Higher Moments of Net Proton Multiplicity Distributions at RHIC

We report the first measurements of the kurtosis ($\kappa$), skewness ($S$), and variance (${\sigma }^2$) of net-proton multiplicity ($N_p-N_{\overline{p}}$) distributions at midrapidity for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=19.6$, 62.4, and 200 GeV corresponding to baryon chemical potentials (${\mu }_B$) between 200 and 20 MeV. Our measurements of the products $\kappa {\sigma }^2$ and $S\sigma$, which can be related to theoretical calculations sensitive to baryon number susceptibilities and long-range correlations, are constant as functions of collision centrality. We compare these products with results from lattice QCD and various models without a critical point and study the $\sqrt{s_{NN}}$ dependence of $\kappa {\sigma }^2$. From the measurements at the three beam energies, we find no evidence for a critical point in the QCD phase diagram for ${\mu }_B$ below 200 MeV.

Figure 1

$\Delta N_p$ multiplicity distribution in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$ for various collision centralities at midrapidity ($\left|y\right|<0.5$). The statistical errors are shown.

Figure 2

Centrality dependence of moments of $\Delta N_p$ distributions for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=19.6$, 62.4, and 200 GeV. The lines are the expected values from the central limit theorem. Error bars are statistical and caps are systematic errors.

Figure 3

Centrality dependence of (a) $S\sigma$ and (b) $\kappa {\sigma }^2$ for $\Delta N_p$ in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=19.6$, 62.4, and 200 GeV compared to various model calculations. The shaded band for $S\sigma$ and $\kappa {\sigma }^2$ reflects contributions from the detector effects. (c) shows the model expectations for $\kappa {\sigma }^2$ from various physical effects in $\mathrm{Au}+\mathrm{Au}$ collisions at 200 GeV. The lattice QCD results are for net baryons corresponding to central collisions [6]. See text for more details.

Figure 4

$\sqrt{s_{NN}}$ dependence of $\kappa {\sigma }^2$ for net-proton distributions measured at RHIC. The results are compared to non-CP model calculations (slightly shifted in $\sqrt{s_{NN}}$). The left-right arrow at the bottom indicates the energy range for the CP search at RHIC.