On the molecular nature of the ${\Omega }_c(3120)$ and its analogy with the $\Omega (2012)$

Abstract

We make a study of the ${\Omega }_c(3120)$, one of the five ${\Omega }_c$ states observed by the LHCb collaboration, which is well reproduced as a molecular state from the ${\Xi }_c^{\ast }\bar{K}$ and ${\Omega }_c^{\ast }\eta$ channels mostly. The state with $J^P=3/2^{-}$ decays to ${\Xi }_c\bar{K}$ in $D$-wave and we include this decay channel in our approach, as well as the effect of the ${\Xi }_c^{\ast }$ width. With all these ingredients, we determine the fraction of the ${\Omega }_c(3120)$ width that goes into ${\Xi }_c\pi \bar{K}$, which could be a measure of the ${\Xi }_c^{\ast }\bar{K}$ molecular component, but due to a relatively big binding, compared to its analogous $\Omega (2012)$ state, we find only a small fraction of about 3%, which makes this measurement difficult with present statistics. As an alternative, we evaluate the scattering length and effective range of the ${\Xi }_c^{\ast }\bar{K}$ and ${\Omega }_c^{\ast }\eta$ channels which together with the binding and width of the ${\Omega }_c(3120)$ state, could give us an answer to the issue of the compositeness of this state when these magnitudes are determined experimentally, something feasible nowadays, for instance, measuring correlation functions.

Comments: 6 pages, 2 figures, 2 tables; References added