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 $-0.0351\:\mbox{kHz}$ and is of the same order of magnitude as the expected accuracy of the current Los Alamos experiment to measure the hyperfine splitting.

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

References in corpus (1)

• Radiative Corrections to the Muonium Hyperfine Structure. II. The $\alpha (Z\alpha {)}^2$ Correction

Cited by in corpus (13)

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• Hard Three-Loop Corrections to Hyperfine Splitting in Positronium and Muonium
• Hard Nonlogarithmic Corrections of Order $m{\alpha }^7$ to Hyperfine Splitting in Positronium
• Three-Loop Radiative-Recoil Corrections to Hyperfine Splitting in Muonium
• Light-by-Light Scattering Nonlogarithmic Corrections to Hyperfine Splitting in Muonium
• Three-Loop Radiative-Recoil Corrections to Hyperfine Splitting in Muonium: Diagrams with Polarization Loops
• Three-Loop Radiative-Recoil Corrections to Hyperfine Splitting Generated by One-Loop Fermion Factors
• Three-Loop Contributions to Hyperfine Splitting: Muon Loop Light-by-Light Insertion and Other Closed Lepton Loops
• Three-Loop Radiative-Recoil Corrections to Hyperfine Splitting in Muonium
• Light-by-Light Scattering Single-Logarithmic Corrections to Hyperfine Splitting in Muonium