The Benchmark Mode $\Omega_c \to \Omega^-\pi^+$ and Its Related Processes

The benchmark mode $\Omega_c^0\to \Omega^- \pi^+$, which receives purely factorization contribution, is of great importance among all the decay channels of $\Omega_c^0$ decays. In this work, within the framework of non-relativistic quark model (NRQM), we calculate all the 6 baryon transition form factors involving $\frac12 ^+\to \frac32 ^+$ decays. The absolute branching fractions of non-leptonic decays $\Omega_c^0\to \Omega^- \pi^+$, $\Omega_c^0\to \Omega^- \rho^+$ and $\Omega_c^0\to \Xi^- \pi^+$ as well as semi-leptonic decays $\Omega_c^0\to \Omega^- \ell^+ \nu_{\ell} \; (\ell=e,\mu)$ are calculated although they cannot be measured directly by current experiment. Based on the prediction $\mathcal{B}(\Omega_c^0\to\Omega^-\pi^+)=(3.43\pm0.48)\%$ in our work, we further predict the ratios between interested modes and the benchmark mode, giving $R(\Xi^-\pi^+)=0.16\pm0.06$, $R(\Omega^-\rho^+)=5.33\pm0.94$, $R(\Omega^- e^+\nu_e)=1.18\pm0.22$ and $R(\Omega^- \mu^+\nu_\mu)=1.11\pm0.20$. The predictions on $\Omega_c^0\to \Xi^-\pi^+$ and $\Omega_c^0\to \Omega^- e^+\nu$ agree well with recent measured ratios reported by LHCb in 2023 and ALICE in 2024, respectively.