Theoretical study of the $Ω(2012)$ state in the $Ω_c^0 \to π^+ Ω(2012)^- \to π^+ (\bar{K}Ξ)^-$ and $π^+ (\bar{K}Ξπ)^-$ decays
We report on a theoretical study of the newly observed $Ω(2012)$ resonance in the nonleptonic weak decays of $Ω_c^0 \to π^+ \bar{K}Ξ^*(1530) (ηΩ) \to π^+ (\bar{K}Ξ)^-$ and $π^+ (\bar{K}Ξπ)^-$ via final-state interactions of the $\bar{K}Ξ^*(1530)$ and $ηΩ$ pairs. The weak interaction part is assumed to be dominated by the charm quark decay process: $c(ss) \to (s + u + \bar{d})(ss)$, while the hadronization part takes place between the $sss$ cluster from the weak decay and a quark-antiquark pair with the quantum numbers $J^{PC} = 0^{++}$ of the vacuum, produces a pair of $\bar{K}Ξ^*(1530)$ and $ηΩ$. Accordingly, the final $\bar{K}Ξ^*(1530)$ and $ηΩ$ states are in pure isospin $I= 0$ combinations, and the $Ω_c^0 \to π^+ \bar{K}Ξ^*(1530)(ηΩ) \to π^+ (\bar{K}Ξ)^-$ decay is an ideal process to study the $Ω(2012)$ resonance. With the final-state interaction described in the chiral unitary approach, up to an arbitrary normalization, the invariant mass distributions of the final state are calculated, assuming that the $Ω(2012)$ resonance with spin-parity $J^P = 3/2^-$ is a dynamically generated state from the coupled channels interactions of the $\bar{K}Ξ^*(1530)$ and $ηΩ$ in $s$-wave and $\bar{K}Ξ$ in $d$-wave. We also calculate the ratio, $R^{\bar{K}Ξπ}_{\bar{K}Ξ} = {\rm Br}[Ω_c^0 \to π^+ Ω(2012)^- \to π^+ (\bar{K}Ξπ)^-] / {\rm Br}[Ω_c^0 \to π^+ Ω(2012)^- \to π^+ (\bar{K}Ξ)^-$]. The proposed mechanism can provide valuable information on the nature of the $Ω(2012)$ and can in principle be tested by future experiments.