The Im portance ofC orrelations and Fluctuations on the InitialSource Eccentricity in H igh-Energy N ucleus{N ucleus C ollisions

In relativisticheavy-ioncollisions,anisotropiccollectiveow isdriven,eventbyevent,bytheinitial eccentricity ofthem attercreated in thenuclearoverlap zone.Interpretation oftheanisotropicow data thusrequiresa detailed understanding ofthe eective initialsource eccentricity ofthe event sam ple. In this paper,we investigate various ways ofdening this eective eccentricity using the M onte Carlo G lauber (M CG ) approach. In particular, we exam ine the participant eccentricity, which quantiesthe eccentricity ofthe initialsource shape by the m ajoraxesoftheellipse form ed by the interaction points ofthe participating nucleons. W e show thatreasonable variation ofthe density param eters in the G lauber calculation,as wellas variations in how m atter production is m odeled,do notsignicantly m odify thealready established behavioroftheparticipanteccentricity asa function ofcollision centrality.Focusing on event-by-eventuctuationsand correlationsofthe distributionsofparticipating nucleonswedem onstratethat,depending on theachieved event-plane resolution,uctuationsin theellipticow m agnitude v2 lead to m ostm easurem entsbeing sensitive to the root-m ean-square, rather than the m ean of the v2 distribution. Neglecting correlations am ong participants,we derive analyticalexpressions for the participant eccentricity cum ulants as a function ofthe num berofparticipating nucleons, Npart,keeping non-negligible contributionsup to O ` 1=N 3 part ´ .W end thatthederived expressionsyield thesam eresultsasobtained from m ixed- eventM CG calculationswhich rem ovethecorrelationsstem m ing from thenuclearcollision process. M ostim portantly,we conclude from the com parison with M CG calculations thatthe fourth order participant eccentricity cum ulant does not approach the spatialanisotropy obtained assum ing a sm ooth nuclearm atterdistribution.In particular,fortheCu+ Cu system ,thesequantitiesdeviate from each other by alm ost a factor oftwo over a wide range in centrality. This deviation reects theessentialrole ofparticipantspatialcorrelationsin theinteraction oftwo nuclei. I. IN T R O D U C T IO N