Probing the QCD Critical End Point with Finite-Size Scaling of Net-Baryon Cumulant Ratios

Abstract

Finite-size scaling (FSS) is applied to net-baryon cumulant ratios $C_2/C_1$, $C_3/C_2$, $C_4/C_2$, $C_3/C_1$, and $C_4/C_1$ measured in Au+Au collisions over the Beam Energy Scan Phase~I range $\sqrt{s_{NN}}=7.7$--$200$~GeV to constrain the location and universality class of the QCD critical end point (CEP). Although finite-size and finite-time effects suppress non-monotonic signatures in unscaled data, the FSS analysis reveals a collapse of measurements from different beam energies and centralities onto universal scaling functions. All cumulant ratios collapse under a single, common set of critical exponents and exhibit divergence patterns characteristic o 3D Ising critical behavior. The scaling results indicate a CEP at ${\sqrt{s}}_{\mathrm{CEP}}\approx 33.0$~GeV, corresponding to ${\mu }_{B,\mathrm{CEP}}\approx 130$~MeV and $T_{\mathrm{CEP}}\approx 158.5$~MeV. These findings demonstrate that finite-size scaling provides a robust, model-independent framework for accessing critical behavior in finite, dynamically evolving systems, where non-equilibrium baryon-number transport can enhance the experimental visibility of susceptibility-driven fluctuations without modifying the underlying universality class.

Comments: 7 pages 4 Figs. Submitted for publication