Chiral phase transition in the linear sigma model within Hartree factorization under $$(1-q)$$ expansion and free particle approximation in the Tsallis nonextensive statistics
We studied chiral phase transition in the linear sigma model within the Tsallis nonextensive statistics under some approximations. The statistics has two parameters: the temperature T and the entropic parameter q. The normalized q-expectation value and the physical temperature $$T_{\mathrm {ph}}$$
 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 $$T_{\mathrm {ph}}\le 200$$
 MeV. In other words, the condensate and the sigma mass are affected by the Tsallis nonextensive statistics with $$|1-q| = 0.1$$
 , and the pion mass is also affected by the statistics of $$|1-q|=0.1$$
 except for $$T_{\mathrm {ph}}\le 200$$
 MeV.