The Benchmark Mode ${\mathrm{\Omega }}_c\to {\mathrm{\Omega }}^{-}{\pi }^{+}$ and Its Related Processes

The benchmark mode ${\mathrm{\Omega }}_c^0\to {\mathrm{\Omega }}^{-}{\pi }^{+}$, which receives purely factorization contribution, is of great importance among all the decay channels of ${\mathrm{\Omega }}_c^0$ decays. In this work, within the framework of non-relativistic quark model (NRQM), we calculate all the 6 baryon transition form factors involving ${\frac{1}{2}}^{+}\to {\frac{3}{2}}^{+}$ decays. The absolute branching fractions of non-leptonic decays ${\mathrm{\Omega }}_c^0\to {\mathrm{\Omega }}^{-}{\pi }^{+}$, ${\mathrm{\Omega }}_c^0\to {\mathrm{\Omega }}^{-}{\rho }^{+}$ and ${\mathrm{\Omega }}_c^0\to {\mathrm{\Xi }}^{-}{\pi }^{+}$ as well as semi-leptonic decays ${\mathrm{\Omega }}_c^0\to {\mathrm{\Omega }}^{-}{\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }}(\mathrm{\ell }=e,\mu )$ are calculated although they cannot be measured directly by current experiment. Based on the prediction $\mathcal{B}({\mathrm{\Omega }}_c^0\to {\mathrm{\Omega }}^{-}{\pi }^{+})=(3.43\pm 0.48)\mathrm{\%}$ in our work, we further predict the ratios between interested modes and the benchmark mode, giving $R({\mathrm{\Xi }}^{-}{\pi }^{+})=0.16\pm 0.06$, $R({\mathrm{\Omega }}^{-}{\rho }^{+})=5.33\pm 0.94$, $R({\mathrm{\Omega }}^{-}{e}^{+}{\nu }_e)=1.18\pm 0.22$ and $R({\mathrm{\Omega }}^{-}{\mu }^{+}{\nu }_{\mu })=1.11\pm 0.20$. The predictions on ${\mathrm{\Omega }}_c^0\to {\mathrm{\Xi }}^{-}{\pi }^{+}$ and ${\mathrm{\Omega }}_c^0\to {\mathrm{\Omega }}^{-}{e}^{+}\nu$ agree well with recent measured ratios reported by LHCb in 2023 and ALICE in 2024, respectively.