$\Omega$ baryon spectrum and their decays in a constituent quark model

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