Two-Loop Polarization Contributions to Radiative-Recoil Corrections to Hyperfine Splitting in Muonium

Abstract

We calculate radiative-recoil corrections of order ${\alpha }^2(Z\alpha )(m/M)E_F$ to hyperfine splitting in muonium generated by the diagrams with electron and muon polarization loops. These corrections are enhanced by the large logarithm of the electron-muon mass ratio. The leading logarithm cubed and logarithm squared contributions were obtained a long time ago. The single-logarithmic and nonlogarithmic contributions calculated here improve the theory of hyperfine splitting, and affect the value of the electron-muon mass ratio extracted from the experimental data on the muonium hyperfine splitting.

15 pages, 11 figures

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