The $\Omega(2012)$ as a hadronic molecule

Abstract

Recently the Belle collaboration has discovered a narrow $S=-3$ baryon, the $\Omega(2012)$. We explore the possibility that the $\Omega(2012)$ is a $\Xi(1530)\,\bar K$ molecule, where the binding mechanism is the coupled channel dynamics with the $\Omega\,\eta$ channel. The characteristic signature of a molecular $\Omega(2012)$ will be its decay into the three body channel $\Xi \pi \bar{K}$, for which we expect a partial decay width of $2-3\,{\rm MeV}$. The partial decay width into the $\Xi \bar{K}$ channel should lie in the range of $1-11\,{\rm MeV}$, a figure compatible with experiment and which we have deduced from the assumption that the coupling involved in this decay is of natural size. For comparison purposes the decay of a purely compact $\Omega(2012)$ into the $\Xi \bar{K}$ and $\Xi \pi \bar{K}$ channels is of the same order of magnitude as and one order of magnitude smaller than in the molecular scenario, respectively. This comparison indicates that the current experimental information is insufficient to distinguish between a compact and a molecular $\Omega(2012)$ and further experiments will be required to determine its nature. A molecular $\Omega(2012)$ will also imply the existence of two- and three-body molecular partners. The two-body partners comprise two $\Lambda$ hyperons located at $1740$ and $1950\,{\rm MeV}$ respectively, the first of which might correspond to the $\Lambda(1800)$ while the second to the $\Lambda(2000)$ or the $\Lambda(2050)$. The three-body partners include a $\Xi(1530) K\bar{K}$ and a $\Xi(1530) \eta \bar{K}$ molecule, with masses of $M = 2385-2445\,{\rm MeV}$ and $M = 2434-2503\,{\rm MeV}$ respectively. We might be tempted to identify the first with the $\Xi(2370)$ and the latter with the $\Omega(2470)$ listed in the PDG.