Muon decays with lepton--number violation via vector leptoquark

Abstract

The decays $μ\rightarrow e γ$, $μ\rightarrow e γγ$, and $μ\rightarrow e e \bar e$ are analysed in the framework of the Pati-Salam type quark-lepton symmetry $SU(4)_V \otimes SU(2)_L \otimes G_R$ where the effects of mixing in the quark-lepton currents are taken into account. It is shown that the $μ\rightarrow e γγ$ and $μ\rightarrow e e \bar e$ decays via the vector leptoquark have not a GIM--type suppression, while the $μ\rightarrow e γ$ decay has. So, the specific hierarchy of the decay probabilities could take place $Γ(μ\rightarrow e e \bar e) \gg Γ(μ\rightarrow e γγ) \gg Γ(μ\rightarrow e γ)$. The existing bounds on the vector leptoquark mass and on the mixing matrix elements, based on the data for the $μe$ conversion in nuclei and for the ratio of the $K_{e 2}$ and $K_{μ2}$ decays allow to set the upper limits on the branching ratios at a level of $10^{-18}$ for the $μ\rightarrow e γγ$ decay and at a level of $10^{-15}$ for the $μ\rightarrow e e \bar e$ decay.