Study of the standard model for elementary particles at the finite temperature

(1)应用捏点技术（PT）获得了热杨-米尔斯气体中与量规无关的恢复胶子自能。由恢复胶子自能和恢复捏贡献之和得到的有效胶子自能不仅与量规无关，而且满足横向关系。利用这种不依赖于量规的有效胶子自能，我们计算了横胶子的领先阶阻尼率，结果与Braaten和Pisarski得到的结果一致。(2)在算子积展开和重整化群方法的框架下，证明了核子的味非单重态自旋结构函数g_2（x, Q^2）的扭转-3部分在大N_C极限下服从简单的dokshitzer - gribov - lipatovv - altarelli - parisi （DGLAP）方程（N_C为色数）。(3)对λ ^2>>P^2>>Q^2的虚光子结构函数g_1^< γ > (x, Q^2, P^2)进行了研究，其中-Q^2 （-P^2）为探测（目标）光子的质量平方。在基于DGLAP进化方程的QCD改进parton模型框架下，对QOD的次领先阶进行了分析。非前导修正显著地修改了前导对数结果，特别是在大x和小x时。

(1) The pinch technique (PT) is applied to obtain the gauge-independent resummed gluon self-energy in a hot Yang-Mills gas. The effective gluon self-energy, which is obtained as the sum of the resummed gluon self-energy and the resummed pinch contributions, is not only gauge-independent but also satisfies the transversality relation. Using this gauge-independent effective gluon self-energy, we calculate the damping rate for transverse gluons in the leading order and show that the result coincides with the one obtained by Braaten and Pisarski.(2) It is shown in the framework of the operator product expansion and the renormalization group method that the twist-3 part of flavor nonsinglet spin structure function g_2(x, Q^2) of nucleon obeys a simple Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equation in the large N_C limit even in the case of massive quarks (N_C is the number of colours).(3) The virtual photon structure function g_1^<gamma> (x, Q^2, P^2), which can be obtained in polarized e^+ +e^- & colliding-beam experiments, is investigated for LAMBDA^2>>P^2>>Q^2, where -Q^2 (-P^2) is the mass squared of the probe (target) photon. The analysis is made to next-to-leading order in QOD, in the framework of the QCD improved parton model with the DGLAP evolution equations. The non-leading corrections significantly modify the leading log result, in particular, at large x as well as at small x.