Indication forK,Λ,ΣRelative Parities from Effective-Range Analysis ofK+pScattering

Abstract

From dispersion relations an effective range formula is derived for $K^{+}p$ scattering. In the expression for the effective range, the integrals over the cross sections are certainly convergent and weighted against the contributions from the unphysical region. This expression is then analyzed under the experimentally suggested hypothesis of rather constant $K^{+}p$ cross sections up to ∼110 Mev; it is observed that the effective range is rather energy independent and the integrals contributing to it are estimated to be all of the same sign. The expression for the effective range is then quantitatively evaluated, and it is shown that the comparison with the low-energy dependence of ${\sigma }^{+}$ indicates equal $\Lambda$ and $\Sigma$ parities with opposite $K$ parity ($K$ pseudoscalar). The possibility of evaluating the coupling constants from the low-energy behavior of the $K^{+}p$ cross section is then briefly discussed.