On the superconvergence of meson-nucleon invariant scattering amplitudes

Using two models, i.e. perturbation theory with the usual PS-PS Hamiltonian and a “relativistic” version of the Lee model with the same type of interaction, it has been tried to clarify the question if there are superconvergent amplitudes in the (π, K) meson-nucleon forward scattering. Does the impressive validity of the well-known sum rule for theB ⁽⁺⁾ amplitude makes a serious support of the assumed superconvergence (becauseB describes the spin-flip scattering)? Indications, obtained from perturbation theory, including all Feynman diagrams up to the sixth order in the coupling constant and from the Lee model, where all allowed diagrams can be summed up, do not support the superconvergence assumption. Therefore the impressive prediction of theB ⁽⁺⁾ amplitude sum rule seems to be accidental.