Muon decays with lepton-number violation via vector leptoquark

The decays μ → eγ, μ → eγγ, and μ → eee are analysed in the framework of the Pati-Salam type quark-lepton symmetry SU (4) v ⊗ SU (2) L ⊗ GR where the effects of mixing in the quark-lepton currents are taken into account. It is shown that the μ → eγγ and μ → eee decays via the vector leptoquark have not a GIM-type suppression, while the μ → eγ decay has So, the specific hierarchy of the decay probabilities could take place Г (μ → eee) ⪢ Г(μ → eγγ) ⪢ Г(μ → eγ). The existing bounds on the vector leptoquark mass on the mixing matrix elements, based on the data for the μe conversion in nuclei and for the ratio of the Ke2 and Kμ2 decays allow to set the upper limits on the branching ratios at a level of 10−18 for the μ → eγγ decay at a level of 10−15 for the μ → eee decay.