Analytic calculation of radiative-recoil corrections to muonium hyperfine splitting: Electron-line contribution

The detailed account of analytic calculation of radiative-recoil corrections to muonium hyperfine splitting, induced by electron-line radiative insertions, is presented. The consideration is performed in the framework of the effective two-particle formalism. A good deal of attention is paid to the problem of the divergence cancellation and the selection of graphs, relevant to radiative-recoil corrections. The analysis is greatly facilitated by use of the Fried-Yennie gauge for radiative photons. The obtained set of graphs turns out to be gauge-invariant and actual calculations are performed in the Feynman gauge. The main technical tricks, with the help of which we have effectively utilized the existence in the problem of the small parameter-mass ratio and managed to perform all calculations in the analytic form are described. The main intermediate results, as well as the final answer, δE rr = ( α(Zα) π 2 )( m M )E F(6ζ(3) + 3π 2 ln 2 + π 2 2 + 17 8 ), are also presented.