# Numerical calculation of 5-loop QED contributions to the electron anomalous magnetic moment

## TL;DR

This paper presents preliminary numerical calculations of the 5-loop QED contributions to the electron and muon anomalous magnetic moments, revealing a discrepancy with known results and introducing contributions of gauge-invariant classes for the first time.

## Contribution

It introduces a novel numerical method for 5-loop QED calculations, including gauge-invariant class contributions, and reports a discrepancy with previous results.

## Key findings

- Discrepancy found with known 5-loop QED results.
- First presentation of gauge-invariant class contributions.
- Uses GPU-based Monte Carlo integration for high-precision calculations.

## Abstract

Preliminary numerical results of calculating the 5-loop QED contributions to the electron (and muon) anomalous magnetic moment are presented. The results include the total contribution of the 5-loop Feynman diagrams without lepton loops and the contributions of nine gauge-invariant classes that form that set. A discrepancy with known results is revealed. The contributions of the gauge-invariant classes are presented for the first time. The method of the computation is briefly described (with the corresponding references). The calculation is based on the following elements: 1) a subtraction procedure for removing infrared (IR) and ultraviolet (UV) divergences point by point in Feynman parametric representation before integration; 2) a nonadaptive Monte Carlo integration method that is founded on probability density functions (PDF) that are constructed for each Feynman diagram individually using its combinatorial structure; 3) a GPU-based numerical integration with the help of the supercomputer "Govorun" (JINR, Dubna, Russia).