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

Abstract: The search for the Quantum Chromodynamics (QCD) critical end point (CEP) is a central objective in heavy-ion physics, offering key insights into the phase structure of strongly interacting matter under extreme conditions. In this study, finite-size scaling (FSS) analysis is applied to 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 across the Beam Energy Scan (BES-I) range of ( \sqrt{s_{NN}} = 7.7\text{--}200\,\text{GeV} ). The observed scaling behavior reflects the influence of finite-size and finite-time effects, which suppress raw non-monotonic signals and render background-subtraction-based approaches to critical point identification severely unreliable. The scaling functions yield a CEP location at ( \sqrt{s}{\text{CEP}} \approx 33.0\,\text{GeV} ), corresponding to ( \mu{B,\text{CEP}} \approx 130\,\text{MeV} ) and ( T_{\text{CEP}} \approx 158.5\,\text{MeV} ) based on empirical freeze-out parametrizations. Distinct divergence patterns -- upward for ( C_2/C_1 ) and ( C_4/C_1 ), and downward for ( C_3/C_1 ), ( C_3/C_2 ), and ( C_4/C_2 ) -- align with predictions from the 3D Ising universality class. These results demonstrate the sensitivity of cumulant ratios as robust, model-independent probes of critical behavior and support the identification of the CEP's location and universality class.