Unitarity, duality and absorption; A general discussion and a definite model

Abstract

We study the problem of incorporating unitarity effects into dual scattering amplitudes. Possible forms and interpretations for amplitudes which have dual properties consistent with experimental data (including the fixed-t zero structure, the dominance of peripheral resonances, etc.) are discussed. A detailed physical interpretation, in terms of absorption effects, is provided at all energies. A specific model is presented which demonstrates that amplitudes of the desired kind do exist and that one can work with them.The model is studied in detail for spinless particles (e.g. [pi][pi] scattering). Apart from a few technical difficulties the resulting amplitude can be studied at all energies and angles and behaves in all aspects essentially as we expect realistic scattering amplitudes (and data) to behave.