Noninvariance Groups and Low-Energy Meson-Baryon Scattering (original) (raw)

The object of the paper is to show that consideration of noninvariance groups as well as the Cook-Goebel-Sakita strong-coupling solution may be used to derive low-energy sum rules for p-wave meson-baryon scattering. In particular we obtained two sum rules for pion-nucleon scattering which are in fair agreement vnth experiment. These are p" = 4p~3 = 4p'j. The method is generalized to 5V(3) to obtain twelve sum rules for the fourteen p-wave amplitudes. Throughout, a rather simple method of using crossing Inatrices of the groups SU(2)1&SU(2)g and SU(3) &(SV(2)q Is employed, Several new results are obtamed whIch were not obtained in the previous treatments. and derive two sum rules that are fairly well sa,tis6ed by the p-wave scattering lengths. In Sec. III, we consider the group SU(3) XSU(2) q and derive some of the consequences of this group. In Sec. IV, we summarize our conclusions.