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

Abstract

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

Comments: 7 pages, 3 figures