Second Order in Mass Ratio Radiative-Recoil Corrections to Hyperfine Splitting in Muonium

Abstract

Radiative-recoil corrections to hyperfine splitting in muonium of orders $\alpha (Z\alpha )(m/M{)}^2{E}_F$ and $(Z^2\alpha )(Z\alpha )(m/M{)}^2{E}_F$ are calculated. These corrections are of the second order in the small electron-muon mass ratio. An analytic expression $[(-6\ln 2-\frac{3}{4})\alpha (Z\alpha )-\frac{17}{12}(Z^2\alpha )(Z\alpha )](\frac{m}{M}{)}^2{E}_F$ is obtained. Numerically the correction is equal to $-0.0351\text{mbox}kHz$ and is of the same order of magnitude as the expected accuracy of the current Los Alamos experiment to measure the hyperfine splitting.

Comments: Revtex, 19 pages, 3 tables; two references added, no other changes