Derivative sum rules and inconsistencies in the low-energy [formula omitted]N scattering parameters

Abstract

The KNΛ and KNΣ coupling constants predicted by kaon-nucleon forward dispersion relations are particularly sensitive to the parametrization used to extrapolate the K N scattering amplitude into the unphysical region. The dispersion relations which have hitherto been considered do not provide a sufficiently stringent and unambiguous consistency test to discriminate between alternative parametrizations which have been proposed. New sum rules are derived from the condition that the coupling constants defined by the dispersion relations should be energy-independent. Although these sum rules utilize the same input data as the conventional dispersion relations, they are entirely independent of the values of the coupling constants and provide a strong consistency requirement. Numerical tests of the sum rules show that all recent parametrizations of the low-energy K N scattering amplitude are inconsistent with the remainder of our knowledge of kaon-nucleon interactions. It is suggested that future parametrizations of the experimental data should incorporate more theoretical constraints.