Calculating the five-loop QED contribution to the electron anomalous magnetic moment: Graphs without lepton loops

TL;DR

This paper computes the 5-loop QED contribution to the electron's anomalous magnetic moment without lepton loops, providing an independent check that slightly differs from previous results and impacts the fine-structure constant prediction.

Contribution

It introduces a novel calculation method for 5-loop QED graphs without lepton loops, including divergence removal and nonadaptive Monte Carlo integration, and provides detailed results for the first time.

Findings

Calculated the 5-loop QED contribution without lepton loops as 6.793(90)

Identified a 4.8σ discrepancy with previous results from 2018

Provided detailed contributions for 3213 individual Feynman graphs

Abstract

This paper describes a computation of a part of the QED contribution to the electron anomalous magnetic moment that was performed by the author with the help of a supercomputer. The computed part includes all 5-loop QED Feynman graphs without lepton loops. The calculation has led to the result $A_1^{(10)}[\text{no lepton loops}]=6.793(90)$ that is slightly different than the value $7.668(159)$ presented by T. Aoyama, T. Kinoshita, and M. Nio in 2018. The discrepancy is about $4.8\sigma$. The computation gives the first independent check for that value. A shift in the fine-structure constant prediction is revealed in the paper. The developed calculation method is based on (a) a subtraction procedure for removing all ultraviolet and infrared divergences in Feynman parametric space before integration; (b) a nonadaptive Monte Carlo integration that uses the probability density functions that are constructed for each Feynman graph individually using its combinatorial structure. The method is described briefly in the paper (with the corresponding references to the previous papers). The values for the contributions of nine gauge-invariant classes splitting the whole set are presented in the paper. Moreover, the whole set of all 5-loop graphs without lepton loops is split into 807 subsets for comparison (in the future) of the calculated values with the values obtained by another methods. These detailed results are presented in the supplemental materials. Also, the supplemental materials contain the contribution values for each of 3213 individual Feynman graphs. An "oscillating" nature of these values is discussed. Technical details of the realization are described.