Decomposition of multi-particle azimuthal correlations in Q-cumulant analysis*

Abstract

he method of Q-cumulants is a powerful tool for studying the fine details of azimuthal anisotropies in high energy nuclear collisions. This paper presents a new method, based on mathematical induction, to evaluate the analytical form of high-order Q-cumulants. The capability of this method is demonstrated via a toy model that uses the elliptic power distribution to simulate the anisotropic emission of particles, quantified in terms of Fourier flow harmonics . The method can help in studying the large amount of event statistics that can be collected in the future and allow measurements of the very high central moments of the distribution. This can, in turn, facilitate progress in understanding the initial geometry, the input to the hydrodynamic calculations of medium expansion in high energy nuclear collisions, and the constraints on it.