Unitarity Constraint on a Regge Trajectory in a Model Amplitude

Abstract

A representation is constructed for the elastic scattering of neutral scalar bosons with crossing symmetry, direct-channel poles, polynomial residues, and Regge behavior based on an arbitrary Regge trajectory. It is shown, within the context of a specific model, how the amplitude can approximately satisfy elastic unitarity. A purely linear trajectory is inconsistent with the unitarity constraint unless the amplitude is zero, while the addition of a complex threshold term of definite strength enables elastic unitarity to be numerically approximated.