and the physical (uneaten) combination of pion fields, as we will show shortly. Because these masses depend on two parameters, $\lambda$ and $\kappa$, we can treat the mass of the top-Higgs and the common mass of the uneaten top-pions as two independent parameters. In addition to generating masses, the potential in Eq.  also induces interactions between the top-Higgs and top-pions which can be important.

Finally, we note that the mass terms for the light fermions arise from Yukawa couplings of the fermionic fields with the nonlinear sigma fields $$\begin{aligned}
\mathcal{L} & = & M_{D}\left[\epsilon_{L}\bar{\psi}_{L0}\Sigma_{01}\psi_{R1}+\bar{\psi}_{R1}\psi_{L1}+\bar{\psi}_{L1}\Sigma_{12}\left(\begin{array}{cc}
\epsilon_{uR} & 0\\
0 & \epsilon_{dR}\end{array}\right)\left(\begin{array}{c}
u_{R2}\\
d_{R2}\end{array}\right)\right].
\label{eqn:Light fermion mass}\end{aligned}$$ We have denoted the Dirac mass that sets the scale of the heavy fermion masses as $M_D$. Here, $\epsilon_{L}$ is a parameter that describes the degree of delocalization of the left handed fermions and is flavor universal. All the flavor violation for the light fermions is encoded in the last term; the delocalization parameters for the right handed fermions, $\epsilon_{fR}$, can be adjusted to realize the masses and mixings of the up and down type fermions. The mass of the top quark arises from similar terms with a unique left-handed delocalization parameter $\epsilon_{tL}$ and also 