Radiative-Recoil Corrections to Muonium Hyperfine Splitting

This paper presents the results of an analytic calculation of radiative corrections to the leading recoil corrections in the muonium ground-state hyperfine splitting. The principal new results are of relative order ${\left(\frac{\alpha }{\pi }\right)}^2\left(\frac{m_e}{m_{\mu }}\right)\ln \left(\frac{m_{\mu }}{m_e}\right)$. Also presented is an estimate of the contribution of the hadronic term in the vacuum polarization. A contribution to the positronium ground-state hyperfine splitting of relative order ${\left(\frac{\alpha }{\pi }\right)}^2$, arising from vacuum polarization of exchanged photons, is also given.