$-\frac{g_{0}}{2 \cos\theta} \cos\omega 
                                                  \left[1 + \frac{x^2}{8} \left(1 + 2\cos 2\theta \right) \sec^2\theta 
                                                                     \right](p_H - p_{\Pi^0})_{\mu}$

        $H_t \Pi_t^0 Z^{\prime}_{\mu}$                        $\frac{g_{0} x}{4 \cos\theta} \cos\omega 
                                                            \sec\theta \cos 2\theta (p_H - p_{\Pi^0})_{\mu}$
  ----------------------------------------------------------------------------------------------------------------------

  : \[tab:H-couplings\] Three-point couplings of the top-Higgs, again calculated to $\mathcal{O}(x^2)$. The Feynman rules for the couplings involving two gauge bosons are obtained by multiplying the coupling strength given here by $i g_{\mu\nu}$.

Notice in particular that the couplings of the heavy gauge bosons $Z^{\prime}$ and $W^{\prime \pm}$ to two top-pions are proportional to the large gauge coupling $\tilde g = g_0/x$ associated with site 1. The leading term in these couplings is in fact $\tilde g \sin^2\omega/2$, with the two $\sin\omega$ factors reflecting the overlap of the $\Pi_t^a$ wavefunction with the combination of nonlinear sigma fields $(\pi_0^a
+ \pi_1^a)/\sqrt{2}$. The couplings of the top-Higgs and top pions to third generation fermions (and their heavy partners) can be likewise computed, by plugging in the mass eigenstates into the top quark mass term, Eq. , with $\Phi$ is given by Eq. ). The results are shown in Table IV, written in terms of the parameter $a= v\,\textrm{sin}\,\omega/ \sqrt{2}M_{D}$.

We have also worked out the four-point interactions. While these are less important phenomenologically, 