QCD chiral phase transition and critical exponents within the nonextensive Polyakov-Nambu-Jona-Lasinio model * *Supported by the National Natural Science Foundation of China (12005192) and the Project funded by China Postdoctoral Science Foundation (2020M672255, 2020TQ0287)

Ya-Peng Zhao,Cheng-Ming Li,Shu-Yu Zuo

doi:10.1088/1674-1137/abf8a2

Abstract

We present a nonextensive version of the Polyakov-Nambu-Jona-Lasinio model that is based on nonextentive statistical mechanics. This new statistics model is characterized by a dimensionless nonextensivity parameter q that accounts for all possible effects violating the assumptions of the Boltzmann-Gibbs (BG) statistics (for , it returns to the BG case). Based on the nonextensive Polyakov-Nambu-Jona-Lasinio model, we discussed the influence of nonextensive effects on the curvature of the phase diagram at and especially on the location of the critical end point (CEP). A new and interesting phenomenon we found is that with an increase in q, the CEP position initially shifts toward the direction of larger chemical potential and lower temperature. However, when q is larger than a critical value , 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. This U-turn phenomenon may be important for the search of CEP in relativistic heavy-ion collisions, in which the validity of BG statistics is questionable due to strong fluctuations and long-range correlations, and nonextensive effects begin to manifest themselves. In addition, we calculated the influence of the nonextensive effects on the critical exponents and found that they remain almost constant with q.

Highlights

The QCD phase diagram, especially its critical end point (CEP), is one of the most important aspects of strongly interacting matter
In this paper, combined with the Tsallis statistics and the PNJL model, we investigated the sensitivity of the QCD phase transition and critical exponents to deviations from usual BG statistics
Regarding the QCD phase diagram, we found that the influence of the nonextensive effects on the CEP position shows a very interesting reentry phenomenon

Summary

INTRODUCTION

The QCD phase diagram, especially its critical end point (CEP), is one of the most important aspects of strongly interacting matter. People use various methods to study the QCD phase diagram Such as chiral perturbation theory [1], finite energy sum rules [2], Dyson-Schwinger equations [3,4,5], Nambu-Jona-Lasinio (NJL) model and Polyakov-Nambu-Jona-Lasinio (PNJL) [6,7,8,9,10]. In order to be as consistent as possible with the real experimental environment in which the QCD phase transition occurs, using Tsallis statistics is a better choice. Compared with NJL model, this model has proven to be more successful in reproducing lattice data concerning QCD thermodynamics [39] Other models such as the linear sigma model and NJL model have been generalized to its nonextensive version to study the thermodynamic quantities of the QCD matter and its phase diagram [13, 14].

PNJL model

QCD phase transition

SUMMARY AND CONCLUSION