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

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 $\sqrt{{\mathrm{s}}_{\mathrm{NN}}}$ = 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.

13 pages, 4 figures

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• Conserved charge fluctuations are not conserved during the hadronic phase
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• Effect of finite particle number sampling on baryon number fluctuations
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• Experimental results on charge fluctuations in heavy-ion collisions
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• A Study of Fluctuations of Voids in Relativistic Ion-Ion Collisions
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