On the parametrization of the Δ residue function

Abstract

The complex residues at the Δ(1236) and Δ(1950) poles in the relevant partial-wave amplitudes provide information on the behaviour of the Δ Regge residue function in the resonance region u > 0. Attempts to incorporate this information in parametrizations of the residue by functions that are real on the real u-axis result in residues which have unsatisfactory behaviour in the region u < 1 GeV 2. The choice of complex functions for the trajectory and residue removes this undesirable feature and provides a better representation of the residue in the resonance region, suggesting that complex parametrizations would be better suited to Regge analyses of near-backward scattering.