Tenth-order lepton g-2: Contribution from diagrams containing a sixth-order light-by-light-scattering subdiagram internally

TL;DR

This paper calculates tenth-order quantum electrodynamics corrections to lepton g-2 from specific Feynman diagrams involving light-by-light scattering, providing precise numerical contributions for electrons and muons.

Contribution

It presents the first detailed evaluation of tenth-order diagrams with sixth-order light-by-light subdiagrams for lepton g-2, including all relevant contributions.

Findings

Electron g-2 contribution: -1.345 (1) (α/π)^5

Muon g-2 contribution: 1.882 (13) (α/π)^5

Negligible tau-lepton contribution to electron g-2

Abstract

This paper reports the result of our evaluation of the tenth-order QED correction to the lepton g-2 from Feynman diagrams which have sixth-order light-by-light-scattering subdiagrams, none of whose vertices couple to the external magnetic field. The gauge-invariant set of these diagrams, called Set II(e), consists of 180 vertex diagrams. In the case of the electron g-2 (a_e), where the light-by-light subdiagram consists of the electron loop, the contribution to a_e is found to be - 1.344 9 (10) (\alpha /\pi)^5. The contribution of the muon loop to a_e is - 0.000 465 (4) (\alpha /\pi)^5. The contribution of the tau-lepton loop is about two orders of magnitudes smaller than that of the muon loop and hence negligible. The sum of all of these contributions to a_e is - 1.345 (1) (\alpha /\pi)^5. We have also evaluated the contribution of Set II(e) to the muon g-2 (a_\mu). The contribution to a_\mu from the electron loop is 3.265 (12) (\alpha /\pi)^5, while the contribution of the tau-lepton loop is -0.038 06 (13) (\alpha /\pi)^5. The total contribution to a_\mu, which is the sum of these two contributions and the mass-independent part of a_e, is 1.882 (13) (\alpha /\pi)^5.