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

Radiative-recoil corrections to hyperfine splitting in muonium of order alpha(Z alpha)(m/M)E-2(F) and (Z(2)alpha)(Z alpha)(m/M)E-2(F) are calculated. These corrections are of the second order in the small electron-muon mass ratio. An analytic expression [(-6 ln 2 - 3/4) alpha(Z alpha) - 17/12 (Z(2)alpha)(Z alpha)](m/M)E-2(F) is obtained. Numerically the correction is equal to - 0.0351 kHz and is of die same order of magnitude as the expected accuracy of the current Los Alamos experiment to measure the hyperfine splitting. [S0556-2821(98)031130].