Translation of collision geometry fluctuations into momentum anisotropies in relativistic heavy-ion collisions

Abstract

We develop a systematic framework for the study of the initial collision geometry fluctuations in relativistic heavy-ion collisions and investigate how they evolve through different stages of the fireball history and translate into final particle momentum anisotropies. We find in our event-by-event analysis that only the few lowest momentum anisotropy parameters survive after the hydrodynamical evolution of the system. The geometry of the produced medium is found to be affected by the preequilibrium evolution of the medium and the thermal smearing of the discretized event-by-event initial conditions, both of which tend to smear out the spatial anisotropies. We find such effects to be more prominent for higher moments than for lower moments. The correlations between odd and even spatial anisotropy parameters during the pre-equilibrium expansion are quantitatively studied and found to be small. Our study provides a theoretical foundation for the understanding of initial state fluctuations and the collective expansion dynamics in relativistic heavy-ion collisions.

Event-by-event shape and flow fluctuations of relativistic heavy-ion collision fireballs

“…The third and fifth order harmonics, which are entirely due to fluctuations (and whose associated angles ψ PP n are therefore completely uncorrelated to the reaction plane -see Ref. [20] and discussion below), show remarkably similar eccentricity values in the two initialization models, except for the most peripheral events. Comparing the viscous suppression of elliptic and triangular flow thus should allow to distinguish experimentally between the MC-Glauber and MC-KLN models [49].…”

“…Still, as first emphasized in [6], the calculated v 2 from single-shot hydrodynamics decreases steeply at large collision centralities [12,[42][43][44], due to the decreasing fireball lifetime, which contrasts with the initially reported experimentally observed behaviour [45,46], but agrees qualitatively with a recent reanalysis [47] where non-flow effects have been largely eliminated and/or corrected for. We do point out that our Monte-Carlo simulations do not include fluctuations in the amount of entropy generated per nucleon-nucleon collision [20]; these could have important effects on the ellipticities in very peripheral collisions.…”

“…Also, as in (1), the minus sign in Eqs. (17)- (20) guarantees that, for a Gaussian density distribution that has only n th -order eccentricity ε n , the angle ψ PP n points in the direction of the steepest density gradient, and thus in the direction of the corresponding hydrodynamically generated n th -order harmonic flow v n (see next subsection). It can be written as −1 = e −in(π/n) and amounts to a rotation of ψ PP n by π/n.…”

“…In addition, widely held beliefs as to which moments of the initial eccentricity distribution are directly related to which moments of the final flow distribution [17,21,26] must be tested by generating the final states hydrodyamically event by event, i.e. separately for each fluctuating initial condition [20,[27][28][29][30][31]. These are the goals addressed in the present article.…”

“…If one assumes that the elliptic flow is linearly proportional to the initial eccentricity, one can distribute the elliptic flow fluctuations around this average v 2 value in the same way as the initial eccentricity fluctuates around its average [17] and use this to predict flow fluctuations from eccentricity fluctuations [18]. This ignores, however, the recently discovered [19] fact that initial-state shape fluctuations of the collision region lead to eventby-event fluctuations not only of the elliptic deformation ε x , but simultaneously of all higher-order harmonic eccentricity coefficients [20,21], and that the simultaneous presence of several harmonic eccentricity coefficients can lead to hydrodynamic cross-talk between anisotropic flows of different harmonic order [20]. Without the possibility to hydrodynamically evolve fluctuating initial conditions event-by-event, the assumption of a linear dependence of v 2 on ε x can thus not be rigorously tested.…”