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

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 $α^3(m/M)E_F$ generated by the diagrams with electron and muon polarization insertions.