On the molecular nature of the $Ω_c(3120)$ and its analogy with the $Ω(2012)$

Abstract

We make a study of the $Ω_c(3120)$, one of the five $Ω_c$ states observed by the LHCb collaboration, which is well reproduced as a molecular state from the $Ξ^*_c \bar K$ and $Ω^*_c η$ channels mostly. The state with $J^P = 3/2^-$ decays to $Ξ_c \bar K$ in $D$-wave and we include this decay channel in our approach, as well as the effect of the $Ξ^*_c$ width. With all these ingredients, we determine the fraction of the $Ω_c(3120)$ width that goes into $Ξ_c π\bar K$, which could be a measure of the $Ξ^*_c \bar K$ molecular component, but due to a relatively big binding, compared to its analogous $Ω(2012)$ 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 $Ξ^*_c \bar K$ and $Ω^*_c η$ channels which together with the binding and width of the $Ω_c(3120)$ 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.