Nonleptonic Hyperon Decays

Abstract

Suzuka and Sugawara's theory of $S$-wave nonleptonic hyperon decay is reviewed to see to what extent their theory tests current algebra and the current\ifmmode\times\else\texttimes\fi{}current form of interaction. The only argument for the current\ifmmode\times\else\texttimes\fi{}current form in nonleptonic decays that it is all compelling is the vanishing of the $S$-wave amplitude $A({{\ensuremath{\Sigma}}_{+}}^{+})$ for the decay ${\ensuremath{\Sigma}}^{+}\ensuremath{\rightarrow}n+{\ensuremath{\pi}}^{+}$. For the $P$-wave decay, to which the soft-pion formalism is inapplicable, an octet pole model is used. To fit the empirical $P$-wave amplitudes, strong-coupling shifts are required in both the $S$ and the $P$ waves. Including $\mathrm{SU}(3)$ symmetry breaking leads to parity-violating Born terms in the $S$ waves; to estimate the parity-violating spurion coupling, the kaon tadpole model and ${K}_{2}\ensuremath{\pi}$ decay rate are used. If pionic and kaonic strong-coupling constants are suppressed by $\frac{2}{3}$ and $\frac{1}{3}$, all the $S$- and $P$-wave amplitudes are given within 20%, but $A({{\ensuremath{\Sigma}}_{+}}^{+})$ now does not precisely vanish. If $A({{\ensuremath{\Sigma}}_{+}}^{+})=0$ exactly is insisted on, then the suppression of pionic strong-coupling constants by $\frac{2}{3}$ and $\frac{1}{3}$ is necessary.