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

We study the lepton-flavor-violating reaction μ+e-→e+e- 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→e+e- 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+e- the extremely small result Br(M→e+e-)<10-19 in both scenarios. Alternatively, for μ+e- collisions up to √(s)∼50 GeV, we find σ(μ+e-→e+e-)<10-5 fb, while for energies above the W+W- threshold we find σ(μ+e-→W+W-) up to ∼1 fb