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 would certainly shed light on the ∼2 ppm 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 us to extract muon g-2 with high precision. Improving the accuracy of QED calculations of these transitions by about 1 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.