K-Meson Dispersion Relations. II. Applications

The present experimental data on $K^{+}$ and $K^{-}$ scattering on protons are used in the dispersion relations of the previous paper. The $\Lambda$ and $\Sigma$ parities are assumed to be both positive and the $K^{+}-p$ potential is taken to be repulsive. The dispersion relations then indicate that an attractive $K^{-}-p$ potential implies pseudoscalar $K$ mesons, and a repulsive $K^{-}-p$ potential implies scalar $K$ mesons. In both cases the coupling constants are of the order of unity. If data on $K-n$ scattering were available it would not be necessary to assume the relative parity for $\Lambda$ and $\Sigma$ hyperons, but this could also be determined from the dispersion relations.