\begin{document}$ \Omega(2012) \to \bar{K}\Xi $\end{document} could be well reproduced with the spin-parity \begin{document}$ J^P=3/2^- $\end{document} state \begin{document}$ \Omega^*|1P_{3/2^-}\rangle $\end{document} classified in the quark model. Stimulated by the new observations of the three-body decay process \begin{document}$ \Omega(2012)^-\to \Xi^*(1530)^0K^-\to \Xi^-\pi^+K^- $\end{document} at Belle, in the present study, we further investigate the three-body strong decay \begin{document}$ \Omega^*|1P_{3/2^-}\rangle \to \Xi^*(1530)\bar{K} \to \Xi\pi\bar{K} $\end{document} within the chiral quark model. It is found that the \begin{document}$ \Omega^*|1P_{3/2^-}\rangle $\end{document} has a sizeable decay rate into the three-body final states \begin{document}$ \Xi\pi\bar{K} $\end{document}. When considering \begin{document}$ \Omega^*|1P_{3/2^-}\rangle $\end{document} as the \begin{document}$ \Omega(2012) $\end{document} resonance, the predicted ratio \begin{document}$R_{\Xi\bar{K}}^{\Xi\pi\bar{K}}=\mathcal{B}[\Omega^*|1P_{3/2^-}\rangle\to \Xi^*(1530)\bar{K}\to \Xi\pi\bar{K}]/ $\end{document}\begin{document}$ \mathcal{B}[\Omega^*|1P_{3/2^-}\rangle \to \Xi\bar{K}]\simeq 12{\text%}$\end{document} is close to the upper limit \begin{document}$ 11{\text%} $\end{document} measured by the Belle Collaboration in 2019; however, it is too small to be comparable to the recent measurement \begin{document}$ 0.97 \pm 0.24\pm 0.07 $\end{document}. In addition, the coupled-channel effects on the bare three-quark state \begin{document}$ \Omega^*|1P_{3/2^-}\rangle $\end{document} from nearby channels \begin{document}$ \Xi \bar{K} $\end{document}, \begin{document}$ \Omega\eta $\end{document}, and \begin{document}$ \Xi^*(1530)\bar{K} $\end{document} are studied. Our theoretical results show that the coupled-channel effects on \begin{document}$ \Omega^*|1P_{3/2^-}\rangle $\end{document} are not very large, and the molecular component is no more than \begin{document}$ 30\% $\end{document}. To clarify the nature of \begin{document}$ \Omega(2012) $\end{document} resonance, precise measurements on the ratio \begin{document}$ R_{\Xi\bar{K}}^{\Xi\pi\bar{K}} $\end{document} are needed, and further investigation on the effects of coupled channels is recommended."> Further study of <inline-formula><tex-math id="M1">\begin{document}${{\boldsymbol{\Omega^*}} \boldsymbol{|1P_{\bf 3/2^-}\rangle} }$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/23325e47-4fb1-4428-9845-f56f5c14c4d6/CPC-2022-0608_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/23325e47-4fb1-4428-9845-f56f5c14c4d6/CPC-2022-0608_M1.png"/></alternatives></inline-formula> within a chiral quark model -
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