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 ${K}^{*}\ensuremath{\rightarrow}\ensuremath{\pi}$ diagram. An effective weak Hamiltonian is used that transforms like ${\ensuremath{\lambda}}_{6}$ under SU(3). The model predicts the sum rule $2{{\ensuremath{\Xi}}_{\ensuremath{-}}}^{\ensuremath{-}}={\ensuremath{\Lambda}}_{\ensuremath{-}}+\sqrt{3}{{\ensuremath{\Sigma}}_{0}}^{+}$ 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.