有限温度下基于NJL模型的GMOR关系研究

The study of GMOR relation in the NJL model at finite temperature

摘要:

在量子色动力学(QCD)中，Gell-Mann-Oakes-Renner(GMOR)关系式是联系夸克凝聚、介子质量和衰变常数的一个零温下低阶近似的恒等式. 本文根据QCD有效理论，从Nambu–Jona-Lasinio(NJL)模型出发，基于双味NJL模型和正时正规化方案(PTR)，推导了有限温下夸克凝聚随温度的变化关系，以及夸克凝聚时夸克质量随温度的变化关系，并研究了GMOR关系式在此条件下随温度变化的成立情况. 结果表明：在零温附近，GMOR等式在误差允许范围内成立；但随着温度的升高，超过某一界限后，等式不再成立，且等式两边的偏差值越来越大.

Abstract:

In quantum chromatic dynamics (QCD) theory, Gell-Mann-Oakes-Renner (GMOR) is a low-order approximate identity which associates with quark condensation, meson mass and pion decay constant at zero temperature. In this paper, according to the QCD efficient theory and the Nambu-Jona-Lasinio (NJL) model, based on the two-flavor NJL model and the Proper Time Regularization (PTR), we derive the temperature dependence of quark condensation and the temperature dependence of quark mass in Quark condensation at finite temperature, and try to study the establishment of GMOR relation under this temperature condition. The results show that near zero temperature, the GMOR equation is valid within the allowable range of error, but with the increase of temperature, beyond a certain limit, the equation is no longer valid, and the deviation between the two sides of the equation is increasing.