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

We study the lepton-flavor-violating reaction μe → ee 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 → ee and in the high energy regime of a muon collider. The two theoretical models we consider are: model I, a typical see-saw 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 ee the extremely small result Br(M → ee) < 10 in both scenarios. Alternatively, for μe collisions up to √ s ∼ 50 GeV we find σ(μe → ee) < 10 fb, while for energies above the WW threshold we find σ(μe → WW) up to ∼ 1 fb.