Polarization contributions of order /spl alpha//sup 2/(Z/spl alpha/)(m/M)E/sub F/ to hyperfine splitting in muonium

We calculate radiative-recoil corrections of order /spl alpha//sup 2/(Z/spl alpha/)(m/M)E/sub F/ to hyperfine splitting in muonium generated by the diagrams with electron and muon polarization loops. The single-logarithmic and nonlogarithmic contributions calculated here improve the theory of hyperfine splitting, and affect the value of the electron-muon mass ratio extracted from the experimental data on the muonium hyperfine splitting.