Higher order moments of multiparticle azimuthal correlations

TL;DR

This paper develops an analytical framework for deriving probability density functions and higher order moments of multiparticle azimuthal correlations, crucial for understanding anisotropic flow in particle physics.

Contribution

It introduces a general method to analytically express multiparticle azimuthal correlators using Q-vectors and Chebyshev polynomials, advancing the theoretical understanding of flow measurements.

Findings

Derived analytic p.d.f.'s for Q-vectors using Chebyshev polynomials

Calculated higher order moments of azimuthal correlators

Provided insights into the sensitivity of flow measurements

Abstract

We introduce a general procedure to pave the road towards the ultimate goal of deriving analytic expressions for the probability density functions (p.d.f.'s) of multiparticle azimuthal correlations. All multiparticle azimuthal correlators can be expressed analytically in terms of the real and imaginary parts of $M$-particle $Q$-vectors. We derive the analytic results for the p.d.f.'s of single-particle $Q$-vectors in the most general case and demonstrate that they can be expressed solely in terms of Chebyshev polynomials of the first kind. This leads analytically to the expressions of the characteristic functions of $M$-particle $Q$-vectors in terms of Bessel functions of the first kind. From the obtained characteristics functions we calculate the higher order moments of the real and imaginary parts of $M$-particle $Q$-vectors and use them to obtain the higher order moments of multiparticle azimuthal correlators. Finally, these results are used to investigate the sensitivity of multiparticle azimuthal correlations and to illuminate requirements necessary for future anisotropic flow measurements.