Measurements of the absolute branching fractions of $\Omega^-$ decays and test of the $\Delta I = 1/2$ rule

TL;DR

This study measures the absolute branching fractions of the three main $ ext{Ω}^-$ decays using BESIII data and tests the $ ext{Δ}I=1/2$ rule by comparing experimental ratios with theoretical predictions.

Contribution

It provides precise measurements of $ ext{Ω}^-$ decay branching fractions and evaluates the validity of the $ ext{Δ}I=1/2$ rule in hyperon decays.

Findings

Measured branching fractions with statistical and systematic uncertainties.

Found the ratio of two decay modes to be 2.97, aligning with PDG but exceeding theoretical predictions.

Challenged the $ ext{Δ}I=1/2$ rule based on the decay ratio comparison.

Abstract

Based on a data set of $(27.12\pm0.10)\times 10^8$ $\psi(3686)$ events collected at the BESIII experiment, the absolute branching fractions of the three dominant $\Omega^-$ decays are measured to be $\mathcal{B}_{\Omega^- \to \Xi^0 \pi^-} = (25.03\pm0.44\pm0.53)\%$, $\mathcal{B}_{\Omega^- \to \Xi^- \pi^0} = (8.43\pm0.52\pm0.28)\%$, and $\mathcal{B}_{\Omega^- \to \Lambda K^-} = (66.3\pm0.8\pm2.0)\%$, where the first and second uncertainties are statistical and systematic, respectively. The ratio between $\mathcal{B}_{\Omega^- \to \Xi^0 \pi^-}$ and $\mathcal{B}_{\Omega^- \to \Xi^- \pi^0}$ is determined to be $2.97\pm0.19\pm0.11$, which is in good agreement with the PDG value of $2.74\pm0.15$, but greater by more than four standard deviations than the theoretical prediction of 2 obtained from the $\Delta I = 1/2$ rule.