Two-loop polarization contributions to radiative-recoil corrections to hyperfine splitting in muonium

Abstract

We calculate radiative-recoil corrections of order ${\ensuremath{\alpha}}^{2}(Z\ensuremath{\alpha}{)(m/M)E}_{F}$ to hyperfine splitting in muonium generated by the diagrams with electron and muon polarization loops. These corrections are enhanced by the large logarithm of the electron-muon mass ratio. The leading logarithm cubed and logarithm squared contributions were obtained a long time ago. 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.