Branch Points in the Complex Angular Momentum Plane and High-Energy Behavior of Scattering Amplitudes

The high-energy behavior of scattering amplitudes is investigated by analyzing the contribution from a certain class of Mandelstam branch points in the complex angular momentum plane. We denote symbolically, for example, by nP the branch point generated by n-Pomeranchon exchange. It is shown that the totality of the contributions from the branch points of the type $X+nP$ (n=1,2,⋯) gives an oscillatory behavior to scattering amplitudes at high energies, and that it results in a simple modification of the one-Regge-pole (X) contribution in the impact-parameter formalism. For the branch points of the type nX (n=2,3,⋯; X≠P), the concept of an effective trajectory is introduced. High-energy proton-proton scattering at 90^∘{} is explained by the effective trajectory generated by the branch points of the type (n-m)P^'+mω (n=2,3,⋯; m=0,⋯,n).