Verification of the tenth-Order QED contribution to the anomalous magnetic moment of the electron from diagrams without fermion loops

TL;DR

This paper investigates a 5-sigma discrepancy in the tenth-order QED contribution to the electron's magnetic moment by decomposing the calculation into parts, identifying the source of differences, and performing a refined recalculation to resolve the issue.

Contribution

The study introduces a detailed diagram-by-diagram comparison and a recalculation approach that resolves the longstanding discrepancy in high-order QED calculations for the electron.

Findings

No significant discrepancies in individual diagrams.

The discrepancy was due to accumulated differences in 98 diagrams.

Recalculation with increased statistics resolved the discrepancy.

Abstract

A discrepancy of approximately 5$\sigma$ exists between the two known results for the tenth-order QED contribution to the anomalous magnetic moment of the electron, calculated from Feynman vertex diagrams without fermion loops. To investigate this, we decomposed this contribution into 389 parts based on a self-energy diagram representation, enabling a diagram-by-diagram numerical comparison of the two calculations. No significant discrepancies were found for individual diagrams. However, the numerical differences of the 98 diagrams sharing a common structure were not randomly distributed. The accumulation of these differences resulted in the 5$\sigma$ discrepancy. A recalculation with increased statistics in the Monte Carlo integration was performed for these 98 diagrams. By replacing the old values with the new ones for these 98 integrals, we have obtained a revised result of $6.800 \pm 0.128$, thereby resolving the discrepancy.