Branch Points, Fixed Poles, and Falling Trajectories in the ComplexJPlane

By means of the $\frac{N}{D}$ equations, analytically continued in complex angular momentum, we consider the details of the mechanism by which cuts in the angular-momentum plane eliminate Gribov-Pomeranchuk singularities. The implications of the two-body unitarity requirement are investigated. A fixed $l$-plane pole in the signatured partial-wave amplitude is shown to exist where the first Gribov-Pomeranchuk singularity would be expected in the absence of cuts. It is also shown in this case that moving (Regge) poles are not asymptotic to the position of the fixed pole.