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The critical endpoint (CEP) is a fundamental feature of the QuantumChromodynamics (QCD) phase diagram, marking the boundary between quark-gluonplasma and hadronic matter. Heavy-ion collision experiments, such as the RHICBeam Energy Scan, aim to probe the QCD phase diagram by varying collisionenergy. However, the short-lived nature of produced particles makes directmeasurements challenging, necessitating theoretical models. This study exploresthe impact of density fluctuations on the CEP using the Polyakov-loop enhancedNambu-Jona-Lasinio (PNJL) model, focusing on quark number densities in bothfinite and infinite volume systems. Quark number densities, derived fromthermodynamic susceptibilities, serve as reliable predictors for the CEP'slocation. We calculate density fluctuations and normalize them by $T^3$ asfunctions of temperature and $T/\mu_x$ (where x represents light quarks,strange quarks, and baryons), analyzing inflection points and maxima toestimate the critical region. To compare the experimental data, the study hasbeen performed at energies identical to those of the RHIC Beam Energy Scan. Theresults highlight the influence of finite volume effects on quark densityfluctuations, and key indicators of QCD phase transitions, and providequantitative comparisons with experimental data. This work enhances ourunderstanding of QCD phase structure and supports the ongoing search for theCEP in high-energy heavy-ion collisions, bridging theoretical predictions andexperimental observations.

Study of finite volume number density fluctuations in the SU(3) Polyakov  loop extended Nambu-Jona-Lasinio model for the search of the QCD Critical  Point