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.
Highlights
Flow measurements are correlation measurements and correlations can be present already in the initial conditions, or they can arise dynamically during the hydrodynamic evolution or during hadronization, respectively
They were sharpened subsequently due to work of Ollitrault and Yan [51] who established a related scaling for eccentricity cumulants at vanishing impact parameter in an analytically accessible model of independent point sources (IPSM) and who showed that this reproduces with good numerical accuracy the eccentricity cumulants in other currently used models of initial conditions
As a significant part of this paper will study in detail the independent point-sources model, we conclude this introduction by asking to what extent the spatial dependence of correlation functions in the IPSM can be expected to have physical significance
Summary
We discuss how flow measurements are related to the n-mode correlation functions of initial density perturbations that we are going to analyze in sections 3 and 4 below. With the help of the perturbative expansion (2.1), one can write flow cumulants as products of event averages of initial fluctuating modes wl(m) times dynamical response functions S(m1,...,mn)l1,...,ln. In the 3-flow correlators, the linear and non-linear dynamic response terms are weighted with a different set of informations about the initial conditions, namely a different set of moments wl(1m1) . This program is not yet carried out, and the initial conditions are currently regarded as the most significant source of uncertainties in the calculation of flow observables This motivates us to investigate in the following what can be said on the basis of general considerations about the structure of n-mode correlators wl(1m1) . This motivates us to investigate in the following what can be said on the basis of general considerations about the structure of n-mode correlators wl(1m1) . . . wl(nmn) ◦
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