Saturation of Superconvergence Relations and Current-Algebra Sum Rules for Forward Amplitudes

Abstract

We use the algebra of charges and their time derivatives, partially conserved axial-vector currents, and Regge high-energy behavior to derive sum rules for strong-interaction forward amplitudes. The saturation of all sum rules by a finite number of states is self-consistent and leads to relations among coupling constants and masses. Saturating all sum rules for $\ensuremath{\pi}\ensuremath{-}\ensuremath{\rho}$ scattering by $\ensuremath{\pi}$, $\ensuremath{\omega}$, and ${A}_{1}$, we predict ${m}_{{A}_{1}}=1100$ MeV, ${m}_{\ensuremath{\omega}}={m}_{\ensuremath{\rho}}$, ${\ensuremath{\Gamma}}_{{A}_{1}}=120$ MeV, ${g}_{\ensuremath{\omega}\ensuremath{\rho}\ensuremath{\pi}}=21$ Be${\mathrm{V}}^{\ensuremath{-}1}$, in good agreement with experiment.