Chiral phase transition within the linear sigma model in the Tsallis nonextensive statistics based on density operator

Abstract

We studied chiral phase transition in the linear sigma model within the Tsallis nonextensive statistics in the case of small deviation from the Boltzmann-Gibbs (BG) statistics. The statistics has two parameters: the temperature T and the entropic parameter q. The normalized q-expectation value and the physical temperature T ph were employed in this study. The normalized q-expectation value was expanded as a series of the value (1 − q), where the absolute value |1 − q| is the measure of the deviation from the BG statistics. We applied the Hartree factorization and the free particle approximation, and obtained the equations for the condensate, the sigma mass, and the pion mass. The physical temperature dependences of these quantities were obtained numerically. We found following facts. The condensate at q is smaller than that at q ′ for q > q ′ . The sigma mass at q is lighter than that at q ′ for q > q ′ at low physical temperature, and the sigma mass at q is heavier than that at q ′ for q > q ′ at high physical temperature. The pion mass at q is heavier than that at q ′ for q > q ′ . The difference between the pion masses at different values of q is small for T ph ≤ 200 MeV. That is to say, the condensate and the sigma mass are affected by the Tsallis nonextensive statistics of small |1 − q|, and the pion mass is also affected by the statistics of small |1 − q| except for T ph ≤ 200 MeV.

Non-extensive effects on the QCD equation of state and fluctuations of conserved charges within Polyakov quark meson model

“…To address the limitations of lattice QCD calculations in dealing with non-extensive Tsallis statistics, researchers utilize various effective models to explore the phase diagram of QCD theoretically. These models include chiral perturbation theory [37], Dyson-Schwinger equations (DSEs) [38][39][40], based on density operator [14], hadron resonance gas and statistical models [41,42], Nambu-Jona-Lasinio model and the Polyakov Nambu-Jona-Lasinio (PNJL) model [18,20,[43][44][45], linear sigma model and Polyakov linear sigma model [46][47][48].…”