Light-by-light scattering in the Lamb shift and the bound electron g factor

TL;DR

This paper calculates higher-order quantum electrodynamics corrections from light-by-light scattering to the hydrogen Lamb shift and the bound electron g-factor, including muon loop effects, refining theoretical predictions.

Contribution

It provides the first detailed computation of $ ext{O}( ext{ extalpha}^2(Z ext{ extalpha})^6)$ corrections to the Lamb shift and related effects on the electron g-factor, including muon loop contributions.

Findings

Calculated $ ext{O}( ext{ extalpha}^2(Z ext{ extalpha})^6)$ correction to the Lamb shift.

Determined contributions to the electron g-factor at $ ext{O}( ext{ extalpha}^2(Z ext{ extalpha})^4)$.

Included muon magnetic loop effects in the g-factor calculation.

Abstract

We compute an $\mathcal{O}\left(\alpha^2(Z\alpha)^6\right)$ contribution to the hydrogen-atom Lamb shift arising from the light-by-light scattering. Analogous diagrams, with one atomic electric field insertion replaced by an external magnetic field, contribute to the gyromagnetic factor of the bound electron at $\mathcal{O}\left(\alpha^2(Z\alpha)^4\right)$. We also calculate the contribution to the gyromagnetic factor from the muon magnetic loop.