Fermion trajectory parametrization and superconvergence

Abstract

A parametrization of the nucleon and Δ trajectory is given, using both the position and the width of the resonances in a dispersion relation. The nucleon trajectory requires and accommodates a D-wave πN resonance in the neighborhood of 1670 MeV. Another significant outcome of the scheme is that the Δ trajectory has an intercept, at W=0, of -0.69 and hence leads to a superconvergence relation for πp scattering invariant amplitudes in the nearly backward direction (u=0). The resulting sum rules are satisfied only if there exists a strong attractive s-wave interaction (for example, a σ meson) or other equivalent effects (such as an f meson) in the ππ→NN̅ channel.