Effective range for K⁺-nucleon interaction from dispersion relations

Abstract

An exact formula for the effective range for K⁺-P interaction, in the S-wave approximation, has been deduced using dispersion theoretic techniques. It is shown that if the assumption of zero effective range which is generally used for a phenomenological fit of K-N data, is valid then our analysis clearly indicates that the K-meson-hyperon relative parity must be odd (the Σ-Λ relative parity being even). The contribution of the dispersion integral over the unphysical region has been fully taken into account in the present analysis. A general discussion of the nature of the coupling is given for a non-vanishing but small effective range. The advantage of the use of the effective range formula to determine the sign of the relative parities is also pointed out.