Radiative-Recoil Corrections to Hyperfine Splitting: Polarization Insertions in the Muon Factor

TL;DR

This paper calculates three-loop radiative-recoil corrections to muonium hyperfine splitting, focusing on polarization insertions in the muon factor, including electron and muon polarization effects with large logarithmic enhancements.

Contribution

It provides the first complete calculation of all single-logarithmic and nonlogarithmic corrections of order α^3(m/M)E_F from polarization insertions in the muon factor.

Findings

All single-logarithmic corrections were obtained.

Nonlogarithmic corrections of the specified order were calculated.

Electron polarization insertions lead to enhanced contributions due to large logarithms.

Abstract

We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium due to insertions of one-loop polarization operator in the muon factor. The contribution produced by electron polarization insertions are enhanced by the large logarithm of the electron-muon mass ratio. We obtained all single-logarithmic and nonlogarithmic radiative-recoil corrections of order $\alpha^3(m/M)E_F$ generated by the diagrams with electron and muon polarization insertions.