Second order in mass ratio radiative-recoil corrections to hyperfine splitting in muonium

Radiative-recoil corrections to hyperfine splitting in muonium of order α(Zα)(m/M)²EF and (Z²α)(Zα)(m/M)²EF are calculated. These corrections are of the second order in the small electron-muon mass ratio. An analytic expression [(-6ln2-3/4)α(Zα)-17/12(Z²α)(Zα)](m/M)²EF is obtained. Numerically the correction is equal to -0.0351kHz and is of the same order of magnitude as the expected accuracy of the current Los Alamos experiment to measure the hyperfine splitting.