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Abstract
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 ${\ensuremath{\alpha}}^{2}(Z\ensuremath{\alpha})(m/M){E}_{F}$ to hyperfine splitting in muonium generated by these diagrams.
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