Net-Charge Fluctuations in Finite Volume PNJL Model: A Probe for the QCD Critical Point

The QCD Critical Point is a pivotal feature of the phase diagram of strongly interacting matter. Signatures of the critical point are expected to manifest through the non-monotonic behavior of higher-order moments of conserved quantities, such as net-baryon ($\Delta B$), net-charge ($\Delta Q$), and net-strangeness ($\Delta S$), as a function of collision energy. These moments are connected to the thermodynamic susceptibilities, as well as to the correlation length developed in the system, which diverges at the critical point. The non-monotonic behavior of higher-order moments and their volume-independent products near the critical region supports the presence of a critical point in a finite system existing for a finite time, due to their sensitivity to critical fluctuations. These fluctuations are believed to provide key evidence in the search for the QCD Critical Point. We present the higher order moments, such as mean (M), variance $(\sigma^2)$, skewness (S), and kurtosis $(\kappa)$ and their volume-independent moment products $(M/\sigma^{2}, s\sigma, \kappa\sigma^{2})$ of net-charge multiplicity distributions in the three-flavor finite volume, finite density Polyakov loop enhanced Nambu-Jona-Lasinio (PNJL) model. The work has been performed at energies similar to RHIC BES energies from 7.7 GeV to 200 GeV, including 2.4 and 3 GeV in the present model. Our findings are compared with the STAR net-charge data at various collision energies to explore signals of the QCD critical point. Additionally, we contrast our results with predictions from the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model, the Hadron Resonance Gas (HRG) model, and available lattice QCD data. The present results offer a useful tool for extracting the freeze-out parameters in the heavy-ion collision by comparing them with the STAR net-charge result and other net-charge theoretical models.