Three-loop contribution to hyperfine splitting in muonium: Polarization corrections to light-by-light scattering contributions

@article{Eides2012ThreeloopCT,
  title={Three-loop contribution to hyperfine splitting in muonium: Polarization corrections to light-by-light scattering contributions},
  author={Michael I. Eides and Valery A. Shelyuto},
  journal={Physical Review A},
  year={2012},
  volume={86},
  pages={024501}
}
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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