Daughter Regge Trajectory in a Field-Theory Model. II

Abstract

Secondary Regge trajectories obtained from a high-energy perturbation-theory treatment of ladder diagrams are compared with those obtained from numerical solutions of the Bethe-Salpeter equation and are found to be qualitatively identical. In particular, the trajectories intersect, become complex, then become real again, all below threshold; they are very model-dependent. However, ladder diagrams in relativistic field theory do not completely determine the secondary trajectories; the self-energy correction to the exchange particle propagator must be included. This modification of ladder diagrams completely eliminates the pathological behavior of the secondary Regge trajectories and the sensitive dependence on the parameters of the model. The first daughter becomes a nonintersecting, everywhere real, slowly rising function of the energy. The requirement that a field theory have well-behaved secondary Regge poles imposes nontrivial constraints on possible interactions.