Dynamical Calculations and Regge Trajectories in the Presence of Spin

Some new features of the Regge trajectory structure of scattering amplitudes for spinning particles, associated with the existence of a nonsense channel, are described. The restrictions imposed by smoothness in angular momentum on the input forces to dynamical calculations are then discussed. Some popular versions of the N/D method are not, in general, consistent with these restrictions, but can be made so by special choice of substractions. We illustrate these ideas in detail for the scalar-vector scattering amplitude. The characteristic new feature is a trajectory α0 which goes to zero in the limit of small coupling constant; it emerges naturally from the N/D method with our special subtractions. The dynamics of particles lying on this trajectory are curious, and may reflect a weakness of the N/D approximation rather than physics, since strong forces (large coupling constants) are not needed to bring it up to a physical value of the angular momentum. As an example, we perform a simple bootstrap calculation for pseudoscalar mesons, assuming that they lie on such a trajectory.