sufficient to give mass to the gauge bosons, the top-pions and top-Higgs remain massless at tree level. Quantum corrections will give the top-pions a mass, however this loop-level mass is far too small to be consistent with experimental constraints. To generate phenomenologically acceptable masses for the top-pions and top-Higgs, we add two additional interactions: $$\mathcal L_M =  - \lambda\, {\rm Tr} 
   \left( M^{\dagger}M - \frac{f^2}{2} \right)^2 
   - \kappa f^2\, {\rm Tr} 
   \left| M - \frac{f}{\sqrt 2} \Sigma_{01}\Sigma_{12} \right|^2,
\label{eq:Vhiggs}$$ where the first of these interactions arises from topcolor interactions, and the second from ETC-like interactions [@Eichten:1979ah]. Here $\lambda$ and $\kappa$ are two new parameters, $f$ is the same vacuum expectation value appearing in Eq. , and $M$ is the $\Phi$ field expressed as a matrix, schematically given by $M = (\tilde \Phi, \Phi)$ with $\tilde \Phi = -i \sigma_2 \Phi^*$: $$M = \left( \begin{array}{cc}
     i \pi_t^+ & (f + H_t + i \pi_t^0)/\sqrt{2} \\
     (f + H_t - i \pi_t^0)/\sqrt{2} & i \pi_t^- \end{array} \right),$$ where $\pi_t^+ = (\pi_t^-)^*$. The first term in Eq.  depends only on the modulus of $M$, and therefore contributes only to the mass of the top-Higgs. The second term gives mass to both the top-Higgs 