# Chiral Phase Transition in Linear Sigma Model with Nonextensive Statistical Mechanics

Zhang, Ben-Wei  (Key Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China) ; Shen, Ke-Ming (Key Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China) ; Zhang, Hui (Key Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China) ; Hou, De-Fu  (Key Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China) ; Wang, En-Ke (Key Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China)

29 November 2017

Abstract: From the nonextensive statistical mechanics, we investigate the chiral phase transition at finite temperature $T$ and baryon chemical potential ${\mu }_{B}$ in the framework of the linear sigma model. The corresponding nonextensive distribution, based on Tsallis’ statistics, is characterized by a dimensionless nonextensive parameter, $q$ , and the results in the usual Boltzmann-Gibbs case are recovered when $q\to \mathrm{1}$ . The thermodynamics of the linear sigma model and its corresponding phase diagram are analysed. At high temperature region, the critical temperature ${T}_{c}$ is shown to decrease with increasing $q$ from the phase diagram in the $\left(T,\mu \right)$ plane. However, larger values of $q$ cause the rise of ${T}_{c}$ at low temperature but high chemical potential. Moreover, it is found that $\mu$ different from zero corresponds to a first-order phase transition while $\mu =\mathrm{0}$ to a crossover one. The critical endpoint (CEP) carries higher chemical potential but lower temperature with $q$ increasing due to the nonextensive effects.

Published in: Advances in High Energy Physics 2017 (2017) 4135329