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

Based on a data set of $(27.12\pm 0.10)\times {10}^8$ $\psi (3686)$ events collected at the BESIII experiment, the absolute branching fractions of the three dominant ${\mathrm{\Omega }}^{-}$ decays are measured to be ${\mathcal{B}}_{{\mathrm{\Omega }}^{-}\to {\mathrm{\Xi }}^0{\pi }^{-}}=(25.03\pm 0.44\pm 0.53)\mathrm{\%}$, ${\mathcal{B}}_{{\mathrm{\Omega }}^{-}\to {\mathrm{\Xi }}^{-}{\pi }^0}=(8.43\pm 0.52\pm 0.28)\mathrm{\%}$, and ${\mathcal{B}}_{{\mathrm{\Omega }}^{-}\to \mathrm{\Lambda }{K}^{-}}=(66.3\pm 0.8\pm 2.0)\mathrm{\%}$, where the first and second uncertainties are statistical and systematic, respectively. The ratio between ${\mathcal{B}}_{{\mathrm{\Omega }}^{-}\to {\mathrm{\Xi }}^0{\pi }^{-}}$ and ${\mathcal{B}}_{{\mathrm{\Omega }}^{-}\to {\mathrm{\Xi }}^{-}{\pi }^0}$ is determined to be $2.97\pm 0.19\pm 0.11$, which is in good agreement with the PDG value of $2.74\pm 0.15$, but greater by more than four standard deviations than the theoretical prediction of 2 obtained from the $\mathrm{\Delta }I=1\mathrm{/}2$ rule.