[@Schecht] has found a nonzero coefficient of a bilinear term in the three flavor [*nonlinear*]{} sigma model. We will not pursue the three flavor world in this paper, but it is certainly worth doing.

One might at first think that $\epsilon_n \propto m_q^n$ (where $m_q$ is the up or down quark mass) so that $\epsilon_1$ is much greater than $\epsilon_2$ and so on. We think it is quite possible that all $\epsilon_n \propto m_q$ and therefore of comparable magnitude (when scaled appropriately with $f_{\pi}$). The argument is that the sigma model is only a low energy effective model of QCD and all possible terms which are allowed should be included. Indeed, even if one started originally with only a linear symmetry breaking term $\epsilon_1'$, loop corrections would generate nonlinear terms. These nonlinear terms would have coefficients equal to $\epsilon_1'$ times some function of $\lambda$ and $c$. Since $\lambda$ and $c$ are big we expect that all $\epsilon_n \,
f_{\pi}^n$ would turn out to be comparable in magnitude.

For clarity of exposition we shall hereafter restrict our attention to the possibility that only $\epsilon_1$ and $\epsilon_2$ are nonzero. This is sufficient to parametrize the effective potential with the freedom to adjust 