Standardized Cumulants of Flow Harmonic Fluctuations

TL;DR

This paper models flow harmonic fluctuations in heavy ion collisions using standardized cumulants, introduces a new parametrization for $v_3$ distribution, and compares theoretical predictions with experimental data.

Contribution

It provides a novel parametrization of the $v_3$ distribution based on standardized cumulants and relates cumulants to multi-particle correlations, improving the modeling of flow fluctuations.

Findings

Standardized cumulants effectively characterize flow harmonic fluctuations.

The new $v_3$ distribution parametrization fits experimental data better than Gaussian.

Comparison shows consistency between simulation and experimental kurtosis values.

Abstract

The distribution of flow harmonics in heavy ion experiment can be characterized by standardized cumulants. We first model the ellipticity and power parameters of the elliptic-power distribution by employing MC-Glauber model. Then we use the elliptic-power distribution together with the hydrodynamic linear response approximation to study the two dimensional standardized cumulants of elliptic and triangular flow ($v_2$ and $v_3$) distribution. For the second harmonic, it turns out that finding two dimensional cumulants in terms of $2q$-particle correlation functions $c_2\{2q\}$ is limited to the skewness. We also show that $c_3\{2\}$, $c_3\{4\}$, and $c_3\{6\}$, are related to the second, fourth, and sixth standardized cumulants of the $v_3$ distribution, respectively. The cumulant $c_{n}\{2q\}$ can be also written in terms of $v_n\{2q\}$. Specifically, $-(v_3\{4\}/v_3\{2\})^4$ turns out to be the kurtosis of the $v_3$ event-by-event fluctuation distribution. We introduce a new parametrization for the distribution $p(v_3)$ with $v_3\{2\}$, kurtosis and sixth-order standardized cumulant being its free parameters. Compared to the Gaussian distribution, it indicates a more accurate fit with experimental results. Finally, we compare the kurtosis obtained from simulation with that of extracted from experimental data for the $v_3$ distribution.

Figures