On a model for saturation of a superconvergent sum rule

Abstract

A superconvergent sum rule, regarded as an identity valid for all values of the momentum transfert in the neighbourhood oft=0, implies such conditions which are quite unlikely to be satisfied by saturating the sum rule by a finite number of resonances. Even though this may imply that there is an infinite number of resonances saturating the sum rule, the contributions from higher resonances to an amplitude are known to decrease rapidly so that they make up only a sort of background over a finite number of low-lying resonances. A model of achieving this using Regge pole theory without introducing a large number of higher resonances is presented.