Light-by-Light Scattering Single-Logarithmic Corrections to Hyperfine Splitting in Muonium

We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by the gauge invariant set of diagrams with virtual light-by-light scattering block. These corrections are enhanced by the large logarithms of the electron-muon mass ratio. We present the results of an analytic calculation of the single-logarithmic radiative-recoil corrections of order ${\alpha }^2(Z\alpha )(m\mathrm{/}M)E_F$ to hyperfine splitting in muonium generated by these diagrams.