Rho-dominance and a new family of sum rules for pion-baryon scattering

Abstract

A family of sum rules for the scattering of pions from spin-one-half baryon targets is presented. The derivation of the sum rules is based on the assumptions of i) unsubtracted dispersion relations for both the forward and the backward amplitudes (nonflip, flip and theA amplitudes) corresponding to unit isospin in thet-channel, and ii) rho-dominance (near direct-channel threshold) of thet-channel contributions in the dispersion relations for the backward amplitudes. In the πN sector, where a direct verification of our sum rules is possible, they are in satisfactory agreement with the available experimental data. Resonance saturation of our sum rules in the πΣ sector together with the assumption of universal rho-hadron coupling yields the isovector magnetic moment of Σ in good agreement with theSU3 prediction. As for pion-baryon coupling our sum rules in both the πΣ and πΞ sectors are consistent withSU3 symmetry withF/D ratio ∼ 2/3. Our analysis of the πΞ sum rules further suggestes the spin-parity assignmentJP=5/2− for Ξ* (1930).