QCD phase diagram and critical exponents within the nonextensive Polyakov-Nambu-Jona-Lasinio model

TL;DR

This paper introduces a nonextensive version of the Polyakov-Nambu-Jona-Lasinio model to study QCD phase transitions, revealing how nonextensive effects influence the critical end point's location and critical exponents.

Contribution

It develops a nonextensive extension of the PNJL model and analyzes the impact of nonextensivity on the QCD phase diagram and critical phenomena.

Findings

CEP shifts with nonextensivity parameter q

Critical exponents remain nearly constant with q

CEP position moves in opposite directions beyond a critical q

Abstract

We present a nonextensive version of the Polyakov-Nambu-Jona-Lasinio model which is based on the nonextentive statistical mechanics. This new statistics is characterized by a dimensionless nonextensivity parameter $q$ that accounts for all possible effects violating the assumptions of the Boltzmann-Gibbs (BG) statistics (when $q\rightarrow1$, it returns to the BG case). Based on the nonextensive Polyakov-Nambu-Jona-Lasinio model, we discussed the influence of the nonextensive effects on the QCD phase transition, especially on the location of the critical end point (CEP). A new and interesting phenomenon we found is that with the increase of $q$, the CEP position initially shifted toward the direction of larger chemical potential and lower temperature. But then, when $q$ is greater than a critical value $q_{c}$, the CEP position moves in the opposite direction. In other words, as $q$ increases, the CEP position moves in the direction of smaller chemical potential and higher temperature. In addition, we calculated the influence of the nonextensive effects on the critical exponents and found that they remain almost constant with $q$.