Toward discovering the excited $\Omega$ baryons through nonleptonic weak decays of $\Omega_c$

Abstract

The nonleptonic weak decay processes $\Omega_c \to \Omega\pi^+/\Omega(1P)\pi^+/\Omega(1D)\pi^+/\Omega(2S)\pi^+$ are studied using the constituent quark model. The branching fraction of $\Omega_c \to \Omega\pi^+$ is predicted to be $1.0\%$. Considering the newly observed $\Omega(2012)$ resonance as a conventional $1P$-wave $\Omega$ excite state with spin-parity $J^P=3/2^-$, the newly measured ratio $\mathcal{B}[\Omega_c\to \Omega(2012)\pi^+ \to (\Xi\bar{K})^-\pi^+ ]/\mathcal{B}[\Omega_c\to \Omega \pi^+]$ at Belle can be well understood. Besides, the production rates for the missing $1P-$wave state $\Omega (1^2P_{1/2^-})$, two spin quartet $1D-$wave states $\Omega (1^4D_{1/2^+})$ and $\Omega (1^4D_{3/2^+})$, and two $2S$-wave states $\Omega(2^2S_{1/2^+})$ and $\Omega(2^4S_{3/2^+})$ are also investigated. It is expected that these missing excited $\Omega$ baryons should have large potentials to be discovered through the nonleptonic weak decays of $\Omega_c$ in forthcoming experiments by Belle II and/or LHCb.