Fluctuations of the number of participants and binary collisions in AA interactions at fixed centrality in the Glauber approach

TL;DR

This paper derives analytical formulas for fluctuations in the number of participants and binary collisions in nucleus-nucleus interactions using the Glauber model, highlighting additional contact terms that significantly affect variances.

Contribution

It introduces new analytical expressions accounting for contact terms in the Glauber approach, improving understanding of fluctuations in AA collisions at fixed centrality.

Findings

Additional contact terms significantly increase variance estimates.

Analytical results agree with Monte Carlo simulations.

Variance of participants and collisions can exceed Poisson expectations.

Abstract

In the framework of the classical Glauber approach, the analytical expressions for the variance of the number of wounded nucleons and binary collisions in AA interactions at a given centrality are presented. Along with the optical approximation term, they contain additional contact terms arising only in the case of nucleus-nucleus collisions. The magnitude of the additional contributions, e.g., for PbPb collisions at SPS energies, is larger than the contribution of the optical approximation at some values of the impact parameter. The sum of the additional contributions is in good agreement with the results of independent Monte Carlo simulations of this process. Due to these additional terms, the variance of the total number of participants for peripheral PbPb collisions and the variance of the number of collisions at all values of the impact parameter exceed several multiples of the Poisson variances. The correlator between the numbers of participants in colliding nuclei at fixed centrality is also analytically calculated.