Relation between the Multi-Regge Model and the Amati-Bertocchi-Fubini-Stanghellini-Tonin Pion-Exchange Multiperipheral Model

Abstract

The 1962 Amati-Bertocchi-Fubini-Stanghellini-Tonin (ABFST) multiperipheral model, with a kernel based on an up-to-date guess for the elastic $\ensuremath{\pi}\ensuremath{\pi}$ cross section, is used to illuminate certain controversial concepts that have arisen in multi-Regge models. The small magnitude of the elastic $\ensuremath{\pi}\ensuremath{\pi}$ cross section above the region of prominent resonances is related to the small diffraction-dissociation cross section and to the small Pomeranchon coupling constant in the Chew-Pignotti (CP) model. Although lower trajectories in the multi-Regge kernel give an inadequate representation of low-subenergy resonances, we show that an artificial CP-model input can be found which roughly simulates the resonance component of the ABFST kernel. Byproducts of our investigations are (1) a generalization of the Berestetsky-Pomeranchuk formula that provides a practical basis for exact numerical evaluation of the ABFST model at any energy, and (2) a perturbative analysis of diffractive dissociation (d.d.) which reconciles a small d.d. cross section at accessible energies with a total cross section that becomes entirely of the d.d. type in the extreme high-energy limit.