Unitary Multiperipheral Models

Abstract

The method of constructing unitary $S$ matrices developed in a recent paper is generalized and applied to two versions of the multiperipheral model. In these models the standard perturbation expansion of the $S$ matrix diverges, so an alternative expansion with improved convergence properties is developed. It is shown that the unitarity condition generates a new type of cut in the angular momentum plane which is dynamical in origin in contrast to the essentially kinematical Mandelstam cuts. This new type of cut ensures that the Froissart bound on the total cross section is obeyed. In an exactly solvable model it is shown that the contribution of the multi-Regge region of phase space to the total cross section always decreases as a power of the energy if the input Regge trajectory is unity or less. It is argued that the qualitative features of the models discussed here will hold for a wide class of multiperipheral-like models.