Three-loop radiative-recoil corrections to hyperfine splitting in muonium: Diagrams with polarization loops

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 α3(m/M)EF generated by gauge invariant sets of diagrams with electron and muon polarization insertions in the electron and muon factors. Combining these corrections with the older results, we obtain total contribution to hyperfine splitting generated by all diagrams with electron and muon polarization loops. The calculation of this contribution completes an important stage in the implementation of the program of reduction of the theoretical uncertainty of hyperfine splitting below 10 Hz. The new results improve the theory of hyperfine splitting and affect the value of the electron-muon mass ratio extracted from experimental data on muonium hyperfine splitting.