Resonance-sum model for Reggeization in the scattering of particles with arbitrary spin

Abstract

Using a field-theoretic description of nonzero-spin particles, we have obtained center-of-mass helicity amplitudes corresponding to pole terms in four-particle reactions with arbitrary-spin external particles. We have discussed how to construct a van Hove-Durand-type model starting from these helicity amplitudes (which have a well specified kinematic structure in the field-theoretic description). Special attention has been paid to boson-fermion scattering. Straightforward Reggeization of helicity amplitudes assuming linear trajectories is known to produce parity doubling. Because of the generalized MacDowell symmetry of the helicity amplitudes, cuts appear in the $J$ plane which prevent the occurrence in our model of parity-degenerate states in the physical $J$ plane. One cannot have a pure fermion Regge pole unaccompanied by cuts. This conclusion has important consequences on both fitting data using Regge formulas in, say, backward scattering in boson-fermion scattering and theoretical considerations such as dual bootstrap models.