Ω baryon spectrum and their decays in a constituent quark model

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Combining the recent developments of the observations of $\mathrm{\ensuremath{\Omega}}$ sates we calculate the $\mathrm{\ensuremath{\Omega}}$ spectrum up to the $N=2$ shell within a nonrelativistic constituent quark potential model. Furthermore, the strong and radiative decay properties for the $\mathrm{\ensuremath{\Omega}}$ resonances within the $N=2$ shell are evaluated by using the masses and wave functions obtained from the potential model. It is found that the newly observed $\mathrm{\ensuremath{\Omega}}(2012)$ resonance is most likely to be the spin-parity ${J}^{P}=3/{2}^{\ensuremath{-}}$ $1P$-wave state $\mathrm{\ensuremath{\Omega}}({1}^{2}{P}_{3/{2}^{\ensuremath{-}}})$, it also has a large potential to be observed in the $\mathrm{\ensuremath{\Omega}}(1672)\ensuremath{\gamma}$ channel. Our calculation shows that the $1P$-, $1D$-, and $2S$-wave $\mathrm{\ensuremath{\Omega}}$ baryons have a relatively narrow decay width of less than 50 MeV. Based on the obtained decay properties and mass spectrum, we further suggest optimum channels and mass regions to find the missing $\mathrm{\ensuremath{\Omega}}$ resonances via the strong and/or radiative decay processes.