Systematic Analysis of Flow Distributions

TL;DR

This paper introduces a generalized method using Gram-Charlier series to analyze flow harmonic distributions and proposes new cumulants for better understanding event-by-event fluctuations in heavy-ion collisions.

Contribution

It develops a generalized distribution framework and new cumulants, enhancing the analysis of flow fluctuations beyond existing methods.

Findings

Flow distributions are better described by the Gram-Charlier series with a normal kernel.

New cumulants $j_n extbackslash{}{2k}$ provide more information on fluctuations.

Joint distributions and cumulants explain experimental data on flow correlations.

Abstract

The information of the event-by-event fluctuations is extracted from flow harmonic distributions and cumulants, which can be done experimentally. In this work, we employ the standard method of Gram-Charlier series with the normal kernel to find such distribution, which is the generalization of recently introduced flow distributions for the studies of the event-by-event fluctuations. Also, we introduce a new set of cumulants $j_n\{2k\}$ which have more information about the fluctuations compared with other known cumulants. The experimental data imply that not only all of the information about the event-by-event fluctuations of collision zone properties and different stages of the heavy-ion process are not encoded in the radial flow distribution $p(v_n)$, but also the observables describing harmonic flows can generally be given by the joint distribution $\mathcal{P}(v_1,v_2,...)$. In such a way, we first introduce a set of joint cumulants $\mathcal{K}_{nm}$, and then we find the flow joint distribution using these joint cumulants. Finally, we show that the Symmetric Cumulants $SC(2,3)$ and $SC(2,4)$ obtained from ALICE data are explained by the combinations $\mathcal{K}_{22}+\frac{1}{2}\mathcal{K}_{04}-\mathcal{K}_{31}$ and $\mathcal{K}_{22}+4\mathcal{K}_{11}^2$.