Muonium-Antimuonium oscillations and massive Majorana neutrinos

The electron and muon number violating muonium-antimuonium oscillation process can proceed provided neutrinos have non-zero masses and mix among the various generations. Modifying the Standard Model only by the inclusion of singlet right handed neutrino fields and allowing for general neutrino masses and mixings, the leading order matrix element contributing to this process is computed. For the particularly interesting case where the neutrino masses are generated by a see-saw mechanism with a very large Majorana mass $M_R>>M_W$, it is found that both the very light and very heavy Majorana neutrinos each give comparable contributions to the oscillation time scale proportional to $M_R^2$. Present experimental limits set by the non-observation of the oscillation process sets a lower limit on $M_R$ of roughly of order $10^4$ GeV.