Towards an independent determination of muon g-2 from muonium spectroscopy

We show that muonium spectroscopy in the coming years can reach a precision high enough to determine the anomalous magnetic moment of the muon below one part per million (ppm). Such an independent determination of muon g-2, which is not limited by hadronic uncertainties, would certainly shed light on the 2ppm difference currently observed between spin-precession measurements and (R-ratio based) Standard Model predictions. The magnetic dipole interaction between electrons and (anti)muons bound in muonium gives rise to a hyperfine splitting (HFS) of the ground state which is sensitive to the muon anomalous magnetic moment. A direct comparison of the muonium frequency measurements of the HFS at J-PARC and the 1S-2S transition at PSI with theory predictions will allow to extract muon g-2 with high precision. Improving the accuracy of QED calculations of these transitions by about one order of magnitude is also required. Moreover, the good agreement between theory and experiment for the electron g-2 indicates that new physics interactions are unlikely to affect muonium spectroscopy down to the envisaged precision.