Consistency tests of the low-energy K −p parametrizations

Abstract

The value of the ΛKN coupling constant g Λ 2 predicted by forward KN dispersion relations is particularly sensitive to the model used to continue the if K N amplitude into the unphysical region. The various parametrizations which have been used to analyse the low-energy K −p scattering data are reviewed and compared, and a simple consistency test of these parametrizations is proposed. The consistency condition is satisfied by the existing constant scattering length parameters and by a new constant K-matrix solution obtained by Martin and Sakitt, but not by the effective-range K-matrix parametrization of Kim. Other recently proposed consistency tests are discussed, and it is shown in particular that an argument used by Chan and Meiere to rule out the determination of g Λ 2 using constant scattering lengths is not valid, since the inconsistency found by them in this case is due entirely to the incorrect behaviour of the extrapolated amplitude at the Σπ threshold. It is concluded that, of the existing low-energy K −p parametrizations, only the constant scattering length and constant K-matrix solutions are consistent. Using either solution, the forward dispersion relations predict g Λ 2 ≈ 4, a value considerably smaller than thant suggested by SU(3) invariance.