QCD sum rules study on weak decays $\Omega_c^0\to\Omega^- (\pi^+, \rho^+, l^+\nu_l)$

We study the weak decays of the charmed baryon $\Omega_c^0$ to the $\Omega^-$ baryon within the framework of QCD sum rules. A three-point correlation function is defined for calculating eight form factors governing the $\Omega_c^0 \to \Omega^-$ transition. The cutting rules are employed to extract the double imaginary parts of the correlation functions, enabling their expression in the form of dispersive integrals. These form factors are then used to determine the branching fractions for the hadronic decays $\Omega_c^0 \to \Omega^- \pi^+$ and $\Omega_c^0 \to \Omega^- \rho^+$, as well as the semi-leptonic decay $\Omega_c^0 \to \Omega^- \ell^+ \nu_\ell$. Our results are compared with existing theoretical predictions and experimental data, providing a comprehensive analysis of $\Omega_c^0$ decays and offering valuable insights into the dynamics of charmed baryon decays.