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

TL;DR

This study applies finite-size scaling to net-baryon cumulant ratios from heavy-ion collisions to locate the QCD critical end point, revealing universal critical behavior consistent with 3D Ising class.

Contribution

It introduces a finite-size scaling analysis of cumulant ratios to identify the QCD critical end point in heavy-ion collision data, demonstrating universality and critical behavior.

Findings

Collapse of data onto universal scaling functions across energies and centralities.

Indication of a critical end point at approximately 33 GeV collision energy.

Evidence of 3D Ising critical behavior in cumulant ratio divergence patterns.

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 $\sqrt{s}_{\rm CEP}\approx33.0$~GeV, corresponding to $\mu_{B,\rm CEP}\approx130$~MeV and $T_{\rm CEP}\approx158.5$~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.