Multi-particle long-range rapidity correlations from fluctuation of the fireball longitudinal shape

TL;DR

This paper develops a method to analyze genuine long-range multi-particle rapidity correlations in high-energy collisions, revealing information about the fluctuating shape of the particle-emitting fireball.

Contribution

It introduces a new approach using orthogonal polynomial expansion cumulants to isolate long-range correlations from short-range effects.

Findings

Derived explicit formulas for $C_n$ for n=3 to 6.

Showed suppression of short-range correlations in the analysis.

Provided a framework to extract fireball shape fluctuations from data.

Abstract

We calculate the genuine long-range multi-particle rapidity correlation functions, $C_{n}(y_1,...,y_n)$ for $n=3,4,5,6$, originating from fluctuations of the fireball longitudinal shape. In these correlation functions any contribution from the short-range two-particle correlations, and in general up to $(n-1)$-particle in $C_n$, is suppressed. The information about the fluctuating fireball shape in rapidity is encoded in the cumulants of coefficients of the orthogonal polynomial expansion of particle distributions in rapidity.