Abstract

The results of calculation of the three-loop radiative correction to the renormalization constant of fermion masses for non-abelian gauge theory interacting with fermions are presented. Dimensional regularization and the t’Hooft-Veltman minimal subtraction scheme are used. The method of calculation is described in detail. The renormalization group function \({{\gamma }_{m}}\) determining the behavior of the effective mass of fermions is presented. The anomalous dimensions of fermions for QED and QCD up to three loops are given. All calculations were performed on a computer with the help of the SCHOOONSCHIP system for analytical manipulations.

中文翻译：

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三环近似中夸克质量的异常维数

摘要

给出了非阿贝尔量规理论与费米相互作用的费米质量重归一化常数的三环辐射校正的计算结果。使用维数正则化和t'Hooft-Veltman最小减法。详细描述了计算方法。提出了确定费米子有效质量行为的重归一化群函数\（{{\ gamma} _ {m}} \）。给出了QED和QCD的费米子的异常尺寸（最多三个环）。借助SCHOOONSCHIP系统，所有计算均在计算机上进行分析操作。