Light-by-Light Scattering Single-Logarithmic Corrections to Hyperfine Splitting in Muonium

TL;DR

This paper calculates the single-logarithmic radiative-recoil corrections to muonium hyperfine splitting caused by light-by-light scattering diagrams, enhancing precision in quantum electrodynamics predictions.

Contribution

It provides the first analytic computation of these specific three-loop corrections involving light-by-light scattering in muonium.

Findings

Derived the order α²(Zα)(m/M)E_F correction terms.

Quantified the impact of light-by-light scattering on hyperfine splitting.

Enhanced theoretical accuracy for muonium hyperfine structure calculations.

Abstract

We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by the gauge invariant set of diagrams with virtual light-by-light scattering block. These corrections are enhanced by the large logarithms of the electron-muon mass ratio. We present the results of an analytic calculation of the single-logarithmic radiative-recoil corrections of order $\alpha^2(Z\alpha)(m/M)E_F$ to hyperfine splitting in muonium generated by these diagrams.