The origin of unitarity and duality in the Nakanishi amplitude

Abstract

The model of strong interaction proposed by VENEZIANO (I) explains many of the strong-interaction phenomena successfully, in a narrow-resonance approximation, such as l inearly rising trajectories, exchange degeneracy, crossing, correct Regge behaviour, etc. However, the Veneziano model violates uni tar i ty , a proper ty which is very fundamental in physics. To overcome the uni tar i ty violation, recently dual models with Mandelstam analytic i ty have been proposed (2). During such a s tudy of dual ampli tudes with Mandelstam analyt ic i ty , TAHA (a) has shown tha t the Nakanishi scattering ampli tude (4) is a very successful model when crossing, Regge behaviour, Mandelstam analyt ic i ty , (~ dual i ty in a generalized sense ,), etc. are concerned, in this let ter , we point out the origin of un i ta r i ty in the Nakanishi scattering ampli tude and show tha t the Nakanishi scattering ampli tude can be expanded in continuous Veneziano terms. The unsubtrac ted form of the Nakanishi scattering ampli tude for two.part icle scattering is given by