$\Omega (2012)$ through the looking glass of flavour SU(3)

Abstract

We perform the flavour $SU(3)$ analysis of the recently discovered $\Omega (2012)$ hyperon. We find that well known (four star) $\Delta (1700)$ resonance with quantum numbers of $J^P=3/2^{-}$ is a good candidate for the decuplet partner of $\Omega (2012)$ if the branching for the three-body decays of the latter is not too large $\le 70$\%. That implies that the quantum numbers of $\Omega (2012)$ are $I(J^P)=0(3/2^{-})$. The predictions for the properties of still missing $\Sigma$ and $\Xi$ decuplet members are made. We also discuss the implications of the $\overline{K}\Xi (1530)$ molecular picture of $\Omega (2012)$. Crucial experimental tests to distinguish various pictures of $\Omega (2012)$ are suggested.

6 pages, discussion of the Omega(2012) width in the molecular picture is added