Testing SU(3) flavor symmetry in semileptonic and two-body nonleptonic decays of hyperons

Abstract

The semileptonic decays and two-body nonleptonic decays of a light baryon octet (${T}_{8}$) and a decuplet (${T}_{10}$) consisting of light $u$, $d$, $s$ quarks are studied with the SU(3) flavor symmetry. We obtain the amplitude relations between different decay modes by the SU(3) irreducible representation approach, and we then predict relevant branching ratios by presenting experimental data within $1\ensuremath{\sigma}$ error. We find that the predictions for all branching ratios except $\mathcal{B}(\mathrm{\ensuremath{\Xi}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}^{0}\ensuremath{\pi})$ and $\mathcal{B}({\mathrm{\ensuremath{\Xi}}}^{*}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Xi}}\ensuremath{\pi})$ are in good agreement with present experimental data, which implies that the neglected ${C}_{+}$ terms or SU(3) breaking effects might contribute on the order of a few percent in $\mathrm{\ensuremath{\Xi}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}^{0}\ensuremath{\pi}$ and ${\mathrm{\ensuremath{\Xi}}}^{*}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Xi}}\ensuremath{\pi}$ weak decays. We predict that $\mathcal{B}({\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Sigma}}}^{0}{\ensuremath{\mu}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}})=(1.13\ifmmode\pm\else\textpm\fi{}0.08)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$, $\mathcal{B}({\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}^{0}{\ensuremath{\mu}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}})=(1.58\ifmmode\pm\else\textpm\fi{}0.04)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, $\mathcal{B}({\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}^{0}{\ensuremath{\mu}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}})=(3.7\ifmmode\pm\else\textpm\fi{}1.8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, $\mathcal{B}({\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Sigma}}}^{0}{e}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{e})=\phantom{\rule{0ex}{0ex}}(1.35\ifmmode\pm\else\textpm\fi{}0.28)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, and $\mathcal{B}({\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}^{0}{e}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{e})=(4.2\ifmmode\pm\else\textpm\fi{}2.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$. We also study ${T}_{10}\ensuremath{\rightarrow}{T}_{8}{P}_{8}$ weak, electromagnetic, or strong decays. Some of these decay modes could be observed by BESIII, LHCb, and other experiments in the near future. Because of the very small lifetimes of ${\mathrm{\ensuremath{\Sigma}}}^{0}$, ${\mathrm{\ensuremath{\Xi}}}^{*0,\ensuremath{-}}$, ${\mathrm{\ensuremath{\Sigma}}}^{*0,\ensuremath{-}}$, and ${\mathrm{\ensuremath{\Delta}}}^{0,\ensuremath{-}}$, the branching ratios of these baryon weak decays are only on the order of $\mathcal{O}({10}^{\ensuremath{-}20}\ensuremath{-}{10}^{\ensuremath{-}13}$), which is too small to be reached in current experiments. The longitudinal branching ratios of ${T}_{8A}\ensuremath{\rightarrow}{T}_{8B}{\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}}(\ensuremath{\ell}=\ensuremath{\mu},e)$ decays are also given.