A Flexible Divergence Elimination Method for Calculating Lepton Magnetic Moments in Quantum Electrodynamics

TL;DR

This paper introduces a flexible divergence elimination method for calculating lepton magnetic moments in QED, effectively handling divergences in high-order Feynman diagram integrals to improve numerical precision.

Contribution

The authors present a novel divergence subtraction technique that operates point-by-point in Feynman space, enhancing the accuracy and efficiency of high-order QED calculations for lepton magnetic moments.

Findings

Successfully tested on 3-loop and 4-loop diagrams

Eliminates UV, IR, and mixed divergences before integration

Compatible with on-shell renormalization procedures

Abstract

A precise calculation of the lepton anomalous magnetic moments (AMM) requires an evaluation of the quantum electrodynamics (QED) Feynman diagrams up to five independent loops. The complicated structure of ultraviolet (UV), infrared (IR) and mixed divergences in the corresponding integrals makes it difficult to calculate these high-order contributions in reasonable computer time frame. We demonstrate a method that eliminates all divergences point by point in Feynman parametric space (before integration) and possesses a flexibility that can be used for improving the precision of the numerical integration. This flexibility is especially actual for calculating the contributions of the Feynman diagrams with electron loops to the muon AMM. 3-loop and 4-loop numerical test results are provided. The subtraction procedure is based on a forest formula with linear operators applied to the Feynman amplitudes of UV divergent subdiagrams. It is similar to BPHZ; the difference is in the linear operators used and in the way of combining them. It is equivalent to the on-shell renormalization after summation over diagrams: no residual renormalization is required.