Tsallis非广延统计量下Hartree分解下线性西格玛模型中的手征相变
Chiral phase transition in the linear sigma model within Hartree factorization in the Tsallis nonextensive statistics
摘要：
研究了Tsallis非广延统计下线性西格玛模型中的手征相变，在此情况下，手征相变与Boltzmann-Gibbs（BG）统计的偏差较小.该统计量具有两个参数：温度$T$和熵参数$q$。在本研究中使用了归一化的$q$期望值和物理温度$\Tph$。将归一化$q$ -期望值扩展为一系列值$(1-q)$，其中绝对值$|1-q|$是与BG统计量的偏差的度量。我们应用Hartree分解和自由粒子近似，得到了凝聚体，σ质量和π质量的方程。这些量的物理温度依赖性的数值。我们发现了以下事实。对于$q>q'$，$q$处的冷凝物小于$q'$处的冷凝物。对于低物理温度下的$q>q'$，$q$处的σ质量比$q'$处的σ质量轻，而对于高物理温度下的$q>q'$，$q$处的σ质量比$q'$处的σ质量重。对于$q>q'$，$q$的π介子质量比$q'$的重。对于$\Tph \le 200$ MeV来说，不同$\Tph \le 200$值下的π介子质量之间的差异很小。也就是说，凝聚态和σ质量受小$|1-q|$的Tsallis非广延统计的影响，而π质量除了受$\Tph \le 200$ MeV的影响外，还受小$|1-q|$的统计的影响.
英文摘要：
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.
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