s-Wave K-N scattering by the N/D method

Abstract

The K-N s-wave scattering lengths and effective-range parameters have been calculated for both isotopic spin states, using the N/D method. The nearby part of the interaction cut has been approximated by two poles, whereas following Balázs' procedure the entire distant cut has been replaced by two effective-range poles at predetermined positions, but with unknown residues. The residues of the effective-range poles are determined by matching the N/D amplitude with that calculated with a fixed energy dispersion relation, at two properly chosen points. In calculating the latter amplitudes only the contributions of Λ, Σ, Y₁*, ρ, and ω exchange terms are retained and the values of Y₁*, ρ, and ω coupling constants are taken from a unitary symmetry scheme. The calculated values of scattering length, effective range, and low-energy phase shifts for the I=1 state are in good agreement with the experimental results of Goldhaber et al. For the I=0 state, the calculated phase shifts are consistent with the large s-wave solution of Goldhaber et al.