# Relating eccentricity fluctuations to density fluctuations in heavy-ion collisions

## TL;DR

This paper explores how fluctuations in the shape of the energy density field after heavy-ion collisions relate to density fluctuations, providing generalized formulas applicable beyond central collisions and point-like sources.

## Contribution

It derives generalized expressions linking eccentricity fluctuations to density correlations, extending previous results to non-central collisions and realistic source models.

## Key findings

- Derived formulas for mean and variance of eccentricities in terms of density correlations
- Applied these formulas within the color glass condensate framework
- Extended previous models to more general collision scenarios

## Abstract

The magnitude of anisotropic flow in a nucleus-nucleus collision is determined by the energy density field, $\rho(x,y,z)$, created right after the collision occurs. Specifically, elliptic flow, $v_2$, and triangular flow, $v_3$, are proportional to the anisotropy coefficients $\varepsilon_2$ and $\varepsilon_3$, which are functionals of $\rho$. We express the mean and the variance of $\varepsilon_2$ and $\varepsilon_3$ as a function of the 1- and 2-point functions of $\rho$. These results generalize results obtained previously, that were valid only for central collisions, or only for identical point-like sources. We apply them to the color glass condensate effective theory, using the recently derived expression of the 2-point function.