Line shapes of $\Omega (2012)$ production in the $\Xi \bar{K}$ and $\Xi \pi \bar{K}$ decay channels

Abstract

We theoretically study the line shape of the experiment for $\Omega (2012)$ production in the ${\Xi }^{-}{\pi }^{+}{K}^{-}$ and ${\Xi }^0{K}^{-}$ decay modes, reflecting the ${\Xi }^{\ast }\bar{K}$ and $\Xi \bar{K}$ decay modes, from the perspective that the $\Omega (2012)$ is a molecular state dynamically generated from the interaction of the ${\Xi }^{\ast }\bar{K}$ and $\Omega \eta$, coupled channels with $\Xi \bar{K}$ as a decay channel. We show the consistency of the picture with the experimental mass distributions, giving support to the molecular picture for the $\Omega (2012)$ state. We also call the attention to the sensitivity of the results to the cut imposed on the $\pi \Xi$ invariant mass, and suggest a different method to obtain the ratio $R_{\Xi \bar{K}}^{\Xi \pi \bar{K}}$ of the three-body to two-body decay widths used so far as a test of the molecular picture. We stress that the direct comparison with the experimental mass distributions done here is a more stringent test of the molecular nature of the $\Omega (2012)$ state than the comparison of the ratio $R_{\Xi \bar{K}}^{\Xi \pi \bar{K}}$ which has been so far obtained using different criteria.

Comments: 5 pages, 4 figures