Muon loop light-by-light contribution to hyperfine splitting in muonium.

Three-loop corrections to hyperfine splitting in muonium, generated by the gauge-invariant sets of diagrams with muon and tauon loop light-by-light scattering blocks, are calculated. These results complete calculations of all light-by-light scattering contributions to hyperfine splitting in muonium.

Three-loop radiative-recoil corrections to hyperfine splitting in muonium: diagrams with polarization loops.

We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by the diagrams with electron and muon vacuum polarizations. We calculate single-logarithmic and nonlogarithmic contributions of order alpha;{3}(m/M)E_{F} generated by gauge invariant sets of diagrams with electron and muon polarization insertions in the electron and muon factors. Combining these corrections with the older results, we obtain total contribution to hyperfine splitting generated by all diagrams with electron and muon polarization loops.