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.

中文翻译：

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Tsallis非广义统计中的$$（1-q）$$（1-q）展开和自由粒子逼近在Hartree分解中线性sigma模型中的手性相变

我们研究了Tsallis非广泛统计量下线性sigma模型中的手性相变。统计信息有两个参数：温度T和熵参数q。本研究采用归一化的q期望值和物理温度\（T _ {\ mathrm {ph}} \）。归一化的q期望值被扩展为一系列值\（（1-q）\），其中绝对值\（| 1-q | \）是与BG统计数据的偏差的度量。我们应用了Hartree分解和自由粒子近似，并获得了冷凝水，sigma质量和pion质量的方程式。这些量的物理温度依赖性通过数字获得。我们发现以下事实。在冷凝水q是小于\（Q '\）为\（Q> Q' \） 。在所述Σ质量q是在比打火机\（Q“\）为\（Q> Q” \）在较低的物理温度，并且在所述Σ质量q是大于较重在\（Q'\）为\（ q> q'\）在高物理温度下。q处的介子质量是在比较重\（Q '\）为\（Q> Q' \） 。对于\（T _ {\ mathrm {ph}} \ le 200 \） MeV，在q的不同值处的中介质量之间的差异很小。换句话说，凝结水和西格玛质量受Tsallis非广义统计量\（| 1-q | = 0.1 \）的影响，而介子质量也受\（| 1-q | = 0.1 \），除了\（T _ {\ mathrm {ph}} \ le 200 \） MeV。