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

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.

💡 Research Summary

The paper presents a comprehensive study of the singly Cabibbo‑suppressed two‑body hadronic weak decays of the Ω⁻ hyperon (strangeness S = ‑3), focusing on the three channels Ω⁻ → Ξ⁰π⁻, Ω⁻ → Ξ⁻π⁰ and Ω⁻ → ΛK⁻. The authors work within a non‑relativistic constituent quark model (NRCQM) to calculate the decay amplitudes at the quark level. Two classes of weak transitions are considered: (i) s → u d \bar{u} processes, which give rise to direct pion emission (DPE) and color‑suppressed (CS) mechanisms, and (ii) su → ud processes that generate baryon‑pole (PT) contributions.

For the s → u d \bar{u} sector, the DPE corresponds to an external W⁻ emission where the produced d \bar{u} pair directly hadronises into a pion; this is color‑allowed. The CS mechanisms involve internal W⁻ emission, leading to a color factor of 1/3 and an additional isospin factor for the neutral pion. The authors distinguish two CS topologies (CS‑1 and CS‑2) depending on which initial‑state quark participates. The weak Hamiltonian is written in parity‑conserving (PC) and parity‑violating (PV) parts, and matrix elements are factorised into flavor, spin and spatial overlap integrals. SU(3) flavor symmetry is imposed at the level of the quark wave functions, while symmetry breaking is introduced through constituent‑quark mass differences and the explicit spatial wave‑function overlaps.

The pole contributions arise from the su → ud transition mediated by a W‑exchange, followed by strong emission of the kaon. Only the ΛK⁻ channel contains such a pole term. The intermediate baryon states are the low‑lying Ξ resonances with J^P = 1/2⁺ (ground‑state Ξ) and 1/2⁻ (first negative‑parity excitation). The pole amplitude is expressed as a product of a strong vertex, a weak transition matrix element, and a propagator 1/(p²‑m² + i m Γ). The authors retain only the near‑on‑shell contributions, which dominate the PT amplitude.

Numerical evaluation shows that the Ξ⁰π⁻ decay is dominated by the DPE mechanism; the CS contribution is small, and the pole term is negligible. Conversely, the ΛK⁻ decay receives comparable contributions from CS‑2 and the pole term, with the pole term providing the bulk of the observed branching ratio. The tree‑level CS contribution to Ω⁻ → Ξ⁻π⁰ is heavily suppressed (color factor 1/3 and isospin factor 1/√2), yielding a branching fraction far below the experimental value.

To resolve this discrepancy, the authors incorporate long‑distance final‑state interactions (FSI) through rescattering among the three channels. They construct a coupled‑channel scattering matrix that allows Ξ⁰π⁻ ↔ ΛK⁻ ↔ Ξ⁻π⁰ transitions via strong interactions. The rescattering enhances the effective amplitude for Ω⁻ → Ξ⁻π⁰ by roughly a factor of three, bringing the predicted branching ratio into agreement with the BESIII measurement (≈ 8 %).

A partial‑wave analysis reveals that all three decays are overwhelmingly dominated by parity‑conserving P‑wave amplitudes; the parity‑violating D‑wave contributions are at the few‑percent level. Consequently, the decay asymmetry parameters α are predicted to be essentially zero, consistent with the angular‑distribution data from BESIII.

The paper concludes that a unified description of Ω⁻ weak decays must combine (1) quark‑level weak vertices (both s → ud \bar{u} and su → ud), (2) baryon‑pole structures involving intermediate Ξ resonances, and (3) long‑range final‑state rescattering dynamics. The resulting branching ratios and asymmetries match the high‑precision experimental results, providing a coherent picture of weak processes in the strange‑baryon sector and offering predictions that can be tested in future measurements of Ξ‑π and Λ‑K scattering and of the properties of the intermediate Ξ resonances.