Moments of event observable distributions and many-body correlations

TL;DR

This paper explores how moments of event observable distributions relate to many-body correlations, clarifying the interpretation of the $\

Contribution

It introduces a framework connecting moments of distributions to multi-body correlations and clarifies the meaning of the $\

Findings

Moments of distributions are linked to multi-body correlations.

Zero $\

Zero $\

Abstract

We investigate event-by-event fluctuations for ensembles with non-fixed multiplicity. Moments of event observable distributions, like total energy distribution, total transverse momentum distribution, etc, are shown to be related to the multi-body correlations present in the system. For classical systems, these moments reduce in the absence of any correlations to the moments of particle inclusive momentum distribution. As a consequence, a zero value for the recently introduced $\Phi$-variable is shown to indicate the vanishing of two-body correlations from one part, and of correlations between multiplicity and momentum distributions from the other part. It is often misunderstood as a measure of the degree of equilibration in the system.