Methods for analysis of two-particle rapidity correlation function in high-energy heavy-ion collisions

TL;DR

This paper develops methods to accurately analyze two-particle rapidity correlations in high-energy heavy-ion collisions by removing centrality span effects, using probability ratios and relative multiplicity, validated with models.

Contribution

It introduces two novel calculation methods to eliminate centrality span influence in rapidity correlation analysis, improving accuracy over traditional approaches.

Findings

Methods effectively remove centrality span effects

Validated using AMPT model simulations

Enhanced understanding of particle density fluctuations

Abstract

Two-particle rapidity (or pseudorapidity) correlation function $C(y_1, y_2)$ was used in analysing fluctuation of particle density distribution in rapidity in high-energy heavy-ion collisions. In our research, we argue that for a centrality window, some additional correlation may be caused by a centrality span, when the mean two- and single-particle densities over a centrality window are used directly in the calculation , just like $\left<N(y_1, y_2) \right> / \left[\left<N(y_1)\right>\left<N(y_2)\right>\right]$. We concentrate on removing the influence of collision-centrality span on correlation function, and two calculation methods are raised. In one method, correlation coefficients are considered to be the ratios of probabilities (not the particle density). In the other method, a relative multiplicity is introduced to unity the events of different centralities. For testing the methods, {\sc ampt} model is used and a toy granular model is built to simulate the fluctuation of particle density in rapidity.