A Way of Fast Calculating Lepton Magnetic Moments in Quantum Electrodynamics

TL;DR

This paper introduces a new divergence subtraction method for Feynman integrals that simplifies and accelerates the calculation of lepton magnetic moments in QED, especially for mass-dependent contributions, demonstrated up to four loops.

Contribution

The paper presents an improved subtraction technique based on a forest formula that reduces redundancies and enhances precision in calculating lepton AMMs in QED.

Findings

Method eliminates divergences before integration

Applicable to calculations up to four loops

Improves accuracy for mass-dependent contributions

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 BPHZ; 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.