  Sigma models are exhibited which have tree amplitudes for Goldstone boson
scattering that satisfy elastic unitarity exactly. The models have imaginary
coupling constants and the scalar propagators have poles on the imaginary axis
in the complex p^2 plane. They are equivalent to K-matrix models, which are ad
hoc unitarizations of low energy theorems for Goldstone boson scattering that
have been used recently to describe strong WW scattering. The sigma model
formulation of the K-matrix models may be used to estimate directly the effect
of strong WW scattering on low energy radiative corrections.
