Dispersion Relations for Pion-Hyperon Production and a Possible Pion-Hyperon Resonance

Abstract

Approximate $P$-wave dispersion relations are derived, but not proved, for the processes $\overline{K}+N\to \pi +\Sigma (or \Lambda )$ under the assumption that all pion-baryon and $K$-baryon interactions are of the odd intrinsic-parity, Yukawa type. By comparing these equations with the analogous equations for pion-hyperon scattering, it is shown that a low-energy resonance is likely to occur in a particular combination of the isotopic spin one, $P_{\frac{3}{2}}$, $\pi +\Lambda$ and $\pi +\Sigma$ scattering states, and this resonance should be recognizable in the $\pi +Y$ production processes. Despite complications associated with the unphysical region in the $\pi +Y$ production dispersion relations, and with the fact that the $K$ interactions are moderately strong, the resonance should occur in the production process in a direct and simple way. Measurements of the cross section for production of this resonance state can give information about the strengths of the strong interactions, particularly the pion-baryon interactions. The present experimental evidence concerning the existence of such a resonance effect in $\pi +Y$ production is favorable, but inconclusive. A short discussion is given of the additional experimental information needed to test the resonance hypothesis.