Colliding Regge Poles and Cuts

A class of models describing the collision of Regge poles and their associated Mandelstam branch cuts is described, from which one concludes that Regge trajectories generally develop left-hand branch cuts as a result of such collisions, and in terms of which the singularities in the $l$ plane of the partial-wave amplitude and the asymptotic behavior of the scattering amplitude can be discussed.