Lepton mass generation and family number violation mechanism in the $SU(6)\otimes U(1)$ model

Lepton family number violation processes arise in the $SU(6)_L \otimes U(1)_Y$ model due to the presence of an extra neutral gauge boson, Z$'$, with family changing couplings, and due to the fact that this model demands the existence of heavy exotic leptons. The mixing of the standard Z with Z$'$ and the mixing of ordinary leptons with exotic ones induce together family changing couplings on the Z and therefore nonvanishing rates for lepton family number violation processes, such as $Z \to e \bar{\mu}$, $\mu \to ee\bar{e}$ and $\mu \to e\gamma$. Additional contributions to the processes $\mu \to e \gamma$ and $\mu \to ee \bar{e}$ are induced from the mass generation mechanism. This last type of contributions may compete with the above one, depending on the masses of the scalars which participate in the diagrams which generate radiatively the masses of the charged leptons. Using the experimental data we compute some bounds for the mixings parameters and for the masses of the scalars.