论文标题
在有限温度和密度下计算一个循环箱积分
Calculation of the one loop box integral at Finite Temperature and Density
论文作者
论文摘要
在Nambu-Jona-lasinio样模型内的非零温度和密度下的强发化，衰减或散射过程的计算需要一些技术来计算Feynmann图表。 Feynman图在一个循环级别的分解导致具有一个，二，三和四效线的基本积分。例如，评估$ππ$散射幅度需要计算具有四个费米昂线的盒子图。在这项工作中，在一个循环级别的盒子积分的真实和虚构部分以适合数值评估的形式提供。获得的表达式适用于温度，颗粒质量和化学势的任何值。我们特别注意出现不当积分的存在条件，并为三个费米管线纠正结果\ cite {klevansky}。结果，我们对粒子矩的可能值的限制获得了限制。在盒子积分的表达式中，具有任意数量线的积分的一般公式是为零或collinear fermion Mongima的情况得出的。
Calculation of hadronization, decay or scattering processes at non-zero temperatures and densities within the Nambu-Jona-Lasinio-like models requires some techniques for computation of Feynmann diagrams. Decomposition of Feynman diagrams at the one loop level leads to the appearance of elementary integrals with one, two, three, and four fermion lines. For example, evaluation of the $ππ$ scattering amplitude requires calculating a box diagram with four fermion lines. In this work, the real and imaginary parts of the box integral at the one loop level are provided in the form suitable for numerical evaluation. The obtained expressions are applicable to any value of temperature, particle mass, and chemical potential. We pay special attention to the conditions for the existence of the appearing improper integrals and correct the results \cite{Klevansky} for the three fermion lines. As a result, we have obtained constraints on possible values of particle momenta. Among the expressions for the box integral, the general formulas for the integral with an arbitrary number of lines are derived for the case with zero or collinear fermion momenta.
