Baryon and lepton number violating effective operators in a non-universal extension of the Standard Model

It is well known that non-abelian Yang-Mills theories present non-trivial minima of the action, the so-called instantons. In the context of electroweak theories these instanton solutions may induce violations of baryon and lepton number of the form $\Delta B = \Delta L = n_f$, with $n_f$ being the number of families coupled to the gauge group. An interesting feature of these violations is that the flavor structure of the gauge couplings is inherited by the instanton transitions. This effect is generally neglected in the literature. We will show that the inclusion of flavor interactions in the instanton solutions may be interesting in certain theoretical frameworks and will provide an approach to include these effects. In particular we will perform this implementation in the non-universal $SU(2)_l \otimes SU(2)_h \otimes U(1)_Y$ model that singularizes the third family. Within this framework, we will use the instanton transitions to set a bound on the $SU(2)_h$ gauge coupling.