One-logarithmic recoil correction in muonium hyperfine splitting

A source of recoil corrections to muonium hyperfine splitting which are linear in the logarithm of the electron-muon mass ratio is detected. The contribution is induced by the simultaneous insertion of muon and electron polarization loops in the external photon lines. This contribution is calculated analytically and is given by the numerical result δE=(${\mathrm{\alpha }}^2$Zα/π)${\mathit{E}}_{\mathit{F}}${0.6455[m/M]ln[M/m] +0.9212[m/M]}=0.011 37 kHz.