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

Abstract

We study the lepton-flavor-violating reaction ${\ensuremath{\mu}}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}}$ 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 $M\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}}$ 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 ${e}^{+}{e}^{\ensuremath{-}}$ the extremely small result $Br(M\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}})l{10}^{\ensuremath{-}19}$ in both scenarios. Alternatively, for ${\ensuremath{\mu}}^{+}{e}^{\ensuremath{-}}$ collisions up to $\sqrt{s}\ensuremath{\sim}50\text{ }\text{ }\mathrm{GeV}$, we find $\ensuremath{\sigma}({\ensuremath{\mu}}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}})l{10}^{\ensuremath{-}5}\text{ }\mathrm{fb}$, while for energies above the ${W}^{+}{W}^{\ensuremath{-}}$ threshold we find $\ensuremath{\sigma}({\ensuremath{\mu}}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{W}^{+}{W}^{\ensuremath{-}})$ up to $\ensuremath{\sim}1\text{ }\mathrm{fb}$.