are input parameters fixed by laboratory experiments. Surprisingly, however, their values, though unconstrained and [*a priori*]{} arbitrary, do display a certain degree of organization. The fermion masses are highly hierarchical and the CKM matrix can be described in terms of the small Wolfenstein expansion parameter $\lambda \sim |V_{12}| \sim 0.22$ [@LWolfenstein]. These results suggest that a broken flavour symmetry might be playing an important role in the setting of the structure of the Yukawa matrices.

In this work we will assume that the “vertical” gauge group is supplemented by an additional $U(1)_X$ “horizontal” flavour symmetry that constraints the nature of the couplings of quarks and leptons to SM singlet fields $\theta$ and $\bar\theta$. The family symmetry, however, is broken at some high energy scale $M_\theta > M_X$ by the VEVs of the $\theta$, $\bar\theta$ fields which under the $U(1)_X$ group have charges $X_\theta = -1$ and $X_{\bar\theta}= +1$. As a consequence of the $U(1)_X$ symmetry breaking, the low energy effective theory includes Dirac interactions between the $F$ and $F^c$ fields of the following form : $$F_A F^c_B h  \left( {\theta}
                    \over M_V \right)^{p_{AB}} \to
F_A F^c_B h \left( \langle\theta\rangle 
                   \over M_V \right)^{p_{AB}} \sim
F_A F^c_B h \epsilon^{p_{AB}}
\label{NonRenTheta}$$ $$F_A F^c_B 