Dynamical Model for Nonleptonic Decays of Hyperons

Abstract

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, ${{Y}_{0}}^{*}(1405)$, 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 $K\ensuremath{-}\ensuremath{\pi}$ 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 ${{K}_{2}}^{0}\ensuremath{-}{{K}_{1}}^{0}$ mass difference.