Dynamical Basis of the Sum Rule2Ξ−−=Λ−+3Σ0+

Abstract

The amplitudes for the nonleptonic decay of hyperons are explained by a simple dynamical model in the framework of SU(3) symmetry. The parity-conserving amplitudes are described by the Feldman-Matthews-Salam model, while the parity-violating amplitudes are given by the dominance of the $K^{*}\to \pi$ diagram. An effective weak Hamiltonian is used that transforms like ${\lambda }_6$ under SU(3). The model predicts the sum rule $2{{\Xi }_{-}}^{-}={\Lambda }_{-}+\sqrt{3}{{\Sigma }_0}^{+}$ for each set of amplitudes; in addition, all other experimental data on the amplitudes can be fitted by the model. These results are obtained without explicitly invoking $\mathrm{RP}$ invariance.