The kaon nucleon interaction

Abstract

The K-matrix formalism for the low energy KN interaction is reviewed. By using the N/D method to compute the scattering matrix for left hand singularities chosen to approximate the physical singularities of the KN and ΣΤ amplitudes the nature of the energy dependence of the inverse K-matrix elements are investigated. From this it is concluded that an effective range parameterisation should be a good approximation to the inverse K-matrix elements and that the off diagonal elements of the effective range matrix may not, ά priori, be neglected. The application of dispersion relations to the prediction of the strange particle coupling constants is discussed. A once subtracted sum rule is introduced which reduces the discrepancy in the prediction of the coupling constants due to the use of different low energy parameterisations for the KN amplitude. The resultant prediction of the coupling constants is incompatible with the SU(3) predictions. A new S-wave zero range fit to the low energy KN data is performed. A good fit is obtained which improves on previous analyses over the low energy KN region. The values of the coupling constants predicted by the standard dispersion relation using this parameterisation are again incompatible with the SU(3) predictions. Finally the effect of the non-negligible P waves in the isospin one channel are investigated using a constant scattering length parameterisation for these waves in the analysis of the low energy KN data.