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

We studied the chiral phase transition for small $|1-q|$ within the Tsallis nonextensive statistics of the entropic parameter $q$, where the quantity $|1-q|$ is the measure of the deviation from the Boltzmann-Gibbs statistics. We adopted the normalized $q$-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 $T_{\mathrm{ph}}$ for various $q$. We found the following facts. The $q$-dependence of the critical physical temperature is $1/\sqrt{q}$. The chiral condensate at $q$ is smaller than that at $q'$ for $q>q'$. The $q$-dependence of the pion mass and that of the sigma mass reflect the $q$-dependence of the condensate. The pion mass at $q$ is heavier than that at $q'$ for $q>q'$. The sigma mass at $q$ is heavier than that at $q'$ for $q>q'$ at high physical temperature, while the sigma mass at $q$ is lighter than that at $q'$ for $q>q'$ at low physical temperature. The quantities which are functions of the physical temperature $T_{\mathrm{ph}}$ and the entropic parameter $q$ are described by only the effective physical temperature defined as $\sqrt{q} T_{\mathrm{ph}}$ under the approximations.