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

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 ext{--}200, ext{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}_{ ext{CEP}} approx 33.0, ext{GeV} ), corresponding to ( mu_{B, ext{CEP}} approx 130, ext{MeV} ) and ( T_{ ext{CEP}} approx 158.5, ext{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.