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

Abstract

We studied the chiral phase transition for small [Formula: see text] within the Tsallis nonextensive statistics of the entropic parameter [Formula: see text], where the quantity [Formula: see text] is the measure of the deviation from the Boltzmann–Gibbs statistics. We adopted the normalized [Formula: see text]-expectation value in this study. We applied the free particle approximation and the massless approximation in the calculations of the expectation values. We estimated the critical physical temperature, and obtained the chiral condensate, the sigma mass, and the pion mass, as functions of the physical temperature [Formula: see text] for various [Formula: see text]. We found the following facts. The [Formula: see text]-dependence of the critical physical temperature is [Formula: see text]. The chiral condensate at [Formula: see text] is smaller than that at [Formula: see text] for [Formula: see text]. The [Formula: see text]-dependence of the pion mass and that of the sigma mass reflect the [Formula: see text]-dependence of the condensate. The pion mass at [Formula: see text] is heavier than that at [Formula: see text] for [Formula: see text]. The sigma mass at [Formula: see text] is heavier than that at [Formula: see text] for [Formula: see text] at high physical temperature, while the sigma mass at [Formula: see text] is lighter than that at [Formula: see text] for [Formula: see text] at low physical temperature. The quantities which are functions of the physical temperature [Formula: see text] and the entropic parameter [Formula: see text] are described by only the effective physical temperature defined as [Formula: see text] under the approximations.