Nonleptonic Hyperon Decays in the Pole Approximation and the Strong-Coupling Constants

We have considered the nonleptonic hyperon decays $Y\to N+\pi$ in the baryon pole approximation, assuming the validity of the $\left|\Delta T\right|=\frac{1}{2}$ rule for the weak two-fermion ($Y\to N$) vertices. The ($\Sigma \Lambda$) relative parity is assumed to be even. We have tried to solve for the two strong-coupling constants $g_{\Sigma }$ and $g_{\Lambda }$ and the four weak-vertex parameters involved in ($\Sigma \to N$) and ($\Lambda \to n$) transitions from the known (experimental) hyperon-decay parameters. We find that there exist three solutions if ${\Sigma }^{+}\to n+{\pi }^{+}$ proceeds via $S$ wave (Case A): Solution (i)A, ${g_{\Lambda }}^2\simeq 4{g_{\Sigma }}^2$, $\frac{g_{\Sigma }}{g_N}\simeq 0.6$; Solution (ii)A, ${g_{\Lambda }}^2\simeq {g_{\Sigma }}^2$, $\frac{g_{\Sigma }}{g_N}\simeq -1.2\mathrm{}$; and Solution (iii)A, ${g_{\Lambda }}^2\simeq \frac{{g_{\Sigma }}^2}{4}$, $\frac{g_{\Sigma }}{g_N}\simeq 1.3$; and only one solution if ${\Sigma }^{+}\to n+{\pi }^{+}$ proceeds via $P$ wave (Case B): Solution B, ${g_{\Lambda }}^2\simeq {g_{\Sigma }}^2$, $\frac{g_{\Sigma }}{g_N}\simeq 0.94$. These solutions are quite different from those given previously by Singh and Udgaonkar; the main reason for the difference is that they use a value of unity for the $\left|\frac{P}{S}\right|$ ratio in $\Lambda \to p+{\pi }^{-}$ decay, while we use a value of nearly 0.36 for the same ratio, as found experimentally. We apply all the four solutions to radiative $Y\to N+\gamma$ decays and point out experiments which could distinguish between these solutions. Given the results of a few experiments, one may be in a position to choose the most favored solution and predict the results of other experiments, thus, subjecting the model to a direct test.