Unitarity in dual models

Abstract

The problem of imposing unitarity on dual models is discussed. We show how one can use the Cheng-Sharp equations, with the Khuri representation of a Regge-pole amplitude, to impose unitarity on the Regge parameters, which are then used as input to a FESR. The potential due to the crossed-channel poles is supposed to be contained already, at least in an average sense, in the direct channel Regge poles, due to the duality hypothesis. The model equations are solved for the exchange-degenerate ϱf o trajectory in ππ scattering. It is found that the results of the narrow resonance approximation (NRA) are substantially unchanged by the unitarization, because there is an approximate cancellation of the unitarity corrections by the Khuri factor. Satisfaction of the FESR is possible for a range of |; t |; and N (the upper limit of integration in the FESR). This is taken to mean (a) that many of the conclusions drawn from NRA dual models are unlikely to be substantially modified by unitarity (at least for the leading trajectories in the low energy region), and (b) that unitarity does not determine the free parameters of the NRA model (the trajectory slope α′ and coupling strength β) so that a proper bootstrap, in the old-fashioned sense, is not achieved.