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Interpretation of the $Ω_c \to π^+ Ω(2012) \to π^+(\bar{K} Ξ)$ relative to $Ω_c \to π^+\bar{K} Ξ$ from the $Ω(2012)$ molecular perspective

We present a mechanism for $Ω_c \to π^+ Ω(2012)$ production through an external emission Cabibbo favored weak decay mode, where the $Ω(2012)$ is dynamically generated from the interaction of $\bar{K}Ξ^*(1530)$, $ηΩ$, with $\bar{K}Ξ$ as the main decay channel. The $Ω(2012)$ decays later to $\bar{K}Ξ$ in this picture, with results compatible with Belle data. The picture has as a consequence that one can evaluate the direct decay $Ω_c^0 \to π^+K^- Ξ^0$ and the decay $Ω_c^0 \to π^+\bar{K} Ξ^*$, $π^+ηΩ$ with direct coupling of $\bar{K}Ξ^*$ and $ηΩ$ to $K^- Ξ^0$. We show that, within uncertainties and using data from a recent Belle measurement, all these three channels account for about (12-20)\% of the total $Ω_c \to π^+K^- Ξ^0$ decay rate. The consistency of the molecular picture with all the data is established by showing that $Ω_c \to Ξ^0 \bar{K}^{*0} \to Ξ^0K^- π^+$ together with $Ω_c \to π^+ Ω^* \to π^+K^- Ξ^0 $ account for about 85\% of the total $Ω_c \to π^+K^- Ξ^0 $.