Continuous description of fluctuating eccentricities

TL;DR

This paper models the initial energy density fluctuations in high-energy nucleus collisions as a local Gaussian random field, deriving model-independent expressions for eccentricities relevant to anisotropic flow, and showing short wavelength fluctuations are negligible.

Contribution

It introduces a Gaussian random field model for initial energy density fluctuations, providing general formulas for eccentricities and their variances that are model-independent.

Findings

Eccentricities depend solely on the 2-point function and average density.

Short wavelength fluctuations do not affect eccentricities, only renormalize the 2-point function.

The model reproduces known results from independent source models.

Abstract

We consider the initial energy density in the transverse plane of a high energy nucleus-nucleus collision as a random field $\rho(\x)$, whose probability distribution $P[\rho]$, the only ingredient of the present description, encodes all possible sources of fluctuations. We argue that it is a local Gaussian, with a short-range 2-point function, and that the fluctuations relevant for the calculation of the eccentricities that drive the anisotropic flow have small relative amplitudes. In fact, this 2-point function, together with the average density, contains all the information needed to calculate the eccentricities and their variances, and we derive general model independent expressions for these quantities. The short wavelength fluctuations are shown to play no role in these calculations, except for a renormalization of the short range part of the 2-point function. As an illustration, we compare to a commonly used model of independent sources, and recover the known results of this model.