Order(memμ)α2lnα−1Corrections to the Muonium Hyperfine Structure

Abstract

We report a calculation of the $\left(\frac{m_e}{m_{\mu }}\right){\alpha }^2\ln {\alpha }^{-1\mathrm{}}$ corrections to the hyperfine splitting (${\nu }_m$) of the muonium ground state. The result, $\Delta {\nu }_m=24\mathrm{}{\left(\frac{m_e}{m_{\mu }}\right)}^2{[1+(\frac{m_e}{m_{\mu }}\left)\right]}^{-5\mathrm{}}c{\alpha }^4{R}_{\infty }\ln {\alpha }^{-1\mathrm{}}=0.0252\mathrm{}$ MHz (5.6 ppm), shifts the theoretical value for ${\nu }_m$ to within one standard deviation of the most recent experimental determination of the muonium hyperfine interval by the Chicago-Illinois group.