Superconvergence Condition and Okubo's Ansatz

Abstract

Recently a class of sum rules) for strong interactions has been derived on the basis of a dispersion theoretic approach. In such a derivation, one makes assumptions*) related to the high energy bounds for scattering amplitudes, which specify the convergence properties of the relevant dispersion relations. If the dispersion integral is approximated by a sum consisting of intermediate particles, the masses and cou piing constants of different particles are related. Thus AFRF considered. the p-n forward scattering and obtained some relations connecting coupling constants and masses, where they made the approximation of keeping only n, w, q; as intermediate states. This approximation leads to inconsistent results.**) This suggests that, in order to obtain consistent results, one should include other higher resonant states in addition to n, w and q; as intermediate states. In view of this situation we consider pseudoscalar-meson-vector-meson scattering within the framework of SU(3) symmetry and investigate possible strong interaction sum rules for the scattering. Our approximation for the dispersion integrals of the sum rules includes as intermediate states the pseudoscalar-meson octet (P), the vector-meson nonet (V) the axial-vector-meson nonet (U) and the tensor-meson nonet (T) .***) In this note we are particular-