Further Consequences of Sugawara's Theory of Hyperon Nonleptonic Decays

The application by Sugawara of the chiral $\mathrm{SU}\left(3\right)\mathrm{}\otimes \mathrm{SU}\left(3\right)\mathrm{}$ of Gell-Mann for nonleptonic decays is discussed. It is shown that one can give a simple group-theoretic interpretation for this theory. It is also shown that his theory predicts the vanishing of parity-conserving decay amplitudes. This difficulty is eliminated by including an octet-type violation of $\mathrm{SU}\left(3\right)\mathrm{}$. Further, in this procedure it is possible to treat the parity-conserving and parity-violating isospin amplitudes together. These isospin considerations suggest that the theory can be recast within the framework of chiral $\mathrm{SU}\left(2\right)\mathrm{}\otimes \mathrm{SU}\left(2\right)\mathrm{}$. The transformation properties of the Hamiltonian consistent with the isospin relations are obtained.