Singly Cabibbo-suppressed hadronic weak decays of the $Ω^-$ hyperon

TL;DR

This work addresses the hadronic weak decays of the Ω^− hyperon into Ξπ and ΛK^− channels, focusing on singly Cabibbo-suppressed modes. It develops a unified framework that combines a non-relativistic constituent quark model for quark-level weak vertices (direct pion emission and pole terms) with hadron-level final-state interactions via meson-baryon rescattering, and includes baryon pole contributions from intermediate Ξ resonances. The analysis demonstrates that quark-level dynamics, baryon-pole effects, and long-distance FSIs must all be included to reproduce BESIII branching ratios, with FSIs essential to explain Ω^−→Ξ^−π^0. The results yield branching ratios in agreement with data and near-zero asymmetries, highlighting the crucial role of non-perturbative dynamics in spin-3/2 hyperon weak decays and providing a coherent picture of Ω^− decay mechanisms.

Abstract

We study the two-body hadronic weak decays of the $Ω^-$ hyperon with strangeness $S=-3$, including three singly Cabibbo-suppressed decay modes: $Ξ^0 π^-$, $Ξ^-π^0$ and $ΛK^-$. 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 $Ξ^0 π^-$ channel is dominated by the color-allowed direct pion emission process, while the $ΛK^-$ channel is well described by one type of pole contribution mediated through intermediate $Ξ$ resonances ($1^2S_{1/2^+}$ and $1^2P_{1/2^-}$ states). However, the contribution from tree-level mechanisms alone to the branching ratio of $Ω^- \to Ξ^- π^0$ is small due to its color-suppressed nature. The discrepancy is resolved by including final state interactions through rescattering processes via intermediate states $Ξ^0π^-$ and $ΛK^-$. This work demonstrates that a unified description of $Ω^-$ 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.

Figures (3)

• Figure 1: Illustrations for the two-body hadronic weak decay of $\Omega^-$ into $\Xi\pi$ and $\Lambda K^-$ at the quark level. (a) Direct pion emission (DPE) processes; (b)-(c) Color suppressed (CS) pion emission processes; (d) Pole terms (PT).
• Figure 2: Schematic diagram of the FSIs from the intermediate channel rescattering to $\Xi^-\pi^0$. Black squares and red dots represent weak and strong vertices respectively.
• Figure 3: The obtained branching ratio of $\Omega^-\to \Xi^-\pi^0$ as a function of the cut-off parameter $\Lambda$, comparing with the experimental data (horizontal blue bands). The vertical dark yellow band indicates the range where our results overlap with the experimental data.