the top sector, associated to the heavy resonances $D_t^{cp'}$ and $D_t^{cp''}$ from $t^{cp}$. The custodial symmetry ensures an effective cancellation between these contributions. Note that, parametrically, the shifts from the gauge contributions in embeddings $[B1]$ and $[B2]$ follow the pattern $\delta g^{b_L}_{[B1]}/\delta g^{b_L}_{[B2]}=3/4$ and $\delta g^{b_R}_{[B1]}/\delta g^{b_R}_{[B2]}=1/2$, meaning that it is easier to achieve a large correction in case $[B2]$.

  ----------------- ------------------------------------------------------ -----------------------------------------------------------------------
      embedding                    $\delta g^{b_L}/(g/c_w)$                                       $\delta g^{b_R}/(g/c_w)$
   \[.1in\] $[T1]$     $\frac{1}{2}(\alpha_{D_t'}^2-\alpha_{D_t''}^2)$                                        -
   \[.1in\]$[T2]$                             -                                                               -
   \[.1in\]$[B1]$    $\frac{3}{2}\Delta g_{q2}+\frac{1}{2}\alpha_{D_b}^2$   $\frac{1}{2}\Delta g_{b}+\frac{1}{2}(\alpha_{D_2'}^2-\alpha_{D_2}^2)$
   \[.1in\]$[B2]$         $2\Delta g_{q2}+\frac{1}{2}\alpha_{D_b}^2$             $\Delta g_{b}+\frac{1}{2}(\alpha_{D_2'}^2-\alpha_{D_2}^2)$
      \[.1in\]                                                             
  ----------------- ------------------------------------------------------ -----------------------------------------------------------------------

  : $\delta g^{b_L}$ and $\delta g^{b_R}$ at leading order expanding in powers of vev insertions. The results correspond to the top and bottom embeddings of Eqs. (\[tembedding1\],\[tembedding2\],\[bembedding1\]) and (\[bembedding2\]).[]{data-label="tdeltagsym"}

Full diagonalization
--------------------

We have given perturbative arguments to show that it is possible to obtain the correct spectrum and $Zb\bar b$ couplings. The perturbative expansion in Higgs vev insertions is a good approximation for the gauge sector, but in general this is not true for the fermionic mixings since in this case $\sin\theta_\psi$ can be $\sim1$. For this reason it is better to make a numerical diagonalization of the mass matrices. In this section we will scan the parameter space and 