Statistics of initial density perturbations in heavy ion collisions and their fluid dynamic response

Abstract

An interesting opportunity to determine thermodynamic and transport properties in more detail is to identify generic statistical properties of initial density perturbations. Here we study event-by-event fluctuations in terms of correlation functions for two models that can be solved analytically. The first assumes Gaussian fluctuations around a distribution that is fixed by the collision geometry but leads to non-Gaussian features after averaging over the reaction plane orientation at non-zero impact parameter. In this context, we derive a three-parameter extension of the commonly used Bessel-Gaussian event-by-event distribution of harmonic flow coefficients. Secondly, we study a model of N independent point sources for which connected n-point correlation functions of initial perturbations scale like 1/N^(n-1). This scaling is violated for non-central collisions in a way that can be characterized by its impact parameter dependence. We discuss to what extent these are generic properties that can be expected to hold for any model of initial conditions, and how this can improve the fluid dynamical analysis of heavy ion collisions.

35 pages, 5 figures, published version

References in corpus (7)

• Glauber Modeling in High Energy Nuclear Collisions
• Correlations from hydrodynamic flow in p-Pb collisions
• GLISSANDO: GLauber Initial-State Simulation AND mOre
• Elliptic flow in the Gaussian model of eccentricity fluctuations
• Eccentricity fluctuations and elliptic flow at RHIC
• Collision Energy Dependence of Viscous Hydrodynamic Flow in Relativistic Heavy-Ion Collisions
• Elliptic flow fluctuations and correlations in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV

Cited by in corpus (12)

• Elliptic and triangular flow in p+Pb and peripheral Pb+Pb collisions from parton scatterings
• Viscous Effects on the Mapping of the Initial to Final State in Heavy Ion Collisions
• Event-shape fluctuations and flow correlations in ultra-relativistic heavy-ion collisions
• Continuous description of fluctuating eccentricities
• Statistical analysis of initial state and final state response in heavy-ion collisions
• Collective Expansion at the LHC: selected ALICE anisotropic flow measurements
• Nonlinear evolution of density and flow perturbations on a Bjorken background
• Quantification of the low-$p_{\mathrm{T}}$ pion excess in heavy-ion collisions at the LHC and top RHIC energy
• Mapping properties of the quark gluon plasma in Pb-Pb and Xe-Xe collisions at energies available at the CERN Large Hadron Collider
• Evidence of Coulomb liquid phase in few-electron droplets
• Statistical analysis of the fluctuations of an initial-state model with independently distributed hot spots
• Mode-by-mode evolution of Pb-Pb collisions at 5.02 TeV in a hybrid model