the mixing angles of the top. After EWSB there are new mixings between the SM states and the heavy resonances, as well as mixings between the three generations arising from non-diagonal composite Yukawa couplings. However we do not attempt to make a theory of flavour in this work, for this reason we will consider diagonal Yukawa couplings and neglect the mixing effects.

The mixings of Eq. (\[Lmix\]) preserve a SU(3)$_c\times$SU(2)$_L\times$U(1)$_Y$ gauge symmetry. The gauge boson couplings are given by: $$\label{gSM}
g=\frac{g_{el}g_{cp}}{\sqrt{g_{el}^2+g_{cp}^2}} \ ,$$ where we have omitted a group index for notation simplicity.

After diagonalization of the elementary/composite mixing the massless fermions couple with the composite vector bosons $A^*$ with couplings depending on the mixing angle [@Contino:2006nn]: $$\label{gA*}
{\cal L}\supset - g\ \bar\psi_L {{\not \!\!A}}^*(\cos^2\theta_\psi\tan\theta_A-\sin^2\theta_\psi\cot\theta_A) \psi_L + \{L\leftrightarrow R,\psi\leftrightarrow\tilde\psi\}\ .$$ Note that for $\psi_L$ almost elementary this interaction does not depend on $\theta_\psi$ at leading order, thus we obtain an almost universal coupling for the fermions with small mixing, approximately given by $-g \tan\theta_A$, that is suppressed compared with the gauge coupling $g$ for $g\ll g_{cp}$. On the other hand, if $\psi_L$ is mostly composite, the coupling is large and it is approximately given by $g \cot\theta_A\sim g_{cp}$.

Inspired by 