  Muonium is a bound state composed of an antimuon and an electron, and it
constitutes a hydrogen-like atom. Because of the absence of the hadronic matter
in the bound state, the muonium is a useful probe to explore new physics being
free from the hadronic uncertainties. The process of the muonium-to-antimuonium
transition is considered to be effective to identify fundamental interactions
which relate to the lepton flavor and lepton number violation. New experiments
are being planned at J-PARC in Japan and CSNS in China, and it is expected to
attract more attention in the near future. In this paper, we will study what
kind of model can be verified in the next generation of the
muonium-to-antimuonium transition search experiments while escaping the
limitations from other experiments. Though the transition probability is
strongly suppressed by the lepton flavor conservation in the standard model, it
can be much larger by the exchanges of neutral and doubly charged bosons, and
by box loop diagrams in new physics beyond the standard model. We study the
neutrino models with heavy Majorana neutrinos at TeV scale, a type-II seesaw
model, left--right models, and models for radiative neutrino masses such as the
Zee-Babu model in particular, in addition to other possible models to induce
the sizable transition probability, which can be tested in the forthcoming
experiments.
