the mass of the heavy partner of the top quark. We will set $M_D$ to the illustrative value $M_D = 400$ GeV in calculations not depending strongly on the precise value, and will otherwise show how results vary with $M_D$.

Within the top-pion sector we will set $M_{H_t}$ and $M_{\Pi_t}$ to the illustrative values $M_{H_t} = 250$ GeV and $M_{\Pi_t} = 200$ GeV when the precise value is not critical and will otherwise show how results vary with the values of these masses. Likewise, we will allow $\sin\omega$ to vary to show how various physical quantities depend on it; when the dependence is not critical, we will tend to use the illustrative value $\sin\omega = 0.5$.

The remaining parameters, $x$ and the top Yukawa coupling $\lambda_t$, are now derived from the quantities above via: $$\begin{aligned}
x &=& \sqrt{2} \, \epsilon_L = \frac{2 \cos\omega M_W}{M_{W^{\prime}}} \nonumber \\
\lambda_t &=& \frac{\sqrt{2} \, m_t}{v \sin\omega}
\left[ \frac{M_D^2 (\epsilon_L^2 + 1) - m_t^2}{M_D^2 - m_t^2} \right],
\label{eq:lambdat}\end{aligned}$$ where $m_t$ is the physical top quark mass and in the last expression we have set $\epsilon_{tR} = 0$. The relationship between $\epsilon_L$ and $x$ is imposed by ideal delocalization; similarly, as discussed below in subsection IV.A.3, 