could imagine that low energy pion scattering measurements could distinguish between (1) and (2). However, by its very nature that occurs in the weak field limit, so the measurements would have to be very precise. Also, low energy pion scattering is influenced by the tails of resonances, such as the $\rho$ meson [@dono], which would tend to mask the effects of the nonlinear symmetry breaking terms. We are not aware of any experimental evidence which prefers one symmetry breaking term over the other. In this paper we shall not consider the possibility [**3**]{}.

If one insists on an effective Lagrangian which is rotationally invariant and renormalizable, then the most general symmetry breaking potential can be written as $$V_{SB} \,=\, - \sum_{n=1}^4 \frac{\epsilon_n}{n!}\sigma^n
\,+\, (\delta_1\sigma + \delta_2 \sigma^2)
\mbox{\boldmath $\pi$}^2 \,.$$ Other symmetry breaking terms one might think of adding simply amount to a redefinition of the 8 parameters $\lambda, c, \epsilon_n, \delta_n$. Relaxation of the renormalizability condition would allow further terms but, as we shall see, there is already sufficient freedom to generate interesting physics. In what follows we will set $\delta_1 = \delta_2 = 0$, mainly for simplicity of presentation.

With the symmetry breaking potential as given above, the 