symmetricevents), the ratioofthe dis- tributions forasymmetric and symmetric eventsmay be written as

(

dN

/

dy

)

asym

(

dN

/

dy

)

sym

=

^f

(

y

−

^y0

)

f

(

y

) ∝

∞

n=0

cn

(

y0

)

yⁿ (1) Foranyfunctionalformoftherapiditydistribution,thisratiomay beexpandedinaTaylorseries.Thecoefficientsc_n ofthedifferent termsin theexpansiondepend onthe shapeandtheparameters oftherapiditydistribution [2].IntheALICEexperiment,thepseu- dorapiditiesoftheemittedparticleswere measured.Theeffectof arapidity-shift y₀ onthepseudorapiditydistributionis discussed inSect.4.2.

Theunequalnumberofparticipatingnucleonswillyieldanon- zero y₀ ofthe participant zone andwill causean asymmetry in thenumberofspectators.Thisasymmetrycanprovideinformation aboutthemeanvaluesof y0 usingtheresponsematrixdiscussed inSect.4.Theasymmetryofeacheventisestimatedbymeasuring theenergyintheZNsonbothsidesoftheinteractionvertex:E_ZNA onthesidereferredtoastheA-side(

η

>0)andEZNC ontheside referred to astheC-side (

η

<0).A smalldifference inthe mean andtherelativeenergyresolutionofthe1npeakat1.38TeVwas observed in theperformance ofthe two ZNs [19]. Foreach cen- tralityinterval,theenergydistributionineachZNisdividedbyits mean,andthe widthofthe E_ZNC/^EZNC distributionis scaledto thewidthofthecorrespondingdistributionusingEZNA.Theasym- metryinZNisdefinedas

α

ZN

= ε

ZNA

− ε

ZNC

ε

ZNA

+ ε

ZNC

(2) where

ε

ZNC(A)isadimensionlessquantityforeachevent,obtained afterscalingthedistributionsofEZNC(A)asdescribedabove.

For the 15–20% centrality interval, Fig. 1 showsthe distribu- tionofthe asymmetry

α

ZN.Toinvestigatethesignificanceofthis distribution,the contributionof theresolutionof ZNsto theres- olution of the asymmetry parameter

α

ZN is evaluated. For each centralityinterval,valuesofEZNC andEZNAaresimulatedforeach eventbyassuminganormaldistributionpeakedatthemeanvalue

Fig. 1.ThedistributionoftheasymmetryparameterαZNforthe15–20%centrality interval.Thedistributionisdemarcatedintothreeregionsusing|α^cut_ZN|.AGaussian fittothedistributionyieldsawidthof0.13.

corresponding tothe average numberofneutrons andthe corre- sponding energy resolution. The average number of neutrons is estimatedby dividing the experimental distribution of energyin ZNby1.38TeV.Thesevaluesareusedtoobtain

α

ZNforeachevent andits distribution.The widthofthe distributioncorresponds to theintrinsicresolutionofthemeasuredparameter

α

ZN andvaries from0.023 to0.050 fromthemostperipheral (30–35%)selection to themostcentral (0–5%) selection.The observed widthof 0.13 ofthedistributionof

α

ZN reportedinFig.1isconsiderablylarger than the resolution of

α

ZN (0.027 for the centralityinterval cor- responding to the data in the figure) and the increase in width maybeattributedtotheevent-by-eventfluctuationsinthenum- ber of neutrons detected in each ZN. To investigatethe effectof

α

ZN on the dN/d

η

distributions, the events are demarcated into three regions of asymmetry by choosing a cut value

α

_ZN^cut. These regions correspond to (i)

α

ZN<−

α

^cut_ZN (Region 1), (ii)

α

ZN≥

α

_ZN^cut

(Region 2)and(iii)−

α

^cut_ZN≤

α

ZN<

α

_ZN^cut (Region3). Regions1and 2 are referred to as the asymmetric regions and Region3 is re- ferredtoasthesymmetricregion.

Theeffectofthemeasuredasymmetry

α

ZNonthepseudorapid- itydistributionsisinvestigatedbystudyingtheratioofdN/d

η

dis- tributionineventsfromtheasymmetricregion tothosefromthe symmetricregion.There aresmalldifferencesinthedistributions ofcentrality andvertexposition inevents ofdifferentregions of asymmetry.Itisnecessarytoensurethatanycorrelationbetween theratioofdN/d

η

andtheasymmetryisnotduetoasystematic effectofashiftintheinteractionvertex.Toeliminateanypossible systematicbiasonthemeasureddistributions,thedN/d

η

distribu- tionsare correctedbyweightfactorsobtainedbynormalisingthe numberofeventsinasymmetricandsymmetricregionsineach1%

centralityintervalandeach1cmrangeofvertexpositions.

For the 15–20% centrality interval, the distributions of these factorsinthetwocasescorrespondingtotheasymmetryregions 1 and 2 havea mean of 1.0and an rms of 0.05 and0.06 respec- tively.Theweightfactorsdonotshowanysystematicdependence onthepositionofthevertex.Thisisexpectedconsideringthelarge distancebetweentheZNsascomparedtovariationsinthevertex position.Thefactorsshowasystematicdependenceon1%central- itybinswithineach centralityinterval.The1% centralitybinwith thegreaternumberofparticipantstendstohavemoreasymmetric events,presumablytocompensateforthedecreaseintheeffective CMenergyduetothemotionoftheparticipantzone;theweight

factoris1.08forthemostcentral15–16%centralitybinandis0.94 forthe19–20%centralitybin.

The ratio of dN/d

η

for events corresponding to different re- gions of asymmetry,asshowninFig. 1,is determined.For |

η

_|<

1.0, the ratio is obtained using dN/d

η

for tracks. For |

η

_|>1.0, the ratioshowninFig.2(a) and(b)isobtainedfromamplitudes measured inV0Aandthe oneshownin Fig.2(c)and(d)isfrom amplitudesmeasuredinV0C.ThesquaresinFig.2(a)and(c)rep- resent the ratio ofdN/d

η

inthe asymmetry Region1 to that in Region3(R13),andthestarsrepresentthecorresponding ratioin Region2toRegion3(R23).Thefilledcircles inFig.2(b)and(d) are obtained by (i) reflecting thedata points labelled R23 across

η

=^{0 and (ii) taking the averages of R13 and} reflected-R23 for

|

η

|<1.0.Athirdorderpolynomial isfittedto thepointsandthe values of the coefficients cn along with the

χ

² are shown. The polynomialfittotheratioofdN/d

η

distributionhasadominantly linearterm.Asmallresidualdetectoreffectisobservedwhende- termining c1 using data measured in V0A andwhen using data measured in V0C. In all subsequent discussion, the values of c₁ quoted are the mean ofvalues obtainedfrom themeasurements inV0AandV0C.

Considering thatthe eventsamplescorresponding to different regions ofasymmetry areidenticalinall aspectsother thantheir valuesofmeasured

α

ZN,theobservationofnon-zerovaluesofc1 can be attributedto the asymmetry.For a fixed centralityinter- val, c₁ depends on the choice of

α

_ZN^cut. The analysis is repeated for differentvalues of

α

_ZN^cut andthe dependenceof c1 on

α

_ZN^cut is shown in Fig. 3, for different centralities. For each centrality in- terval thecoefficient c1 has alineardependenceon

α

_ZN^cut andthe slope increaseswithdecreasingcentrality;c1 increasesforevents corresponding to larger values of average event asymmetry. The rangeofvaluesof

α

_ZN^cutwasguidedbytheresolutionandthewidth of the distribution of

α

ZN, as mentioned in reference to Fig. 1.

Increasing thevalue of

α

_ZN^cut increasesthe mean

α

ZN ^forevents from theasymmetric class (Region 1or Region2), andincreases theRMSof

α

ZNforeventsfromthesymmetricclass(Region3).

3.2. Systematicuncertainties

The current method of analysisuses the ratio of two dN/d

η

distributions from events divided on the basis of measurements inZNs,within acentralityinterval.Alleffects duetolimitedeffi- ciency,acceptanceorcontamination wouldcancelwhileobtaining the value oftheratio.The contributionsto thesystematicuncer- taintiesonc₁ areestimatedduetothefollowingsources:

1. Centralityselection: the ratioofdN/d

η

is obtainedfromthe measurements of tracks in the ITS+TPC at midrapidity and charge particlesignalamplitudesintheV0atforwardrapidi- ties. For theformer, theeventcentrality isdetermined using themeasurementsintheV0andforthelatterusingthetrack multiplicityintheTPC.Theanalysisisrepeatedbyinterchang- ingthecentralitycriteriaandtheresultantchangeintheval- uesofc1 fordifferentcentralityintervalsisintherange0.1%

to3.6%.

2. V0AandV0C:thesystematicuncertaintyonthemeanvalueof c₁ isestimatedbyassumingauniformprobabilitydistribution forthecorrectvalue ofc₁ to lie betweenthe twovaluesob- tainedusingthecharged-particle signalamplitudesmeasured intheV0AandtheV0C.The uncertaintyisintherange2.1%

to4.6%anddoesnotdependonthecentralityvalue.

3. Vertexposition:theanalysisis repeatedforthe zpositionof theinteraction vertex|Vz|≤3.0 cm.Forthemostcentralin- terval, the results change by lessthan 0.1%. For the 15–20%

Fig. 2.TheratioofdN/dηdistributionforeventsfromthedifferentregionsofαZN distributionofFig.1.ThedN/dηdistributionsareobtainedasdescribedinSect.2.

(a) Thesquare(star)symbolscorrespondingtoR13(R23)areobtainedbytakingtheratioofdN/dηofeventsfromRegion1(Region2)toRegion3.(b)Thedatapointsare obtainedafterreflectionacrossη=^{0 asdescribedinthetext.Thedatafor}|η|>1.0 inpanels(a)and(b)arefrommeasurementsinV0Aandinpanels(c)and(d)arefrom measurementsinV0C.

Fig. 3.Thecoefficientc1characterisingthechangeindN/dηdistributionforasym- metricregionsisshownfordifferentvaluesofα^cut_ZN (α_ZN^cutdemarcatestheasymmet- ricandsymmetricevents)foreachcentralityinterval.

centralityinterval,theresultschangeby3.3%andforallother centralityintervals,thechangesarelessthan1.3%.

4. Weightfactorsfornormalisation:theanalysisisalsorepeated withouttheweightfactorsmentionedinSect.3.1forthecen- tralityandthevertexnormalisationinthenumberofevents.

Thechangeintheresultsis4.9%inthemostcentralclassand lessthan1%forallothercentralityintervals.

Thetotalsystematicuncertaintyisobtainedbyaddingthefour uncertainties in quadrature. The resultant uncertainty is in the range2.3%to5.8%andisshownbythebandinFig.8.

4. Simulations

Thesimulationusedforobtaining arelationbetweenrapidity- shift y0 andthe measurableasymmetry

α

ZN is described in this section.Thissimulationhasthreecomponents:(i)aGlauberMonte Carlo to generate number of participants and spectator protons andneutrons, (ii) a function parametrised to fit the average loss ofspectator neutrons dueto spectatorfragmentation(the loss of spectatorneutrons ineacheventissmeared aroundthisaverage) and (iii)the response of the ZNto single neutrons. The simula- tion encompassing the above is referred to in the presentwork asTunedGlauberMonteCarlo(TGMC),andreproducestheenergy distributions in the ZNs. The effect of y0 on the pseudorapidity distributionshasbeenestimatedusingadditionalsimulationsfora GaussiandN/dyandarealsodescribedinthissection.

4.1. Asymmetryandrapidity-shift

TheGlauberMonteCarlomodel [21] usedinthepresentwork assumesa nucleon–nucleoninteractioncrosssection of64mb at

√sNN = ^{2.76TeV. The model yields the numberof} participating nucleonsintheoverlapzonefromeachofthecollidingnuclei.The rangeofimpactparametersforeach5%centralityintervalistaken fromourPb–Pbcentralitypaper [20].Foreach centralityinterval, 0.4millioneventsaregenerated.

Foreachgenerated event,thenumberofparticipatingprotons andneutronsisobtained,enablingadeterminationoftherapidity- shift y0 andthevarious longitudinalasymmetries.IfAandBare thenumberofspectators(spectatorneutrons)inthetwocolliding nuclei,theasymmetryisreferredtoas

α

spec(

α

spec−neut).Fig.4(a) showsthe correspondencebetween y0 and

α

part.Figs. 4 (b)and (c) show the relation between y0 and

α

spec and

α

spec−^neut re- spectively [2].Thesefiguresshowthattherapidity-shifty0 canbe estimatedbymeasuring

α

specor

α

spec−^neutinanyexperimentthat uses Zero DegreeCalorimeters. However, the lack of information

Fig. 4.Rapidity-shifty0asafunctionofasymmetryin(a)numberofparticipants, (b)numberofspectators, (c)numberofspectatorneutronsand(d)energyinZNobtained usingTGMCasdescribedinthetext.Theresultsinallfourpanelsareshownforthe15–20%centralityinterval.

Fig. 5.(a)DistributionofenergyinZNCineach5%centralityintervalforeventssimulatedusingTGMCandfortheexperimentaldata.Thepeakofthedistributionshiftsto smallervaluesofEZNCwithincreasingcentrality.(b) DistributionoftheasymmetryparameterαZNinthesimulatedeventsandinexperimentaldatafordifferentcentralities.

Thewidthofthedistributionincreaseswithincreasingcentrality.Forclarity,only5distributionsareshown.Thedistributionscorrespondingto20–25% and25–30%lie betweenthoseof15–20%and30–35%.

onthenumberofparticipantsworsenstheprecisionindetermin- ing y0.Fig.4(d)showstherelationbetweeny0and

α

ZNobtained inTGMC,asdescribedinthenextparagraph.

The Glauber MonteCarloistuned to describe theexperimen- tal distributions of ZN energy. For each 1% centrality interval, the mean number of spectator neutrons (N_s) is obtained in the GlauberMonteCarlo.FoldingtheZNresponseyieldsthesimulated valuesofmeanenergyasafunctionofcentrality.Theexperimen- tallymeasuredmeanenergyintheZNisalsodeterminedforeach 1%centralityinterval.Theratioofthemeasuredvalueofmeanen- ergy to the simulated value of mean energy gives the fractional loss(f)ofneutronsduetospectatorfragmentsthatveerawaydue tothemagneticfield. Thevalueoff forthe0–5%centralityinter- valis0.19. Forallother centralities itvariesfrom0.40 for5–10%

to0.55for30–35%centralityinterval.Afluctuationproportionalto thenumberofremaining neutrons(Ns×(1−^f))is incorporated toreproducetheexperimentaldistributionoftheenergydeposited intheZNshowninFig.5(a).ThepeakandtheRMSoftheenergy distributions matchwell.The fractional difference intheposition of the peak varies between3.7% for the 0–5% centrality interval and0.1% for the30–35% centrality interval. The fractional differ- enceinRMSforthemostcentralclassis8.6%andisintherange 1.0–2.0%forall other centralityintervals. Thedistributions ofthe asymmetryparameterfortheTGMCeventsandthemeasureddata foreachcentralityintervalareshowninFig.5(b).TheTGMCcon-

tains information of y0 and

α

ZN for each event. A scatter plot between y0 and

α

ZNisshowninFig.4(d)forthe15–20%central- ityinterval.Thisconstitutestheresponsematrix.Foranymeasured value of

α

ZN,the distribution of y0 can be obtained. Any differ- ence in the experimental and TGMC distributions of

α

ZN can be accountedforby scalingthe y0 distributionbythe ratioofnum- berofeventsindatatothenumberinTGMCas

f

(

y0

, α

_ZN^Data

) =

^f

(

y0

, α

_ZN^TGMC

)

^N

Dataevents

N^TGMC_events

,

(3)

withData(TGMC)inthesuperscriptofnumberofevents,Nevents, denoting the experimental data (TGMC events). For each of the three regions of asymmetry shown in Fig. 1, corresponding to a chosenvalueof

α

^cut_ZN=⁰.1,thedistributionofrapidity-shift y0ob- tained using the response matrix is shown in Fig. 6. It isworth mentioningthatthewidthofthedistributionofy₀foreventsfrom Region 3,corresponding to −

α

^cut_{ZN ≤}

α

ZN<

α

^cut_ZN, is comparableto thewidthsofthecorresponding distributionsfromRegions1and 2.Theeffectofdifferenceinthevalueofthemeansofthey₀ dis- tributionsisinvestigatedinthepresentwork.

4.2. Effectofrapidity-shiftonpseudorapiditydistributions

The effect ofa shift inthe rapidity distribution by y0 on the measurablepseudorapiditydistribution(dN/d

η

)isinvestigatedus- ingsimulations.Foreachevent,therapidityofchargedparticlesis

Fig. 6.Thedistributionofrapidity-shifts forthe eventsfromthe threedifferent regionsofmeasuredasymmetryshowninFig.1.Determinationofy0usesthedif- ferenceinnumberofnucleons.Forsmallvaluesofthisdifference,thechangesin valuesneary0=0 arediscrete,andaresmearedintoacontinuousdistributionas y0increases.

generatedfromaGaussiandistributionofachosenwidth

σ

y [22].

ThepseudorapidityisobtainedbyusingtheBlast-Wavemodelfit to the data for the transverse momentum distributions and the experimentally measured relativeyields ofpions, kaonsand pro- tons [23].Tosimulatetheeffectofdifferentwidthsoftheparent rapidity distribution fordifferent centralities, different

σ

y widths arechosentoreproducethemeasured FWHM(FullWidthatHalf Maximum) of the pseudorapidity distribution [24]. Forthe most central(0–5%)class,a value3.86isusedforthewidthofthera- pidity distribution,anda value 4.00 isused forthe widthofthe leastcentralclassemployedinthisanalysis(30–35%).

Thedistributionof rapidity-shift y0,similar tothe oneshown in Fig. 6, is obtained for each centrality interval and each

α

^cut_ZN

usingTGMC.Fig.7(a)showsthe^y0^{asafunctionof}

α

^cut_ZN fordif- ferentcentralities.Oneobservesalinearrelationbetweenthetwo quantities, showing that an asymmetry in the ZN measurement, arisingfromtheunequal numberofparticipatingnucleons, isre- latedtothe meanrapidity-shift ^y0^{.The rapidity} distributionof theparticlesproducedineacheventisgeneratedassumingaGaus- sianformcentred abouta y0,which isgeneratedrandomly from the y0 distribution.Events witharapidity distributionshifted by

y0=^{0 yieldanasymmetric}pseudorapiditydistribution.Athirdor- derpolynomialfunctionin

η

isfittedtotheratioofthesimulated dN/d

η

fortheasymmetricregiontothesimulateddN/d

η

forthe symmetricregion. Thevaluesofthe coefficientsintheexpansion dependupontherapidity-shift y0andtheparameterscharacteris- ingthedistribution [2].

The simulations described above were repeated for different valuesof

α

_ZN^cut to obtainthepseudorapiditydistributions forsym- metric and asymmetric regions. Fitting third order polynomial functions to the ratios of the simulated pseudorapidity distribu- tions determines the dependenceof c1 on

α

_ZN^cut.Fig. 7 (b)shows that c₁ hasalineardependenceon

α

^cut_ZN foreachcentralityinter- val. The difference in the slopes for different centralities is due to differencesinthedistributions of y0 andtodifferencesin the widthsoftherapiditydistributions.

Itisimportanttonotethattheparameterc₁,characterisingthe asymmetry inthe pseudorapidity distribution,showsa linearde- pendence on the parameter

α

_ZN^cut in the event sample generated usingTGMCandsimulationsforaGaussiandN/dy,akintothede- pendenceoftheestimatedvalueofrapidity-shift y₀ forthesame sampleofevents.

5. Results

The longitudinalasymmetry ina heavy-ioncollision has been estimatedfromthedifference intheenergyofthespectatorneu- tronson both sidesofthe collisionvertex. The effectof thelon- gitudinal asymmetry is observed in the ratioof dN/d

η

distribu- tions corresponding to differentasymmetries. The linear term in a polynomial fitto thedistribution ofthe ratiois dominant, and ischaracterisedbyitscoefficientc1.Thecentralitydependenceof the coefficient c1 for

α

_ZN^cut₌0.1 is shown in Fig. 8. It is worth emphasising thatthevaluesofc₁ andhenceits centralitydepen- dence are affected by (i) the distribution of rapidity-shift y0 for each centralityinterval, (ii) the chosen value of

α

_ZN^cut, as seen in Fig.7and(iii) the shapeorthewidthofthe parentrapidity dis- tributionforeachcentrality.Fig.8alsoshowstheresultsobtained usingsimulationsasdescribed inSec. 4.2for

α

^cut_ZN=⁰.1.The sys- tematicuncertaintyonthesimulatedeventsampleisestimatedby (i) varying the resolution ofZNs from 20% to 30%, (ii) assuming all charged particles are pions and(iii) varying thewidth of the parentrapiditydistributionwithintherangecorresponding tothe uncertainties onFWHMquoted inRef. [24]. Thesimulatedevents showagoodagreementwiththeexperimentaldataprovidingcre-

Fig. 7.(a)Theestimatedmeanvalueofrapidity-shifty0fortheasymmetricregioncharacterisedbydifferentvaluesofα_ZN^cutforeachcentralityinterval.(b)Thecoefficient c1characterisingthechangeinthepseudorapiditydistributionsfordifferentvaluesofα_ZN^cut,foreachcentralityinterval.TheseresultsareobtainedusingTGMCandsimulated pseudorapiditydistributions,asdescribedinthetext.

Fig. 8.Themeanvaluesofthecoefficientc1areshownasfilledcirclesfordifferentcentralities.ThesecorrespondtotheratioofdN/dηdistributionsofpopulationsofevents demarcatedbyαZN^cut=⁰.1.Thesquaresshowthecorrespondingvaluesfromsimulations,andcorrespondtoα^cutZN=⁰.1 inFig.7,fordifferentcentralities.Thesystematic uncertaintiesareshownasbands.

Fig. 9.Foreachsetofeventscharacterisedbyα^cutZN,themeasuredvaluesofcoef- ficientc1asafunctionofestimatedvaluesofmeanrapidity-shiftobtainedusing TGMCasdescribedinthetext.Theresultsareshownfordifferentcentralities.The uncertaintiesfory0shownarestatisticalandwithinitssymbolsize.Thelinesare linearfitspassingthroughtheorigin.

dencetotheassumptions ofthesimulation,inparticularthatthe asymmetryinthedistributionsarisesfromtheshiftofrapidity of theparticipantzone.

There are two quantities fromindependent measurements for eachselection ofasymmetricevents.Theseare (i) c1,theparam- eter characterising the effect of asymmetry in the dN/d

η

distri- butions andshowninFig.3and(ii) themeanrapidity-shift ^y0 obtainedfromthemeasured asymmetry,filteredthrough thecor- responding responsematrix (Fig. 4 (d)), andshown inFig. 7 (a).

Therelationbetweenc1 and^y0^{isshowninFig.9.Theparame-} terc1 showsalineardependenceon^y0^foreachcentrality.The differenceintheslopesindicatesthesensitivityofthelongitudinal asymmetry tothedetails oftherapidity distribution.ForaGaus- sianrapiditydistributionthecorrespondingparameterc₁wouldbe relatedtotherapidity-shiftasc1=_σ^y0

y2

[2],implyingthattheslope isinverselyproportionaltothesquareofthewidthofthedistribu- tion.Theobservationofan increaseintheslopewithanincrease in the centrality in the present data indicates a decrease in the widthofthepseudorapiditydistributionwithincreasingcentrality.

Such a decrease in the width of the pseudorapidity distribution withincreasingcentralityhasbeenobservedindependentlybyfit-

tingthe pseudorapiditydistributions ina broadrangeofpseudo- rapidity [24].

6. Conclusions

The present analysis demonstratesthe existence ofa longitu- dinalasymmetry inthe collisionofidenticalnucleiduetofluctu- ationsin thenumberofparticipants fromeachcollidingnucleus.

This asymmetry has beenmeasured in the ZNs inthe ALICEex- periment (Fig. 1), andaffects thepseudorapidity distributions, as demonstratedbytakingtheratioofdistributionofeventsfromthe asymmetric region tothe corresponding onefromthe symmetric region(Fig.2).Theeffectcanbecharacterisedbythecoefficientof thelinearterminthepolynomialexpansionoftheratio.Thecoef- ficientsshowalineardependenceon

α

^cut_ZN,aparametertoclassify the events into symmetric and asymmetric regions (Fig. 3). Dif- ferent values of

α

_ZN^cut correspond to different valuesof the mean rapidityshift^y0^{(Fig.7(a)).Theparameterdescribingthechange} inthepseudorapiditydistributions(c₁)hasasimpleexplanationin the rapidity-shift^y0^{of the}participantzone (Fig.9). The analy- sisconfirms thatthelongitudinaldistributions areaffectedbythe rapidity-shiftoftheparticipantzonewithrespecttothenucleon–

nucleonCMframe.Theresultsprovidesupporttotherelevanceof numberofnucleons affectingtheproductionofchargedparticles, evenatsuchhighenergies.

The longitudinal asymmetry is a good variable to classify the eventsandprovidesinformationontheinitialstateofeach event.

Asystematicstudyoftheeffectsoflongitudinalasymmetryondif- ferentobservables, e.g.theoddharmonicsofanisotropicflow, the forward-backwardcorrelations, thesourcesizes, inheavy-ioncol- lisions may reveal other characteristics ofthe initial state andof particleproductionphenomena.

Acknowledgements

The ALICECollaboration would like to thank all its engineers andtechniciansfortheirinvaluablecontributionstotheconstruc- tion of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collab- oration gratefully acknowledges the resources and support pro- videdbyallGridcentresandtheWorldwideLHCComputingGrid (WLCG) collaboration. The ALICE Collaboration acknowledges the following fundingagenciesfortheir supportin buildingandrun- ningthe ALICEdetector:A.I. AlikhanyanNationalScience Labora- tory(YerevanPhysicsInstitute)Foundation (ANSL),State Commit- teeofScienceandWorldFederationofScientists(WFS),Armenia;

AustrianAcademy ofSciences andNationalstiftung fürForschung, Technologie und Entwicklung, Austria; Ministry of Communica- tions and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Universidade Federal do Rio Grande do Sul (UFRGS), Financiadora de Estudos e Projetos (Finep) and Fun- dação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil; Ministry of Science & Technology of China (MSTC), Na- tional Natural Science Foundation of China (NSFC) and Ministry of Education of China (MOEC), China; Ministry of Science, Edu- cation andSport and Croatian Science Foundation, Croatia; Min- istryofEducation,YouthandSportsoftheCzechRepublic, Czech Republic; The Danish Council for Independent Research | Natu- ral Sciences, the Carlsberg Foundation and Danish National Re- search Foundation (DNRF), Denmark;Helsinki Institute ofPhysics (HIP),Finland;Commissariatàl’EnergieAtomique(CEA)andInsti- tut Nationalde Physique Nucléaire etde Physique des Particules (IN2P3)andCentre National de laRecherche 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,Ministry ofEducation, Researchand Reli- gions,Greece;NationalResearch,DevelopmentandInnovationOf- fice,Hungary;DepartmentofAtomicEnergy,GovernmentofIndia (DAE),DepartmentofScienceandTechnology,GovernmentofIndia (DST),University Grants Commission, Governmentof India(UGC) andCouncil ofScientificandIndustrialResearch(CSIR), India;In- donesian Institute of Science, Indonesia; Centro Fermi – Museo StoricodellaFisicaeCentroStudieRicercheEnricoFermiandIsti- tutoNazionalediFisicaNucleare(INFN),Italy;InstituteforInnova- tiveScienceandTechnology,NagasakiInstituteofAppliedScience (IIST),Japan Societyforthe PromotionofScience(JSPS)KAKENHI andJapanese Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan; Consejo Nacional de Ciencia (CONA- CYT)yTecnología,throughFondodeCooperaciónInternacionalen CienciayTecnología (FONCICYT)andDirección Generalde Asun- tosdelPersonalAcademico(DGAPA),Mexico;NederlandseOrgan- isatievoorWetenschappelijk Onderzoek(NWO),Netherlands; The ResearchCouncil ofNorway, Norway;CommissiononScienceand TechnologyforSustainableDevelopmentintheSouth(COMSATS), Pakistan;PontificiaUniversidadCatólicadelPerú,Peru;Ministryof ScienceandHigherEducationandNationalScienceCentre,Poland;

KoreaInstituteofScienceandTechnologyInformationandNational ResearchFoundationofKorea(NRF),RepublicofKorea;Ministryof EducationandScientificResearch,Institute ofAtomicPhysicsand Romanian National Agency for Science, Technology and Innova- tion,Romania;JointInstituteforNuclear Research(JINR),Ministry ofEducation andScience of the Russian FederationandNational Research Centre Kurchatov Institute, Russia; Ministry of Educa- tion,Science,ResearchandSportoftheSlovakRepublic, Slovakia;

NationalResearch Foundation of SouthAfrica, South Africa; Cen- tro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía,Cuba,Ministeriode CienciaeInnovacion andCentro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT),Spain; Swedish Research Council (VR) and Knut& Al- iceWallenbergFoundation(KAW),Sweden;EuropeanOrganization forNuclear Research, Switzerland; NationalScience andTechnol- ogyDevelopment Agency (NSDTA), Suranaree University ofTech- nology(SUT)andOfficeoftheHigherEducationCommissionunder NRUprojectofThailand,Thailand;TurkishAtomic EnergyAgency (TAEK),Turkey;NationalAcademyofSciencesofUkraine,Ukraine;

ScienceandTechnologyFacilitiesCouncil(STFC),UnitedKingdom;

NationalScienceFoundationoftheUnitedStatesofAmerica(NSF)

andUnitedStatesDepartmentofEnergy,OfficeofNuclearPhysics (DOENP),UnitedStatesofAmerica.

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