Event-by-event cumulants of azimuthal angles
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.
Keywords
Cite
@article{arxiv.2106.05760,
title = {Event-by-event cumulants of azimuthal angles},
author = {Ante Bilandzic},
journal= {arXiv preprint arXiv:2106.05760},
year = {2022}
}
Comments
15 pages, 5 figures. Prepared for "Offshell-2021" conference. This version was accepted for publication in EPJC. Most important change between v1 and v2: It was realized and acknowledged that analytic expressions in Eqs. (16) and (24) for combinatorial background can be further generalized - the generalization will be presented in the follow-up work