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$Ω$ baryon spectrum and their decays in a constituent quark model

Combining the recent developments of the observations of $Ω$ sates we calculate the $Ω$ spectrum up to the $N=2$ shell within a nonrelativistic constituent quark potential model. Furthermore, the strong and radiative decay properties for the $Ω$ 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 $Ω(2012)$ resonance is most likely to be the spin-parity $J^P=3/2^-$ $1P$-wave state $Ω(1^{2}P_{3/2^{-}})$, it also has a large potential to be observed in the $Ω(1672)γ$ channel. Our calculation shows that the 1$P$-, 1$D$-, and 2$S$-wave $Ω$ 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 $Ω$ resonances via the strong and/or radiative decay processes.