The sixth order cumulant of net-proton number in Binomial distribution at $\sqrt{s_{NN}} = $ 200 GeV

TL;DR

This paper investigates the sixth to second order cumulant ratio of net-proton numbers in Au+Au collisions at 200 GeV, using a Binomial distribution model to understand its behavior and compare with experimental data.

Contribution

It introduces a Binomial distribution-based baseline for net-proton cumulant ratios at RHIC energies, highlighting the potential for negative $C_6/C_2$ and differences from theoretical expectations.

Findings

$C_6/C_2$ can be negative in the Binomial distribution model.

Simulated $C_6/C_2$ decreases with experimental statistics.

Significant difference observed between simulation and theory in central collisions.

Abstract

It is proposed that ratios of the sixth order to the second order cumulant ($C_6/C_2$) of conserved quantities are sensitive to the chiral crossover transition. Recently, the negative $C_6/C_2$ was obtained both in theoretical Lattice QCD and experiments at $\sqrt{s_{NN}} = $ 200 GeV. In this study, we investigate the behavior of net-proton $C_6/C_2$ in statistical Binomial distribution (BD) at $\sqrt{s_{NN}} = $ 200 GeV in Au + Au collisions. With the BD parameters extracted from RHIC/STAR, it is found that $C_6/C_2$ can be negative. Furthermore, the obtained $C_6/C_2$ becomes smaller when applying the same magnitude of experimental statistics and calculation method to simulations. In 0-10\% centrality, there is a significant difference between the simulated result and theoretical expectation. Based on the extracted parameters and experimentally collected statistics, the baseline of net-proton $C_6/C_2$ in BD is presented.