A unified approach for the hadronic weak decays of $\Lambda$ and $\Sigma^{\pm}\to N\pi$

We provide a unified approach for the two-body hadronic weak decays of hyperons with $S=-1$, i.e. $\Lambda$ and $\Sigma^\pm$, in the framework of the non-relativistic constitute quark model (NRCQM). A combined analysis shows that the branching ratios and asymmetry parameters of the decay channels $\Lambda\to p\pi^-$ and $\Sigma^\pm\to N\pi$ can be well described in the same framework with the direct pion emission, color suppressed internal $W$ emission, and pole terms included. However, the channel $\Lambda\to n\pi^0$ indicates significant deviations from the experimental data based on these mentioned transition mechanism. We demonstrate that the final state interactions (FSIs) via the coupled-channel rescatterings play a crucial role in $\Lambda\to n\pi^0$. Namely, the dominant decay channel of $\Lambda\to p\pi^-$ can contribute to $\Lambda\to n\pi^0$ via the $p\pi^-\to n\pi^0$ rescatterings. This is a leading correction effect for $\Lambda\to n\pi^0$ at the one-loop level. We find that such FSIs only become the leading effects in $\Lambda\to n\pi^0$, but contribute as subleading contributions in other channels. We also demonstrate that the pole terms are indispensable in these hyperon decays. In particular, for $\Sigma^-\to n\pi^-$ and $\Sigma^+\to n\pi^+$, it shows that $\Lambda(1405)$ as the intermediate state in the pole term amplitude is necessary for reproducing the experimental data. We also find that a dynamic selection rule forbids the radial excitation state $N(1710)$ of the quark model multiplet $|70, ^28,2,0^+,1/2^+\rangle$ from contribution. To some extent, the hyperon hadronic weak decays serve as a special probe for the underlying transition mechanisms and can provide some constraints on the intermediate $J^P=1/2^\pm$ baryon resonances.