Narrow-Resonance Model with Regge Behavior forππScattering

A model for $\pi \pi$ scattering of the type recently proposed by Veneziano is discussed. It is a narrow-resonance model with exchange-degenerate, linearly rising trajectories, which obeys crossing symmetry and has the proper Regge behavior in all channels. The general form for the amplitude is discussed, and phase shifts, resonance widths, and high-energy diffraction are calculated, assuming the amplitude takes on the simplest of the possible forms. The condition that the partial widths be positive is extensively discussed. The model is also considered as a testing ground for other theories based on the same assumptions, such as finite-energy sum rules and the Schmid-circle hypothesis.