Three-Loop Contributions to Hyperfine Splitting: Muon Loop   Light-by-Light Insertion and Other Closed Lepton Loops
  The muon and tauon light-by-light scattering contributions to hyperfine splitting in muonium are calculated. These results conclude calculation of all hard three-loop contributions to hyperfine splitting containing graphs with closed fermion loops. We discuss the special role that the lepton anomalous magnetic moments play in these calculations. The full result for all three-loop radiative-recoil corrections to hyperfine splitting generated by the graphs with closed lepton loops is presented. 
Michael I. Eides and Valery A. Shelyuto
hep-ph physics.atom-ph