Baselines for Abelian Charge Fluctuations in Nuclear Collisions:Theory and Comparison with Experimental Data

TL;DR

This paper develops a theoretical framework for analyzing charge fluctuations in nuclear collisions, deriving analytical expressions for cumulants, and compares these with experimental data to highlight the importance of multi-particle interactions.

Contribution

It introduces a comprehensive analytical approach to cumulants of baryon number fluctuations, including local interactions, and demonstrates their relevance in experimental data analysis.

Findings

Multiparticle interactions are crucial for matching experimental fluctuation data.

Repulsive two-proton interactions explain high-energy fluctuation patterns.

Attractive three-particle interactions are needed at lower energies.

Abstract

We investigate fluctuations in the canonical ensemble of an Abelian charge, such as baryon number. Our focus is on cumulants and factorial cumulants of baryon and antibaryon multiplicity distributions, including their sum and difference, in both the full phase space and subsystems. In particular, we establish a correlation between net-baryon number fluctuations within a subsystem, which is pertinent for fluctuation analyses in nucleus-nucleus collisions, and fluctuations of baryon and antibaryon numbers in the total system. We derive analytical expressions for factorial cumulants of arbitrary order and present concise results in terms of the cumulants of the total baryon number. To account for dynamics beyond global conservation, we introduce local attractive and repulsive multi-particle interactions within a phenomenological framework. A comparison of calculated and generated cumulants with STAR and HADES data indicates that multiparticle interactions play a decisive role in the description of observed fluctuation patterns. At high collision energies, the data are well-reproduced by incorporating repulsive two-proton interactions, while at lower energies, attractive three-particle interactions become essential. Furthermore, our framework facilitates realistic event generation, enabling a direct comparison with experimental measurements.