Chiral phase transitions in the linear sigma model in the Tsallis nonextensive statistics

TL;DR

This study investigates how the Tsallis nonextensive statistics affects chiral phase transitions within the linear sigma model, revealing that the critical temperature decreases with increasing q and that various particle masses and energy density are q-dependent.

Contribution

It introduces the application of Tsallis nonextensive statistics to the linear sigma model, analyzing the q-dependence of phase transition properties and particle masses.

Findings

Critical temperature decreases as q increases.

Condensate is smaller for q>1 compared to q=1.

Energy density increases significantly with q.

Abstract

We studied chiral phase transitions in the Tsallis nonextensive statistics which has two parameters, the temperature $T$ and entropic parameter $q$. The linear sigma model was used in this study. The critical temperature, condensate, masses, and energy density were calculated under the massless free particle approximation. The critical temperature decreases as $q$ increases. The condensate at $q>1$ is smaller than that at $q=1$. The sigma mass at $q>1$ is heavier than the mass at $q=1$ at high temperature, while the sigma mass at $q>1$ is lighter than the mass at $q=1$ at low temperature. The pion mass at $q>1$ is heavier than the mass at $q=1$. The energy density increases remarkably as $q$ increases. The $q$ dependence in the case of the $q$-expectation value is weaker than that in the case of the conventional expectation value with a Tsallis distribution. The parameter $q$ should be smaller than $4/3$ from energetic point of view. The validity of the Tsallis statistics can be determined by the difference in $q$ of the restriction for $5/4 < q < 4/3$ when the interaction is weak, because the parameter $q$ is smaller than $5/4$ in the case of the conventional expectation value with a Tsallis distribution.