A unified approach for the hadronic weak decays of $Λ$ and $Σ^{\pm}\to Nπ$

Abstract

We provide a unified approach for the two-body hadronic weak decays of hyperons with $S=-1$, i.e. $Λ$ and $Σ^\pm$, 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 $Λ\to pπ^-$ and $Σ^\pm\to Nπ$ 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 $Λ\to nπ^0$ 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 $Λ\to nπ^0$. Namely, the dominant decay channel of $Λ\to pπ^-$ can contribute to $Λ\to nπ^0$ via the $pπ^-\to nπ^0$ rescatterings. This is a leading correction effect for $Λ\to nπ^0$ at the one-loop level. We find that such FSIs only become the leading effects in $Λ\to nπ^0$, but contribute as subleading contributions in other channels. We also demonstrate that the pole terms are indispensable in these hyperon decays. In particular, for $Σ^-\to nπ^-$ and $Σ^+\to nπ^+$, it shows that $Λ(1405)$ 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.