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

Abstract: The method of Q-cumulants is a powerful tool to study 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 the high-order Q-cumulants. The ability of this method is demonstrated via a toy model that uses the elliptic power distribution to simulate anisotropic emission of particles, quantified in terms of Fourier flow harmonics v_{n}. The method can help in studying the large amount of event statistics that can be collected in the future, and to allow measurements of very high central moments of the v_{2} distribution. This can in turn facilitate progress in understanding the initial geometry, input to hydrodynamic calculations of medium expansion in high energy nuclear collisions, as well as constraints on it.