A Novel Approach to Fast Calculation of High-Order Q-Cumulants

TL;DR

This paper introduces a fast, efficient method for calculating high-order Q-cumulants in high-energy nucleus-nucleus collisions, enabling detailed analysis of azimuthal anisotropies and the properties of Quark-Gluon Plasma.

Contribution

A new computational approach significantly simplifies the calculation of high-order Q-cumulants, improving practicality over standard methods.

Findings

Validated with a toy model using elliptic power distribution

Allows analysis of higher-order moments of v2 distribution

Enables study of hydrodynamic behavior of Quark-Gluon Plasma

Abstract

The method of Q-cumulants has been shown as a powerful tool to study the fine details of the azimuthal anisotropies in high-energy nucleus-nucleus collisions. A new method for the fast calculation of arbitrary order Q-cumulant $v_{n}\{2k\}$ values, based on the partition of a non-negative integer l $\le$ m for calculation of the 2m-particle azimuthal correlations is presented in this paper. Unlike the standard Q-cumulants method in which the calculation of high-order multi-particle calculations is impractical, the newly proposed method enables easy calculation. The validity of the method is proven via a toy model that uses the elliptic power distribution to simulate anisotropic emission of particles. The method enables the study of fine details of the $v_{2}$ distribution, such as higher-order central moments of the $v_{2}$ distribution, as well as the hydrodynamic behavior of the Quark-Gluon Plasma.