Dynamics and Symmetries of Nonleptonic Hyperon Decays; Scalar Meson Couplings

We investigate the dynamics and symmetries of nonleptonic hyperon decays under the following assumptions: (i) the parity-violating (p.v.) and parity-conserving (p.c.) amplitudes are dominated by the $K_1$ and ${\kappa }_1$ tadpoles, respectively; (ii) the corresponding inverse associated production amplitudes $K_1\left({\kappa }_1\right)+Y\to \pi +N$ are dominated by the baryon octet pole terms in $s$ and $u$ channels and by $\kappa$ (p.v. case) and $K$ (p.c. case) pole terms in the $t$ channel; and (iii) the strong vertices satisfy $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry, although the particles are allowed to have their observed masses. [The reason for assuming the dominance of the p.v. amplitudes by the $K_1$ tadpole, even though the latter is forbidden in the limit of $\mathrm{SU}\left(3\right)\mathrm{}$, has been discussed in a previous work by Pati and Oneda. It is essentially based upon the observed rate of the $K_1\to 2\pi$ decay, which is also forbidden in the limit of $\mathrm{SU}\left(3\right)\mathrm{}$.] The model, thus described, involves six unknowns. Having solved for these in terms of a convenient set of input experimental parameters, the model predicts the $\gamma$ parameter of $\Lambda \to p+{\pi }^{-}$ decay, as well as the rate, the asymmetry parameter, and the $\gamma$ parameter of ${\Xi }^{-}\to \Lambda +{\pi }^{-}$ decay. All of these four predictions, except for the magnitude of $\gamma \left(\Xi _{-}^{}{}_{}{}^{-}\right)$, are in good agreement with experiments [this includes the sign of $\gamma \left(\Xi _{-}^{}{}_{}{}^{-}\right)$ as well]. Furthermore, we predict that ${\Sigma }^{+}\to n+{\pi }^{+}$ decay must proceed via $P$ wave ($S$-wave assumption is shown to be inconsistent with the model). By using the observed values of (1) the rates of ${\Lambda }_{-}$, $\Sigma _{+}^{}{}_{}{}^{+}$, and $\Sigma _{-}^{}{}_{}{}^{-}$ decay, (2) the asymmetry parameter of $\Sigma _{+}^{}{}_{}{}^{+}$ decay, and (3) the signs of $\alpha \left({\Lambda }_{-}\right)$, $\alpha \left(\Xi _{-}^{}{}_{}{}^{-}\right)$, and $\gamma \left(\Xi _{-}^{}{}_{}{}^{-}\right)$, we obtain the unique prediction that ${\Sigma }^{-}\to n+{\pi }^{-}$ decay must proceed via pure $S$ wave. In obtaining this last prediction we do not utilize the observed values of the $\Sigma _0^{}{}_{}{}^{+}$-decay parameters, but instead obtain them as predictions as well. In addition we arrive at a host of other interesting conclusions regarding (a) the $\frac{d}{f}$ ratio in baryon-pseudoscalar meson coupling (this is predicted to be nearly 1.8), (b) the over-all strength and the $\frac{d^{\prime }}{f^{\prime }}$ ratio in baryon-scalar meson coupling, (c) the strengths of scalar and pseudoscalar tadpoles, and (d) the degree of validity of Lee's sum rule for p.v. and p.c. decays. Comment is also made on the radiative ${\Sigma }^{+}\to p+\gamma$ decay in an analogous model.