Low-Energy Zeros and Regge Poles from an Extended Amati-Bertocchi-Fubini-Stanghellini-Tonin Multiperipheral Model

Abstract

By inserting the elastic absorptive part from a multiperipheral model into a fixed-momentum-transfer dispersion relation, it is possible to obtain the low-energy amplitude in the crossed channel. We use the ABFST (Amati-Bertocchi-Fubini-Stanghellini-Tonin) version of this model so that the amplitude satisfies a BS (Bethe-Salpeter) equation. The Veneziano model for the $\ensuremath{\pi}\ensuremath{\pi}$ amplitude is used to calculate the ABFST input kernel, for which off-shell effects are neglected. We go beyond the usual pion-exchange dominance of the ABFST model by including an "inelasticity" factor in our BS equation. The strength of this factor is fixed by requiring that the Chew-Mandelstam $\ensuremath{\pi}\ensuremath{\pi}$ symmetry-point crossing condition is satisfied. It is then found that zeros arise in the $S$-wave amplitudes, which can presumably be identified with the zeros which are predicted from the Adler self-consistency condition. As a by-product, we also calculate the leading Regge trajectories in our model. These have no difficulty in rising to fairly high angular momenta and lead to relatively narrow reduced widths for the $\ensuremath{\rho}$ and ${f}^{0}$ resonances, as well as a high-energy total cross section in approximate agreement with experiment.