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

TL;DR

This paper calculates three-loop radiative-recoil corrections to hyperfine splitting in muonium, focusing on electron polarization insertions, including all single-logarithmic and nonlogarithmic terms of order (m/M)E_F.

Contribution

It provides the first complete calculation of single-logarithmic and nonlogarithmic radiative-recoil corrections from polarization insertions at three loops.

Findings

Calculated all single-logarithmic corrections.

Derived nonlogarithmic radiative-recoil corrections.

Enhanced precision of hyperfine splitting predictions.

Abstract

We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium due to insertions of one-loop polarization operator in the electron factor. The contribution generated by electron polarization insertions is a cubic polynomial in the large logarithm of the electron-muon mass ratio. The leading logarithm cubed and logarithm squared terms are well known for some time. We calculated 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.