Theoretical Difficulties with the Regge-Eikonal Model

Abstract

Dynamical models are used to discuss the theoretical justification of the Regge-eikonal formula for scattering amplitudes. A generalized ladder-diagram model with Reggeon exchange replacing single-particle exchange yields the eikonal result only if the Reggeon amplitude has no mass-shell dependence, since the intermediate-state particles are far from their mass shells at high energy. This result is contrasted with a nonperturbative model of a Regge-pole amplitude which has strong mass-shell dependence. Next, a theory in which the coupling of the Reggeons to the external particles is nonplanar is examined. The double-Reggeon-exchange amplitude does not satisfy the eikonal representation. The perturbation-theory model of Cicuta and Sugar is shown to break down if higher-order corrections to the residue function are calculated. The conclusion of the paper is that there does not exist any theoretical justification for considering the Regge-eikonal model to be a valid description of high-energy scattering.