Line shapes of $Ω(2012)$ production in the $Ξ\bar K $ and $Ξπ\bar K$ decay channels

RESUMO

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 $\Xi^* \bar K$ 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^* \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 $R^{\Xi \pi \bar K}_{\Xi \bar K}$ 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 $R^{\Xi \pi \bar K}_{\Xi \bar K}$ which has been so far obtained using different criteria.