Hyperfine splitting in muonium: Accuracy of the theoretical prediction

In the last twenty years, the theory of hyperfine splitting in muonium developed without any experimental input. Finally, this situation is changing and a new experiment on measuring hyperfine splitting in muonium is now in progress at J-PARC. The goal of the MuSEUM experiment is to improve by an order of magnitude experimental accuracy of the hyperfine splitting and muon-electron mass ratio. Uncertainty of the theoretical prediction for hyperfine splitting will be crucial for comparison between the forthcoming experimental data and the theory in search of a possible new physics. In the current literature estimates of the error bars of the theoretical prediction differ roughly by a factor of two. We explain the origin of this discrepancy and obtain the theoretical prediction for the muonium hyperfine splitting Delta nu(th)( )(HFS)(Mu) = 4 463 302 872 (515) Hz, delta = 1.2 X 10(-7). (C) 2019 The Author(s). Published by Elsevier B.V.