h  \left( {\bar\theta}
                    \over M_V \right)^{p_{AB}} \to
F_A F^c_B h \left( \langle\bar\theta\rangle 
                   \over M_V \right)^{p_{AB}} \sim
F_A F^c_B h \epsilon^{p_{AB}}
\label{NonRenThetaBar}$$ where $p_{AB}$ is the modulos of the sum of the $U(1)_X$ charges of the $F_A$, $F^c_B$ and $h$ fields, [*i.e.*]{} $p_{AB} = |X_{AB}| = |X_{F_A}+X_{F^c_B}+X_h|$. Thus Eq.  holds if $X_{AB} > 0$ whereas Eq.  holds if $X_{AB} < 0$. The non-renormalizable terms in Eqs. , might originate from interactions between the $F$ and $\theta$ fields with additional exotic vector matter with mass $M_V > M_X$ that lead to “spaghetti” diagrams as discussed in Ref. [@AlKiSpaghetti]. In summary, the equations above show that, in the context of a $U(1)_X$ symmetry, the observed hierarchy in the fermion masses and mixing angles might be the result of the flavour charges carried by the fields of the 422 model which act to suppress the Yukawa couplings by some $\epsilon$-power.

The introduction of the $U(1)_X$ symmetry provides a way to relate the various flavour parameters of the model thus making it more predictive. However, one should be careful. Generally the $U(1)_X$ group is potentially dangerous since it can introduce, through triangle diagrams, mixed anomalies with the SM gauge group. [^10] In the last part 