Singly Cabibbo-suppressed hadronic weak decays of the ${\Omega }^{-}$ hyperon

Abstract

We study the two-body hadronic weak decays of the ${\Omega }^{-}$ hyperon with strangeness $S=-3$, including three singly Cabibbo-suppressed decay modes: ${\Xi }^0{\pi }^{-}$, ${\Xi }^{-}{\pi }^0$ and $\Lambda K^{-}$. The decay amplitudes at the quark level, arising from $s\to ud\bar{u}$ transitions (direct pion emission and color-suppressed processes) and $su\to ud$ transitions (pole terms), are calculated in the framework of the non-relativistic constituent quark model.The theoretical results show that the ${\Xi }^0{\pi }^{-}$ channel is dominated by the color-allowed direct pion emission process, while the $\Lambda K^{-}$ channel is well described by one type of pole contribution mediated through intermediate $\Xi$ resonances ($1^2{S}_{1/2^{+}}$ and $1^2{P}_{1/2^{-}}$ states). However, the contribution from tree-level mechanisms alone to the branching ratio of ${\Omega }^{-}\to {\Xi }^{-}{\pi }^0$ is small due to its color-suppressed nature. The discrepancy is resolved by including final state interactions through rescattering processes via intermediate states ${\Xi }^0{\pi }^{-}$ and $\Lambda K^{-}$. This work demonstrates that a unified description of ${\Omega }^{-}$ hadronic weak decays necessitates the interplay of quark-level weak vertices, baryon pole structures, and long-distance final state rescattering dynamics. With these mechanisms, the obtained branching ratios are in agreement with the high-precision experimental data from the BESIII. Furthermore, these above decays are found to be dominated by the parity-conserving $P$-wave transitions, thus the asymmetry parameters are almost zero.

Comments: arXiv admin note: text overlap with arXiv:2512.10346