# Nonextensive effects on QCD chiral phase diagram and baryon-number fluctuations within Polyakov-Nambu-Jona-Lasinio model

## TL;DR

This paper introduces a nonextensive statistical mechanics version of the PNJL model to study QCD phase transitions and baryon fluctuations, revealing non-monotonic CEP behavior and aligning with experimental data.

## Contribution

It develops a nonextensive PNJL model incorporating the parameter q, extending the traditional model to account for non-BG effects and analyzing their impact on the QCD phase diagram.

## Key findings

- CEP moves non-monotonically with q
- Results align with experimental data for q=1.07
- Baryon fluctuation moments are consistent with observations

## Abstract

In this paper, a version of the Polyakov-Nambu-Jona-Lasinio (PNJL) model based on nonextensive statistical mechanics is presented. This new statistics summarizes all possible factors that violate the assumptions of the Boltzmann-Gibbs (BG) statistics to a dimensionless nonextensivity parameter $q$, and when $q$ tends to 1, it returns to the BG case. Within the nonextensive PNJL model, we found that as $q$ increases, the location of the critical end point (CEP) exhibits non-monotonic behavior. That is, for $q<1.15$, CEP moves in the direction of lower temperature and larger quark chemical potential. But for $q>1.15$, CEP turns to move in the direction of lower temperature and lower quark chemical potential. In addition, we studied the moments of the net-baryon number distribution, that is, the variance ($\sigma^{2}$), skewness (S), and kurtosis ($\kappa$). Our results are generally consistent with the latest experimental data, especially for $\sqrt{S_{NN}}>19.6\ \mathrm{GeV}$, when $q$ is set to $1.07$.