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

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 $T$ and the entropic parameter $q$. The normalized $q$-expectation
value and the physical temperature \Tph 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 \Tph \le 200 MeV. That is
to say, the condensate and the sigma mass are affected by the Tsallis
nonextensive statistics of small $|1-q|$, and the pion mass is also affected by
the statistics of small $|1-q|$ except for \Tph \le 200 MeV.Comment: 9 pages, 6 figure

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