Subtraction Procedure for Calculation of Anomalous Magnetic Moment of Electron in QED and its Application to Numerical Computation at 3-loop Level

TL;DR

This paper introduces a new subtraction method for removing divergences in Feynman integrals, enabling precise numerical calculations of the electron's anomalous magnetic moment at 3-loop level in QED.

Contribution

A novel subtraction procedure formulated as a forest formula with linear operators, improving the numerical computation of high-order QED corrections.

Findings

Successfully applied to 2-loop and 3-loop calculations

Produces finite Feynman-parametric integrals for each graph

Enhances accuracy of electron anomalous magnetic moment computations

Abstract

A new subtraction procedure for removal both ultraviolet and infrared divergences in Feynman integrals is proposed. This method is developed for computation of QED corrections to the electron anomalous magnetic moment. The procedure is formulated in the form of a forest formula with linear operators that are applied to Feynman amplitudes of UV-divergent subgraphs. The contribution of each Feynman graph that contains propagators of electrons and photons is represented as a finite Feynman-parametric integral. Application of the developed method to the calculation of 2-loop and 3-loop contributions is described.