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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 $σ$, skewness $S$ and kurtosis $κ$ 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 $Sσ$ and $κσ^2 $, which are directly related to the hgher-order baryon number susceptibility ratios $χ^{(3)}_B/χ^{(2)}_B$ and $χ^{(4)}_B/χ^{(2)}_B$, 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 ($T,μ_B$) of the QCD phase diagram. The resulting scaling functions validate the earlier estimates of $T^{\text{cep}} \sim 165$ MeV and $μ_B^{\text{cep}} \sim 95$ MeV for the location of the CEP, and the critical exponents used to assign its 3D Ising model universality class.