Finite-Size Scaling of Non-Gaussian Fluctuations Near the QCD Critical Point

An effective Finite-Size Scaling (FSS) of moment products from recent STAR measurements of the variance $\sigma$, skewness $S$ and kurtosis $\kappa$ of net-proton multiplicity distributions, are reported for a broad range of collision centralities in Au+Au ($\sqrt{s_{NN}}= 7.7 - 200$ GeV) collisions. The products $S\sigma $ and $\kappa \sigma^2 $, which are directly related to the hgher-order baryon number susceptibility ratios $\chi^{(3)}_B/\chi^{(2)}_B$ and $\chi^{(4)}_B/\chi^{(2)}_B$, show scaling patterns consistent with earlier indications for a second order phase transition at a critical end point (CEP) in the plane of temperature vs. baryon chemical potential ($T,\mu_B$) of the QCD phase diagram. The resulting scaling functions validate the earlier estimates of $T^{\text{cep}} \sim 165$ MeV and $\mu_B^{\text{cep}} \sim 95$ MeV for the location of the CEP, and the critical exponents used to assign its 3D Ising model universality class.