S-wave nonleptonic hyperon decays and $\Xi^-_b \to \pi^- \Lambda_b$

TL;DR

This paper relates the decay of the bottom baryon $ ext{Xi}_b^-$ to hyperon nonleptonic decay amplitudes, predicting a branching fraction consistent with LHCb data and analyzing uncertainties from U(3) symmetry violations.

Contribution

It introduces a method to connect $ ext{Xi}_b^-$ decay amplitudes with hyperon nonleptonic decay amplitudes using duality, providing a theoretical estimate of the branching fraction.

Findings

Predicted branching fraction: (6.3 ± 4.2) × 10^{-3}

Estimate consistent with LHCb measurements

Reduced error estimate to 2.0 × 10^{-3} using sum rules

Abstract

The decay $\Xi^-_b \to \pi^- \Lambda_b$ 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 $\Xi_b$, 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 $\Lambda$, $\Sigma$, and $\Xi$ in a picture inspired by duality. The calculated branching fraction ${\cal B}(\Xi^-_b \to \pi^- \Lambda_b) = (6.3 \pm 4.2) \times 10^{-3}$ 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 $2.0 \times 10^{-3}$.