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

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.

Comments: 6 pages, 5 figures v2: some references added, accepted for publication in Phys. Rev. A