Abstract
We calculate corrections of order ${\ensuremath{\alpha}}^{3}(Z\ensuremath{\alpha}){E}_{F}$ to hyperfine splitting in muonium generated by the gauge invariant set of diagrams with polarization insertions in the light-by-light scattering diagrams. This nonrecoil contribution turns out to be $\ensuremath{-}2.63$ Hz. The total contribution of all known corrections of order ${\ensuremath{\alpha}}^{3}(Z\ensuremath{\alpha}){E}_{F}$ is equal to $\ensuremath{-}4.28$ Hz.
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