A unified approach for the hadronic weak decays of $\hat{I}›$ and $\hat{I}{\pounds }^{\pm }\to N\ddot{I}€$

Abstract

We provide a unified approach for the two-body hadronic weak decays of hyperons with $S=-1$, i.e. $\hat{I}›$ and $\hat{I}{\pounds }^{\pm }$, 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 $\hat{I}›\to p\ddot{I}{€}^{-}$ and $\hat{I}{\pounds }^{\pm }\to N\ddot{I}€$ 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 $\hat{I}›\to n\ddot{I}{€}^0$ 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 $\hat{I}›\to n\ddot{I}{€}^0$. Namely, the dominant decay channel of $\hat{I}›\to p\ddot{I}{€}^{-}$ can contribute to $\hat{I}›\to n\ddot{I}{€}^0$ via the $p\ddot{I}{€}^{-}\to n\ddot{I}{€}^0$ rescatterings. This is a leading correction effect for $\hat{I}›\to n\ddot{I}{€}^0$ at the one-loop level. We find that such FSIs only become the leading effects in $\hat{I}›\to n\ddot{I}{€}^0$, but contribute as subleading contributions in other channels. We also demonstrate that the pole terms are indispensable in these hyperon decays. In particular, for $\hat{I}{\pounds }^{-}\to n\ddot{I}{€}^{-}$ and $\hat{I}{\pounds }^{+}\to n\ddot{I}{€}^{+}$, it shows that $\hat{I}›(1405)$ 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 $|70{,}^{2}8,2,0^{+},1/2^{+}⟩$ 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.

Revtex, 35 pages, 6 Figures, 19 Tables