# New method of computing the contributions of graphs without lepton loops to the electron anomalous magnetic moment in QED

## TL;DR

This paper introduces a fully automated numerical method for calculating QED contributions to the electron's anomalous magnetic moment from specific Feynman graphs, effectively handling divergences and employing importance sampling Monte Carlo techniques.

## Contribution

The paper presents a novel, automated approach combining divergence subtraction and importance sampling Monte Carlo for precise computation of specific Feynman graphs in QED.

## Key findings

- Successfully applied to 2-, 3-, 4-, and some 5-loop graphs
- Effectively removes divergences point-by-point in parametric space
- Provides accurate numerical results for complex Feynman diagrams

## Abstract

This paper presents a new method of numerical computation of the QED contributions to the electron anomalous magnetic moment which arises from Feynman graphs containing electron and photon lines and not containing electron loops. The method consists of two parts. The first part is the forest-like subtraction formula that removes all ultraviolet and infrared divergences in each Feynman graph point-by-point in Feynman-parametric space. The second part is the importance sampling Monte-Carlo algorithm with the probability density function that is constructed for each Feynman graph individually. The method is fully automated at any order of the perturbation series. The results of applying the method to 2-loop, 3-loop, 4-loop Feynman graphs and to some individual 5-loop graphs are presented.