Beam Energy Dependence of Moments of the Net-Charge Multiplicity Distributions in $\mathrm{Au}+\mathrm{Au}$ Collisions at RHIC

We report the first measurements of the moments—mean ($M$), variance (${\sigma }^2$), skewness ($S$), and kurtosis ($\kappa$)—of the net-charge multiplicity distributions at midrapidity in $\mathrm{Au}+\mathrm{Au}$ collisions at seven energies, ranging from $\sqrt{s_{\mathit{\text{NN}}}}=7.7$ to 200 GeV, as a part of the Beam Energy Scan program at RHIC. The moments are related to the thermodynamic susceptibilities of net charge, and are sensitive to the location of the QCD critical point. We compare the products of the moments, ${\sigma }^2/M$, $S\sigma$, and $\kappa {\sigma }^2$, with the expectations from Poisson and negative binomial distributions (NBDs). The $S\sigma$ values deviate from the Poisson baseline and are close to the NBD baseline, while the $\kappa {\sigma }^2$ values tend to lie between the two. Within the present uncertainties, our data do not show nonmonotonic behavior as a function of collision energy. These measurements provide a valuable tool to extract the freeze-out parameters in heavy-ion collisions by comparing with theoretical models.

Figure 1

The efficiency and centrality bin width corrected (a) mean, (b) standard deviation, (c) skewness, and (d) kurtosis of the net-charge multiplicity distributions as a function of number of participating nucleons $⟨N_{\text{part}}⟩$ for $\mathrm{Au}+\mathrm{Au}$ collisions. The dotted lines represent calculations from the central limit theorem. The error bars are statistical and systematic errors are within the symbol sizes.

Figure 2

Centrality dependence of $S\sigma$ in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{\text{NN}}}}=7.7$ to 200 GeV. The results are efficiency and centrality bin width corrected. Results from the Poisson and NBD baselines are superimposed. The error bars are statistical and the caps represent systematic errors.

Figure 3

Centrality dependence of $\kappa {\sigma }^2$ in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{\text{NN}}}}=7.7$ to 200 GeV. The results are efficiency and centrality bin width corrected. Results from the Poisson and NBD baselines are superimposed. The error bars are statistical and the caps represent systematic errors.

Figure 4

Beam-energy dependence of (a) ${\sigma }^2/M$, (b) $S\sigma$, and (c) $\kappa {\sigma }^2$, after all corrections, for most central (0%–5%) and peripheral (70–80%) bins. The error bars are statistical and the caps represent systematic errors. Results from the Poisson and NBD baselines are superimposed. The values of $\kappa {\sigma }^2$ for the Poisson baseline are always unity.