Saturation of Sum Rules in Particle Representation of Resonances

Abstract

The saturation of various sum rules of the Adler-Weisberger (AW) type for the strangeness-conserving and strangeness-nonconserving cases are investigated by including all the observed hadrons, both particles and resonances, with a mass up to about 2 BeV. General expressions for the sum rules are derived in the "particle" representation of resonances; the sum rules are given in terms of the experimentally known axial-vector weak coupling constants ${G}_{A}(\ensuremath{\beta}\ensuremath{\rightarrow}\ensuremath{\alpha})$ and strong coupling constants ${f}_{\ensuremath{\pi}(K)\ensuremath{\alpha}\ensuremath{\beta}}$, using relations of the Goldberger-Treiman (GT) type. The details of numerical analyses are presented. The saturation of the AW-type sum rules can indeed be greatly improved, allowing, of course, for the relatively large uncertainties due to the GT-type relations and the presently available experimental data.