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

Abstract: We explore the two-body non-leptonic weak decays of $\Omega_c<sup>0$ into final states ${\bf B}<sup>{(*)}M$ and ${\bf B}<sup>{(*)}V$, where ${\bf B}<sup>{(*)}$ 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 $${\cal B}(\Omega_c^0\to \Omega<sup>-\pi<sup>+)$$, 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 $${\cal B}(\Omega_c⁰ \to \Omega^- K^+)/{\cal B}(\Omega_c⁰ \to \Omega^- \pi^+)=0.06\pm 0.01$$. In particular, we present $${\cal B}(\Omega_c⁰ \to \Xi⁰ \pi^{0)=(2.3\pm0.2)\times} 10<sup>{-4}$$ as half the value of $${\cal B}(\Omega_c⁰ \to \Xi^- \pi<sup>+)$$ in the approximate isospin relation, and highlight potential candidates for testing $SU(3)_f$ symmetry breaking.