Dynamics Based on Rising Regge Trajectories

An outline is given of a dynamical scheme based on rising Regge trajectories. The fundamental approximation is that the scattering amplitude can be approximated by the contribution of a finite number of Regge poles. An additional simplifying assumption is that the Regge trajectories are straight lines or, equivalently, that the scattering amplitude is dominated by narrow resonances. Unitarity is introduced by means of the Cheng-Sharp equations, but, in the narrow-resonance approximation, we adopt a very trivial solution of these equations. Crossing is introduced by means of the generalized superconvergence relations due to Igi and to Horn and Schmid. Levinson's theorem is not used; the bootstrap condition is the absence of Kronecker-$\delta$ singularities in the $J$ plane. It is hoped that this scheme avoids some of the disadvantages of conventional schemes. In the narrow-resonance approximation one has to solve numerical equations, not integral equations. The scheme is applied to the pseudoscalar, vector, and axial-vector nonets considered as bound states of the $N\overline{N}$ system. As only one channel is being examined, we have to introduce certain parameters from experiment, but we obtain reasonable values for the other parameters.