Muon decays with lepton--number violation via vector leptoquark

Abstract

The decays $\mu \to e\gamma$, $\mu \to e\gamma \gamma$, and $\mu \to ee\bar{e}$ 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 $\mu \to e\gamma \gamma$ and $\mu \to ee\bar{e}$ decays via the vector leptoquark have not a GIM--type suppression, while the $\mu \to e\gamma$ decay has. So, the specific hierarchy of the decay probabilities could take place $\Gamma (\mu \to ee\bar{e})\gg \Gamma (\mu \to e\gamma \gamma )\gg \Gamma (\mu \to e\gamma )$. The existing bounds on the vector leptoquark mass and on the mixing matrix elements, based on the data for the $\mu e$ conversion in nuclei and for the ratio of the $K_{e2}$ and $K_{\mu 2}$ decays allow to set the upper limits on the branching ratios at a level of $10^{-18}$ for the $\mu \to e\gamma \gamma$ decay and at a level of $10^{-15}$ for the $\mu \to ee\bar{e}$ decay.

Comments: 10 pages, LaTeX, Submitted to Phys.Lett.B