Abstract
We present results for the corrections of order ${\ensuremath{\alpha}}^{2}(Z\ensuremath{\alpha}){E}_{F}$ to the hyperfine splitting of muonium. We compute all the contributing Feynman diagrams in dimensional regularization and a general covariant gauge using a mixture of analytical and numerical methods. We improve the precision of previous results.
Highlights
Muonium is the hydrogen-like bound state of a positive muon and an electron
Any other bound state involving hadrons, muonium is free from the complications introduced by the finite size or the internal structure of any of its constituents
The value of μμ/μp is required for obtaining the muon anomalous magnetic moment from experiment [2]
Summary
Muonium is the hydrogen-like bound state of a positive muon and an electron. Any other bound state involving hadrons, muonium is free from the complications introduced by the finite size or the internal structure of any of its constituents. It allows for a very precise test of bound-state QED and can be used to restrict models of physics beyond the standard model. We are interested in corrections to the hyperfine splitting of the ground state of muonium of order α2(Zα)EF and leading order in m/M, where. G is the gyromagnetic factor of the nucleus1 [in our case, a muon, but our final result in Eq (19) applies to any hydrogen-like atom]. The triplet and singlet states are often denoted by the prefixes ortho- and para-, respectively, and their wave functions are given by [8]
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