Three-Loop Radiative-Recoil Corrections to Hyperfine Splitting in Muonium: Diagrams with Polarization Loops

TL;DR

This paper calculates three-loop radiative-recoil corrections to muonium hyperfine splitting involving electron and muon polarization loops, providing a comprehensive result for these quantum electrodynamics effects.

Contribution

It presents the first complete calculation of three-loop radiative-recoil corrections with polarization loops, including both logarithmic and nonlogarithmic terms.

Findings

Derived single-logarithmic contributions of order α^3(m/M)E_F.

Computed nonlogarithmic corrections of the same order.

Provided a complete set of results for diagrams with polarization loops.

Abstract

We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by the diagrams with electron and muon vacuum polarizations. We calculate single-logarithmic and nonlogarithmic contributions of order $\alpha^3(m/M)E_F$ generated by gauge invariant sets of diagrams with electron and muon polarization insertions in the electron and muon factors. Combining the new contributions with our older results we present complete result for all three-loop radiative-recoil corrections generated by the diagrams with electron and muon polarization loops.