Event-by-event cumulants of azimuthal angles

TL;DR

This paper refines the mathematical framework for event-by-event cumulants of azimuthal angles, emphasizing symmetry considerations and deriving universal solutions for combinatorial backgrounds in multiparticle correlations.

Contribution

It introduces a new event-by-event definition of cumulants, preserves their properties, and derives analytic solutions for combinatorial backgrounds in azimuthal correlation measurements.

Findings

Event-by-event cumulants preserve mathematical properties.

Universal analytic solutions for combinatorial backgrounds.

New relations between multiparticle correlators and flow parameters.

Abstract

We develop further the recently proposed event-by-event cumulants of azimuthal angles. The role of reflection symmetry, permutation symmetry, frame independence, and relabeling of particle indices in the cumulant expansion is discussed in detail. We argue that mathematical and statistical properties of cumulants are preserved if cumulants of azimuthal angles are defined event-by-event in terms of single-event averages of azimuthal angles, while they are violated in the traditional approach in which cumulants are defined in terms of all-event averages. We derive for the first time the example analytic solutions for the contribution of combinatorial background in the measured 2- and 3-particle correlations. We demonstrate that these solutions for the combinatorial background are universal as they can be written generically in terms of multiplicity-dependent combinatorial weights and marginal probability density functions of starting multivariate distribution. The new general results between multiparticle azimuthal correlators and flow amplitudes and symmetry planes are presented.