  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 $\Delta
\nu^{th}_{\scriptscriptstyle HFS}(Mu)=4~463~302~872~(515)~\mbox{Hz},\;
\delta=1.2\times 10^{-7}$.
