Nonleptonic decays in a renormalizable gauge model of chiral symmetry

Abstract

We present a model based on chiral SU(3) × SU(3) for the nonleptonic decays of mesons and baryons. The model is fully gauge-invariant and renormalizable. The basic fields in the model are the spin-1 and spin-0 mesons. All symmetry-breaking effects, including the nonleptonic weak mixings, are achieved through the spontaneous-symmetry-breaking mechanism. Our choice of the Higgs-Kibble scalars automatically ensures octet dominance for the nonleptonic weak vertex. Since we find it hard to include baryons in the model, a phenomenological treatment of the baryon decays, assuming SU(3) invariance of the baryonic couplings, is presented. In the model we calculate the two-pion and three-pion decays of the kaon, the $s$-wave amplitudes for the hyperon decays, and the $K_L-K_S$ mass difference. The results for $K\to 2\pi$ and $K\to 3\pi$ decay widths are in excellent agreement with experiment. The slope parameter for the $K\to 3\pi$ decay, however, comes out with the wrong sign. The $s$-wave amplitudes for the hyperon decays agree reasonably well with experiment. The estimate for the $K_L-K_S$ mass difference is of the correct order of magnitude. $K^{+}\to {\pi }^{+}{\pi }^0$ decay is calculated by using the known current-algebra estimate of $\eta {\pi }^0$ mixing. The decay width obtained by us is rather low. Our conclusion is that $\eta {\pi }^0$ mixing alone is not sufficient to explain the $K^{+}$ decay. On extending the model to chiral SU(4) × SU(4), we predict the existence of a component transforming as the 15 representation of SU(4) in the nonleptonic Hamiltonian. Therefore, the nonleptonic decays of charmed mesons will provide a definitive test for the model.