Lepton flavor violation in muonium decay and muon colliders in models with heavy neutrinos

We study the lepton-flavor-violating reaction {mu}{sup +}e{sup -}{yields}e{sup +}e{sup -} within two extensions of the standard model that include heavy neutrinos. The reaction is studied in the low energy limit in the form of muonium decay M{yields}e{sup +}e{sup -} and in the high energy regime of a muon collider. The two theoretical models we consider are: model I, a typical seesaw model that violates lepton flavor and number by inclusion of extra right-handed neutrinos; and model II, a variant where lepton number is conserved and which includes extra right-handed as well as left-handed neutrinos, singlets under the gauge group. We find for muonium decay into e{sup +}e{sup -} the extremely small result Br(M{yields}e{sup +}e{sup -})<10{sup -19} in both scenarios. Alternatively, for {mu}{sup +}e{sup -} collisions up to {radical}(s){approx}50 GeV, we find {sigma}({mu}{sup +}e{sup -}{yields}e{sup +}e{sup -})<10{sup -5} fb, while for energies above the W{sup +}W{sup -} threshold we find {sigma}({mu}{sup +}e{sup -}{yields}W{sup +}W{sup -}) up to {approx}1 fb.