Chiral phase transition in the linear sigma model within Hartree factorization in the Tsallis nonextensive statistics

TL;DR

This paper investigates how small deviations from Boltzmann-Gibbs statistics, modeled by Tsallis nonextensive statistics, influence the chiral phase transition in the linear sigma model, revealing parameter-dependent effects on condensate and meson masses.

Contribution

It introduces a novel analysis of the chiral phase transition within Tsallis nonextensive statistics using Hartree factorization, highlighting the impact of the entropic parameter q on physical quantities.

Findings

Condensate decreases with increasing q.

Sigma mass varies with q and temperature, being lighter at low T and heavier at high T for larger q.

Pion mass slightly affected by q, especially above 200 MeV.

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 $\Tph$ 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 $\Tph \le 200$ 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 $\Tph \le 200$ MeV.