The benchmark mode \(\Omega _c \rightarrow \Omega ^-\pi ^+\) and its related processes

Abstract

The benchmark mode \(\Omega _c^0\rightarrow \Omega ^- \pi ^+\), 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 \(\frac{1}{2} ^+\rightarrow \frac{3}{2} ^+\) decays. The absolute branching fractions of non-leptonic decays \(\Omega _c^0\rightarrow \Omega ^- \pi ^+\), \(\Omega _c^0\rightarrow \Omega ^- \rho ^+\) and \(\Omega _c^0\rightarrow \Xi ^- \pi ^+\) as well as semi-leptonic decays \(\Omega _c^0\rightarrow \Omega ^- \ell ^+ \nu _{\ell } \; (\ell =e,\mu )\) are calculated although they cannot be measured directly by current experiment. Based on the prediction \(\mathcal {B}(\Omega _c^0\rightarrow \Omega ^-\pi ^+)=(3.43{\pm 0.48})\%\) in our work, we further predict the ratios between interested modes and the benchmark mode, giving \(R(\Xi ^-\pi ^+)=0.16\pm {0.06}\), \(R(\Omega ^-\rho ^+)=5.33{\pm 0.94}\), \(R(\Omega ^- e^+\nu _e)=1.18{\pm 0.22}\) and \(R(\Omega ^- \mu ^+\nu _\mu )=1.11{\pm 0.20}\). The predictions on \(\Omega _c^0\rightarrow \Xi ^-\pi ^+\) and \(\Omega _c^0\rightarrow \Omega ^- e^+\nu \) agree well with recent measured ratios reported by LHCb in 2023 and ALICE in 2024, respectively.