Improved theory of the muonium hyperfine structure

Terms contributing to the hyperfine structure of the muonium ground state at the level of few tenths of kHz have been evaluated. The α³(Z{α}) radiative correction has been calculated numerically to the precision of 0.02 kHz. Leading ln(Z{α}) terms of order α^4-n(Z{α})ⁿ, n=1, 2, 3, and some relativistic corrections have been evaluated analytically. The theoretical uncertainty is now reduced to 0.17 kHz. At present, however, it is not possible to test QED to this precision because of the 1.34 kHz uncertainty due to the muon mass.