Further understanding the nature of $\mathrm{\Omega }(2012)$ within a chiral quark model

In our previous works, we have analyzed the two-body strong decays of the low-lying $\mathrm{\Omega }$ baryon states within a chiral quark model. The results show that the $\mathrm{\Omega }(2012)$ resonance favors the three-quark state with $J^P=3\mathrm{/}{2}^{-}$ classified in the quark model. With this assignment, in the present work we further study the three-body strong decay $\mathrm{\Omega }(2012)\to {\mathrm{\Xi }}^{\ast }(1530)\bar{K}\to \mathrm{\Xi }\pi \bar{K}$ and coupled-channel effects on $\mathrm{\Omega }(2012)$ from nearby channels $\mathrm{\Xi }\bar{K}$, $\mathrm{\Omega }\eta$ and ${\mathrm{\Xi }}^{\ast }(1530)\bar{K}$ within the chiral quark model as well. It is found that the $\mathrm{\Omega }(2012)$ resonance has a sizeable decay rate into the three-body final state $\mathrm{\Xi }\pi \bar{K}$. The predicted ratio $R_{\mathrm{\Xi }\bar{K}}^{\mathrm{\Xi }\pi \bar{K}}=\mathcal{B}[\mathrm{\Omega }(2012)\to {\mathrm{\Xi }}^{\ast }(1530)\bar{K}\to \mathrm{\Xi }\pi \bar{K}]\mathrm{/}\mathcal{B}[\mathrm{\Omega }(2012)\to \mathrm{\Xi }\bar{K}]\simeq 12\mathrm{\%}$ is close to the up limit $11\mathrm{\%}$ measured by the Belle Collaboration in 2019, however, our predicted ratio is too small to be comparable with the recent data $0.97\pm 0.31$. Furthermore, our results show that the coupled-channel effects on the $\mathrm{\Omega }(2012)$ is not large, its components should be dominated by the bare three-quark state, while the proportion of the molecular components is only $\sim 16\mathrm{\%}$. To clarify the nature of $\mathrm{\Omega }(2012)$, the ratio $R_{\mathrm{\Xi }\bar{K}}^{\mathrm{\Xi }\pi \bar{K}}$ is expected to be tested by other experiments.