Topological diagrams of ${\mathrm{\Omega }}_c^0$ decays in the $SU(3{)}_F$ limit

The ${\mathrm{\Omega }}_c^0$ baryon is unique among charmed sextet baryons because it decays through the weak interaction. In this work, we investigate the topological amplitudes of ${\mathrm{\Omega }}_c^0$ decays in the $SU(3{)}_F$ limit. The complete set of tree- and penguin-induced diagrams contributing to ${\mathrm{\Omega }}_c^0$ decays into decuplet and octet baryons is presented. The linear relations between the topological amplitudes and the $SU(3)$ irreducible amplitudes are derived through tensor analysis. Several isospin relations are obtained, and additional relations are derived to test the K"orner-Pati-Woo theorem.