Tenth-Order QED Contribution to the Lepton Anomalous Magnetic Moment -- Sixth-Order Vertices Containing an Internal Light-by-Light-Scattering Subdiagram

TL;DR

This paper calculates the tenth-order quantum electrodynamics (QED) contributions to the anomalous magnetic moments of leptons, specifically focusing on complex Feynman diagrams involving light-by-light scattering, providing precise numerical results for electron and muon g-2.

Contribution

It presents the first detailed evaluation of tenth-order QED contributions from a specific gauge-invariant set of diagrams with internal light-by-light scattering subdiagrams.

Findings

Electron g-2 contribution: 4.9247(104) (alpha/pi)^5

Muon g-2 contribution from electron loops: 7.435(134) (alpha/pi)^5

Total leptonic loop contribution to muon g-2: 12.556(135) (alpha/pi)^5

Abstract

This paper reports the tenth-order QED contribution to the lepton g-2 from the gauge-invariant set, called Set III(c), which consists of 390 Feynman vertex diagrams containing an internal fourth-order light-by-light-scattering subdiagram. The mass-independent contribution of Set III(c) to the electron g-2 (a_e) is 4.9210(103) in units of (alpha/pi)^5. The mass-dependent contributions to a_e from diagrams containing a muon loop is 0.00370(37) (alpha/pi)^5. The tau-lepton loop contribution is negligible at present. Altogether the contribution of Set III(c) to a_e is 4.9247 (104) (alpha/pi)^5. We have also evaluated the contribution of the closed electron loop to the muon g-2 (a_mu). The result is 7.435(134) (alpha/pi)^5. The contribution of the tau-lepton loop to a_mu is 0.1999(28)(alpha/pi)^5. The total contribution of variousleptonic loops (electron, muon, and tau-lepton) of Set III(c) to a_mu is 12.556 (135) (alpha/pi)^5.