First Study of the Negative Binomial Distribution Applied to Higher Moments of Net-charge and Net-proton Multiplicity Distributions

TL;DR

This study applies negative binomial and binomial distributions to analyze higher moments of net-charge and net-proton multiplicity distributions in heavy-ion collisions, aiming to identify signals of the QCD critical point.

Contribution

It is the first to use NBD/BD to describe higher moments of net-charge and net-proton distributions in nucleus-nucleus collisions.

Findings

NBD/BD effectively describes multiplicity distributions.

Differences from Poisson assumptions are explained by NBD/BD.

Proposed moments are sensitive probes for QCD critical point detection.

Abstract

A study of the first four moments (mean, variance, skewness, and kurtosis) and their products ($\kappa\sigma^{2}$ and $S\sigma$) of the net-charge and net-proton distributions in Au+Au collisions at $\sqrt{\rm s_{NN}}$ = 7.7-200 GeV from HIJING simulations has been carried out. The skewness and kurtosis and the collision volume independent products $\kappa\sigma^{2}$ and $S\sigma$ have been proposed as sensitive probes for identifying the presence of a QCD critical point. A discrete probability distribution that effectively describes the separate positively and negatively charged particle (or proton and anti-proton) multiplicity distributions is the negative binomial (or binomial) distribution (NBD/BD). The NBD/BD has been used to characterize particle production in high-energy particle and nuclear physics. Their application to the higher moments of the net-charge and net-proton distributions is examined. Differences between $\kappa\sigma^{2}$ and a statistical Poisson assumption of a factor of four (for net-charge) and 40% (for net-protons) can be accounted for by the NBD/BD. This is the first application of the properties of the NBD/BD to describe the behavior of the higher moments of net-charge and net-proton distributions in nucleus-nucleus collisions.