Study of net-baryon higher moments in PNJL model and their expectation for net-proton using the Subensemble Acceptance Method for the search of QCD critical point

Abstract: One of the most important parts of the QCD phase diagram of strongly interacting matter is the Critical End Point. The non-monotonic behavior of the conserved quantities like net-baryon ($\Delta B$), net-charge ($\Delta Q$), and net-strangeness ($\Delta S$) are believed to be the signatures of the QCD Critical End Point (CEP) as a function of the energy. We study the effect of the QCD critical point on moments of net-baryon in the Polyakov loop enhanced Nambu-Jona-Lasinio (PNJL) model of QCD with six quark and eight quark interactions. The study is performed at energies similar to RHIC beam energy scan (BES). Experimentally measuring conserved quantities is difficult due to systematic limitations, therefore net-proton, net-pion, and net-kaon are measured as the proxy of $\Delta B$, $\Delta Q$, and $\Delta S$. Thus the need for different models becomes predominant to estimate the value of different observables. Higher-order moments like skewness ($S$), kurtosis ($\kappa$), and their system volume independent products ($ M/\sigma^{2}, s\sigma$, $\kappa\sigma^{2}$) which are calculated in the PNJL model, are sensitive to the produced correlation length of the hot and dense medium, making them more prone to search for the critical point. Recent studies in the subensemble acceptance method (SAM) on the HRG model shows the dependency of the measure higher order moment on the experimental acceptance. We used SAM to analyze the behavior of $\kappa\sigma^{2}$ of net baryon distribution within the subvolume system for various acceptance fractions. These results can be directly mapped to the percentage of the subvolume (particle) of the total volume (conserved quantities). The results are compared to the STAR net-proton and proton data with different energies to understand the existence of critical point. For reference, results are also compared with the theoretical UrQMD and HRG models.