We consider three-loop corrections to hyperfine splitting in muonium generated by the gauge invariant set of diagrams with a virtual light-by-light scattering block. These diagrams produce both recoil and nonrecoil contributions to hyperfine splitting. Recoil corrections are enhanced by large logarithms of the muon-electron mass ratio. Both nonrecoil and logarithmically enhanced radiative-recoil corrections were calculated some time ago. Here we calculate nonlogarithmic radiative-recoil corrections generated by the insertions of the light-by-light scattering block.
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This work was supported by the NSF Grant No. PHY-1066054. The work of V. S. was also supported in part by the RFBR Grant No. 12-02-00313 and by the DFG Grant No. GZ:HA 1457/7-2.
Eides, Michael I. and Shelyuto, Valery A., "Light-By-Light Scattering Nonlogarithmic Corrections to Hyperfine Splitting in Muonium" (2014). Physics and Astronomy Faculty Publications. 235.