Dynamical Model for Nonleptonic Decays of Hyperons

A dynamical model based on broken unitary symmetry is developed for nonleptonic decays of hyperons. The contributions to these decays are taken from the primary current-current interaction and from poles due to the baryons, the $K$ meson, ${Y_0}^{*}\mathrm{}\left(1405\right)\mathrm{}$, and the decuplet of baryon resonances (${B_{10}}^{*}$). The contributions from the baryon and $K$-meson poles are calculated on the assumption that weak baryon-baryon and $K-\pi$ transitions transform like divergences of the relevant weak currents, which are members of octets. The contributions from poles due to ${Y_0}^{*}$ and the ${B_{10}}^{*}$ resonances must be included to explain the $p$-wave amplitudes. Both $s$- and $p$-wave amplitudes then satisfy the triangular relations and fit the experimental values for the signs and magnitudes. The model predicts the correct sign of the ${K_2}^0-{K_1}^0$ mass difference.