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 $\pi -\rho$ scattering by $\pi$, $\omega$, and $A_1$, we predict $m_{A_1}=1100\mathrm{}$ MeV, $m_{\omega }=m_{\rho }$, ${\Gamma }_{A_1}=120\mathrm{}$ MeV, $g_{\omega \rho \pi }=21\mathrm{}$ Be${\mathrm{V}}^{-1\mathrm{}}$, in good agreement with experiment.