Chiral Symmetry Limit in the SU(3)σModel with Bilinear Breaking

We add to the usual $\sigma$ model a (3*, 3) + (3, 3*) term which is bilinear in the scalar-meson fields and study the behavior of the tree-approximation solutions as the explicit symmetry breaking is turned off. We find that both $c\simeq -\sqrt{2}$ and $c\simeq 0$ occur for the same mass spectrum, 0-8 mixing, and $\frac{F_K}{F_{\pi }}$. Solutions with different $c$ values approach the symmetry limit differently, but in this limit one can smoothly reach either a Goldstone pseudoscalar octet, or a symmetric vacuum, or neither for both values of $c$. No clear indication is found that solutions are near a critical value of the mass parameter.