Topological $SU(3)_f$ approach for two-body $\Omega_c$ weak decays

We explore the two-body non-leptonic weak decays of $\Omega_c^0$ into final states ${\bf B}^{(*)}M$ and ${\bf B}^{(*)}V$, where ${\bf B}^{(*)}$ 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 ${\cal B}(\Omega_c^0\to \Omega^-\pi^+)$, recombined or kept as the following ratios: ${\cal B}(\Omega_c^0\to\Xi^{*0}\bar K^{*0})/{\cal B}(\Omega_c^0\to\Omega^-\rho^+)=0.28\pm 0.11$, ${\cal B}(\Omega_c^0\to\Xi^-\pi^+)/{\cal B}(\Omega_c^0\to\Xi^{0}\bar K^{0})=0.10\pm 0.02$, and ${\cal B}(\Omega_c^0 \to \Omega^- K^+)/{\cal B}(\Omega_c^0 \to \Omega^- \pi^+)=0.06\pm 0.01$. In particular, we present ${\cal B}(\Omega_c^0 \to \Xi^0 \pi^0)=(2.3\pm0.2)\times 10^{-4}$ as half the value of ${\cal B}(\Omega_c^0 \to \Xi^- \pi^+)$ in the approximate isospin relation, and highlight potential candidates for testing $SU(3)_f$ symmetry breaking.