Abstract

A new method of divergence subtraction in Feynman parametric integrals is presented. The method is suitable for calculating the lepton anomalous magnetic moments (AMM) in quantum electrodynamics (QED). The subtraction procedure eliminates all divergences before integration and leads to a finite Feynman parametric integral for each individual Feynman diagram. It is based on a forest formula with linear operators applied to the Feynman amplitudes of ultraviolet-divergent subdiagrams. The formula is similar to Bogoliubov–Parasiuk–Hepp–Zimmermann summation; the difference is only in the linear operators used and in the way of combining them. The subtraction is equivalent to the on-shell renormalization from the beginning: for obtaining the final result we should only sum up the contributions of all Feynman diagrams after subtraction. The developed method is an improvement of the method presented by the author in 2016. The modification is specifically designed for calculating the contributions dependent on the relations of particle masses. In comparison with the old version, the new subtraction formula does not contain redundant terms and possesses some flexibility that can be used for improving the precision of calculations. Numerical test results are presented up to four loops.

中文翻译：

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一种快速计算量子电动力学中轻子磁矩的方法

摘要

提出了一种费曼参数积分中散度减法的新方法。该方法适用于计算量子电动力学（QED）中的轻子反常磁矩（AMM）。减法过程在积分之前消除了所有发散，并导致每个单独的费曼图的有限费曼参数积分。它基于一个森林公式，其中线性算子应用于紫外发散子图的费曼振幅。该公式类似于 Bogoliubov-Parasiuk-Hepp-Zimmermann 求和；不同之处仅在于使用的线性运算符和组合它们的方式。减法相当于从一开始就进行壳上重整化：为了获得最终结果，我们只需将减法后所有费曼图的贡献相加即可。开发的方法是作者在 2016 年提出的方法的改进。该修改专门用于计算依赖于粒子质量关系的贡献。与旧版本相比，新的减法公式没有多余的项，具有一定的灵活性，可用于提高计算精度。数值测试结果最多显示四个循环。