The kaon nucleon interaction

Abstract

A new forward dispersion relation is developed to describe the kaon nucleon interaction by observing that the real part of resonant partial wave amplitude goes through a zero at the resonance position. This relation eliminates some of the practical deficiencies inherent in the conventional forward dispersion relations. The nKN and ΣKN coupling constants are determined by using the combinations of dispersion relations suggested by Lusignoli et al. evaluated at the kaon nucleon threshold. Initially the energy independent scattering lengths of Kim are used to parametrise the K(^-)N amplitudes in the low energy region in terms of a single channel s-wave zero-range approximation. Just above threshold the K(^+)N amplitudes are parametrised in terms of the constant s-wave scattering lengths and effective range terms found by Goldhaber et al. and Stenger et al. Subsequently, the K(^-)N s-wave scattering lengths are given an energy dependence in the unphysical region through the multi-channel K matrix formalism. Various constraints are placed on these I = 0 K(^-)N scattering lengths such that the constant elements ɤₒ, βₒ, ɤₒ of the corresponding R-matrix should reproduce the Yₒ*(1405) resonance with its correct position and width in the Σπ-Σπ channel, and also the values of the energy independent scattering lengths at the K(^-)N threshold. Furthermore, an energy dependence is then introduced ɤₒ, βₒ, ɤₒ. Similarly, using the 1=1 K(^-)N energy independent and dependent scattering lengths in the appropriate dispersion relation gives an equation for the ΣKN coupling constant which involves the p-wave Y*(1385) resonance. The effects of this resonance are approximated in terms of its position and width and the Y*(_1)KN coupling constant. A brief survey of previous determinations of the n, Σ coupling constants shows that these predictions are consistent within the large errors, except for a very recent calculation performed by Kim. By differentiating specific forward dispersion relations an attempt is made to calculate the nKN, ΣKN and Y*KN coupling constants explicitly. However, the results indicate a slight inconsistency in the values obtained from conventional forward dispersion relations, while the predictions of the new relations are reasonable within the large errors. Finally, the predictions of the new relations are conpared with the experimental data for the K-(^+)p interactions and the charge exchange processes. The results are found to be in good agreement.