Radiative-recoil corrections to hyperfine splitting: Polarization insertions in the muon factor

Abstract

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