Topological $SU(3{)}_f$ approach for two-body ${\mathrm{\Omega }}_c$ weak decays

We explore the two-body non-leptonic weak decays of ${\mathrm{\Omega }}_c^0$ into final states ${\mathbf{B}}^{(\ast )}M$ and ${\mathbf{B}}^{(\ast )}V$, where ${\mathbf{B}}^{(\ast )}$ denotes an octet (a decuplet) baryon and $M(V)$ represents a pseudoscalar (vector) meson. We employ the topological $SU(3{)}_f$ approach to depict and parameterize the $W$-emission and $W$-exchange processes. We find that the topological parameters can be associated and combined, making them extractable for calculation. Consequently, we explain the partially measured branching fractions relative to $\mathcal{B}({\mathrm{\Omega }}_c^0\to {\mathrm{\Omega }}^{-}{\pi }^{+})$, recombined or kept as the following ratios: $\mathcal{B}({\mathrm{\Omega }}_c^0\to {\mathrm{\Xi }}^{\ast 0}{\bar{K}}^{\ast 0})\mathrm{/}\mathcal{B}({\mathrm{\Omega }}_c^0\to {\mathrm{\Omega }}^{-}{\rho }^{+})=0.28\pm 0.11$, $\mathcal{B}({\mathrm{\Omega }}_c^0\to {\mathrm{\Xi }}^{-}{\pi }^{+})\mathrm{/}\mathcal{B}({\mathrm{\Omega }}_c^0\to {\mathrm{\Xi }}^0{\bar{K}}^0)=0.10\pm 0.02$, and $\mathcal{B}({\mathrm{\Omega }}_c^0\to {\mathrm{\Omega }}^{-}{K}^{+})\mathrm{/}\mathcal{B}({\mathrm{\Omega }}_c^0\to {\mathrm{\Omega }}^{-}{\pi }^{+})=0.06\pm 0.01$. In particular, we present $\mathcal{B}({\mathrm{\Omega }}_c^0\to {\mathrm{\Xi }}^0{\pi }^0)=(2.3\pm 0.2)\times {10}^{-4}$ as half the value of $\mathcal{B}({\mathrm{\Omega }}_c^0\to {\mathrm{\Xi }}^{-}{\pi }^{+})$ in the approximate isospin relation, and highlight potential candidates for testing $SU(3{)}_f$ symmetry breaking.