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 $Ssigma $ 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.