Phase Contours of Scattering Amplitudes. III. High-Energy Behavior at Fixed Angles

The method of phase contours is applied to some problems concerned with scattering at fixed angles. The crossing-symmetric generalized Regge model developed in a previous paper is used to illustrate possible characteristics of the behavior of scattering amplitudes. These characteristics are discussed both in the complex energy plane at fixed angle and in the complex $cos\theta$ plane at fixed high energy. The former leads to a procedure for studying fixed-angle behavior by means of entire functions on whose orders some limits can be established. The latter leads to a generalization of the lower bounds on high-energy behavior obtained earlier by Cerulus and Martin, and by Chiu and Tan.