Eighth-Order Vacuum-Polarization Function Formed by Two Light-by-Light-Scattering Diagrams and its Contribution to the Tenth-Order Electron g-2

TL;DR

This paper calculates the tenth-order electron and muon g-2 contributions from complex Feynman diagrams involving eighth-order vacuum polarization formed by light-by-light scattering, using two consistent computational methods.

Contribution

It introduces two different methods to evaluate complex Feynman diagrams and confirms their consistency for precise quantum electrodynamics calculations.

Findings

Electron g-2 contribution: 0.0003999(18) (α/π)^5

Muon g-2 contribution: -1.26344(14) (α/π)^5

Validated two computational approaches for high-order QED diagrams

Abstract

We have evaluated the contribution to the anomalous magnetic moment of the electron from six tenth-order Feynman diagrams which contain eighth-order vacuum-polarization function formed by two light-by-light scattering diagrams connected by three photons. The integrals are constructed by two different methods. In the first method the subtractive counter terms are used to deal with ultraviolet (UV) singularities together with the requirement of gauge-invariance. In the second method, the Ward-Takahashi identity is applied to the light-by-light scattering amplitudes to eliminate UV singularities. Numerical evaluation confirms that the two methods are consistent with each other within their numerical uncertainties. Combining the two results statistically and adding small contribution from the muons and/or tau leptons, we obtain $ 0.000 399 9 (18) (\alpha/\pi)^5$. We also evaluated the contribution to the muon $g-2$ from the same set of diagrams and found $ -1.263 44 (14) (\alpha/\pi)^5$.