S-Waveπ−NScattering Lengths, Current Algebra, andρ+ρ′Dominance

Various predictions of the $\rho \pi \pi$ coupling constant $\frac{{f_{\rho }}^2}{4\pi }$ are discussed. A $\rho +{\rho }^{\prime }$ meson dominance model is considered with $M_{{\rho }^{\prime }}\simeq 1600$ MeV and ${\Gamma }_{{\rho }^{\prime }}\simeq 200$ MeV. This model predicts a value of the $S$-wave $\pi -N$ scattering length formula $a_1-a_3$ in better agreement with experiment than the $\rho$-dominance model when ${\Gamma }_{\rho }=128\mathrm{}$ MeV, and the modified Kawarabayashi-Suzuki-Riazuddin-Fayyazuddin relation is well satisfied.