An Approach to Regge Behaviour and Duality Based on an Infinite Sum of One-Particle-Exchange Amplitudes

Abstract

The implication of Regge asymptotic behaviour is studied on the basis of an infinite sum of one-particle-exchange (lOPE) amplitude, which provides a wide framework including vari­ ous versions of dual amplitudes. The imaginary part of Regge-behaved amplitude comes from the s-u crossing term of the convergent lOPE amplitude, accompanied with the diver­ gence of lOPE expression. Duality between t-poles and u- or s-singularities is necessarily contained in Regge behaviour. A general expression for the lOPE amplitude satisfying full Regge behaviour is persued and comments on related models are made in connection with our approach. Phenomenological aspects of various solutions are also discussed. The analysis of hadron scattering using finite energy sum rules has revealed the existence of an intimate connection between Regge pole exchanges and re­ sonant states in direct channel and has developed into Veneziano amplitude. This has created a problem of understanding of the physical implication of Regge pole exchanges. Regge pole exchange originally gave an exchange picture of composite par­ ticles at high energies. Its connection with the one-particle-exchange (OPE) mo­ del (which was proposed as an application to hadron reactions of the Sakata model) is quite interesting, especially when we consider its success in describ­ ing low energy scattering phenomena, such as nucleon-nucleon scattering. Among the interpretations of Regge behaviour so far proposed, that of an infinite sum of single exchanges of Regge recurrences is the most attractive one for a gener­ alization of OPE model. The purpose of the present paper is to give a general expression for the scattering amplitude based on the infinite sum of one-particle-exchange (lOPE) model/), 2 ) in which Regge behaviour is imposed at the asymptotic energy region. As an a posteriori result, the duality concept comes from the requirement of Regge behaviour in all the complex u plane except a positive real axis, where