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

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    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 TT and the entropic parameter qq. The normalized qq-expectation value and the physical temperature \Tph were employed in this study. The normalized qq-expectation value was expanded as a series of the value (1βˆ’q)(1-q), where the absolute value ∣1βˆ’q∣|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 qq is smaller than that at qβ€²q' for q>qβ€²q>q'. The sigma mass at qq is lighter than that at qβ€²q' for q>qβ€²q>q' at low physical temperature, and the sigma mass at qq is heavier than that at qβ€²q' for q>qβ€²q>q' at high physical temperature. The pion mass at qq is heavier than that at qβ€²q' for q>qβ€²q>q'. The difference between the pion masses at different values of qq 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 ∣1βˆ’q∣|1-q|, and the pion mass is also affected by the statistics of small ∣1βˆ’q∣|1-q| except for \Tph \le 200 MeV.Comment: 9 pages, 6 figure
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