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

Abstract

The critical endpoint (CEP) is a fundamental feature of the Quantum Chromodynamics (QCD) phase diagram, marking the boundary between quark-gluon plasma and hadronic matter. Heavy-ion collision experiments, such as the RHIC Beam Energy Scan, aim to probe the QCD phase diagram by varying collision energy. However, the short-lived nature of produced particles makes direct measurements challenging, necessitating theoretical models. This study explores the impact of density fluctuations on the CEP using the Polyakov-loop enhanced Nambu-Jona-Lasinio (PNJL) model, focusing on quark number densities in both finite and infinite volume systems. Quark number densities, derived from thermodynamic susceptibilities, serve as reliable predictors for the CEP's location. We calculate density fluctuations and normalize them by $T^3$ as functions of temperature and $T/\mu_x$ (where x represents light quarks, strange quarks, and baryons), analyzing inflection points and maxima to estimate the critical region. To compare the experimental data, the study has been performed at energies identical to those of the RHIC Beam Energy Scan. The results highlight the influence of finite volume effects on quark density fluctuations, and key indicators of QCD phase transitions, and provide quantitative comparisons with experimental data. This work enhances our understanding of QCD phase structure and supports the ongoing search for the CEP in high-energy heavy-ion collisions, bridging theoretical predictions and experimental observations.