Three-Loop Contribution to Hyperfine Splitting in Muonium: Polarization   Corrections to Light by Light Scattering Blob
  We calculate corrections of order $\alpha^3(Z\alpha)E_F$ 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 -2.63 Hz. The total contribution of all known corrections of order $\alpha^3(Z\alpha)E_F$ is equal to -4.28 Hz. 
Michael I. Eides and Valery A. Shelyuto
physics.atom-ph hep-ph