Influence of statistics on the measured moments of conserved quantities in relativistic heavy ion collisions

TL;DR

This paper investigates how statistical limitations affect the measurement of moments of conserved quantities in relativistic heavy ion collisions, emphasizing the importance of sufficient data for accurate results.

Contribution

It provides an analysis of statistical dependencies of measured moments and proposes methods to reliably estimate higher-order moments with planned experimental statistics.

Findings

Second and third order moments can be reliably measured with current statistics.

Fourth order moments are challenging to measure at low energies due to insufficient statistics.

Improved methods and future data will enable better understanding of energy and centrality dependence.

Abstract

We study statistics dependence of the probability distributions and the means of measured moments of conserved quantities, respectively. The required statistics of all interested moments and their products are estimated based on a simple simulation. We also explain why the measured moments are underestimated when the statistics are insufficient.With the statistics at RHIC/BES, the second and third order moments can be reliably obtained based on the method of Centrality bin width correction (CBWC), which can not be applied for the fourth order moments at low energy. With planning statistics at RHIC/BES II, and improved CBWC method, $\kappa\sigma^2$ in a finer centrality bin scale should be measurable. This will help us to understand the current observation of energy and centrality dependence of high-order moments.