Net-Strangeness Fluctuations and Their Experimental Implications in the SU(3) PNJL Model Using the Subensemble Acceptance Method for the search of QCD Critical Point

Abstract: The critical end point (CEP) is a key feature of the Quantum Chromodynamics (QCD) phase diagram, where critical phenomena cause higher-order moments of conserved charges net-baryon ($\Delta B$), net-charge ($\Delta Q$), and net-strangeness ($\Delta S$) to exhibit non-monotonic behavior. These moments and their volume-independent products are sensitive to the correlation length, making them crucial observables in the search for the CEP. In this study, we investigate net-strangeness fluctuations using the finite-volume Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model, incorporating six-quark and eight-quark interactions at energy scales relevant to the RHIC beam energy scan. Our results are compared to STAR net-kaon data and the Hadron Resonance Gas (HRG) model to assess the CEP's existence. Since direct measurement of conserved charges is experimentally challenging, net-proton, net-pion, and net-kaon are used as proxies for $\Delta B$, $\Delta Q$, and $\Delta S$. We employ the Subensemble Acceptance Method (SAM) to analyze the acceptance dependence of $\kappa\sigma^{2}$ for net-strangeness fluctuations. Our findings establish a direct mapping between the subvolume (particle fraction) and the total volume (conserved quantities), providing insights into the role of experimental acceptance in fluctuation measurements.