Study of Net-Baryon Higher Moments in the PNJL Model at RHIC Energies for the Signature of the QCD Critical Point

We study the effect of the QCD critical point on the higher moments and their system-volume-independent products of net-baryon in the finite volume Polyakov loop extended Nambu-Jona-Lasinio (PNJL) model with six and eight quark interactions. The study has been performed at energies similar to RHIC beam energy scan (BES) energies. The non-monotonic behaviour of a number of fluctuation observables as a function of the collision energy can be used in heavy-ion collision studies to determine the QCD critical point. The event-by-event particle multiplicity fluctuations can be characterised by the moments of the event-by-event multiplicity distributions. The increase and divergence of fluctuations are the fundamental characteristics of a critical point. The hadronic and QGP phases exhibit distinctly different levels of fluctuations in conserved quantities like net-baryon, net-charge, and net-kaon at finite temperatures. Due to experimental restrictions, it is challenging to measure conserved quantities; consequently, net-proton, net-pion, and net-kaon are measured as a substitute for ( \(\Delta {B}, \Delta {Q}, \Delta {S}\) ). Thus, several models are needed to calculate the values of various observables. The Polyakov loop enhanced Nambu-Jona-Lasinio (PNJL) model of QCD is a particularly successful model because it benefits from having properties that are similar to the observables. Results have been compared with the HRG model and available STAR experimental data on net proton.