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S-wave nonleptonic hyperon decays and $Ξ^-_b \to π^- Λ_b$

The decay $Ξ^-_b \to π^- Λ_b$ has recently been observed by the LHCb Collaboration at CERN. In contrast to most weak decays of $b$-flavored baryons, this process involves the decay of the strange quark in $Ξ_b$, and thus has features in common with nonleptonic weak decays of hyperons. Thanks to the expected pure S-wave nature of the decay in question in the heavy $b$ quark limit, we find that its amplitude may be related to those for S-wave nonleptonic decays of $Λ$, $Σ$, and $Ξ$ in a picture inspired by duality. The calculated branching fraction ${\cal B}(Ξ^-_b \to π^- Λ_b) = (6.3 \pm 4.2) \times 10^{-3}$ is consistent with the range allowed in the LHCb analysis. The error is dominated by an assumed 30\% uncertainty in the amplitude due to possible U(3) violation. A more optimistic view based on sum rules involving nonleptonic hyperon decay S-wave amplitudes reduces the error on the branching fraction to $2.0 \times 10^{-3}$.