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

Abstract

An effective Finite-Size Scaling (FSS) of moment products from recent STAR measurements of the variance $\ddot{I}ƒ$, skewness $S$ and kurtosis $\hat{I}º$ 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 $S\ddot{I}ƒ$ and $\hat{I}º\ddot{I}{ƒ}^2$, which are directly related to the hgher-order baryon number susceptibility ratios $\ddot{I}{‡}_B^{(3)}/\ddot{I}{‡}_B^{(2)}$ and $\ddot{I}{‡}_B^{(4)}/\ddot{I}{‡}_B^{(2)}$, 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 ($T,\hat{I}{¼}_B$) of the QCD phase diagram. The resulting scaling functions validate the earlier estimates of $T^{\text{cep}}\sim 165$ MeV and $\hat{I}{¼}_B^{\text{cep}}\sim 95$ MeV for the location of the CEP, and the critical exponents used to assign its 3D Ising model universality class.

5 pages, 3 figures, submitted for publication. Effective Finite-Size-Scaling procedure clarified in this version