The $\Omega$ baryons with $J^P=3/2^\pm, 1/2^\pm$ are studied on the lattice in the quenched approximation. Their mass levels are ordered as $M_{ 3/2^+}<M_{ 3/2^-}\approx M_{ 1/2^-}<M_{ 1/2^+}$, as is expected from the constituent quark model. The mass values are also close to those of the four $\Omega$ states observed in experiments, respectively. We calculate the Bethe-Salpeter amplitudes of $\Omega(3/2^+)$ and $\Omega(1/2^+)$ and find there is a radial node for the $\Omega(1/2^+)$ Bethe-Salpeter amplitude, which may imply that $\Omega(1/2^+)$ is an orbital excitation of $\Omega$ baryons as a member of the $(D,L_N^P)=(70,0_2^+)$ supermultiplet in the $SU(6)\bigotimes O(3)$ quark model description. Our results are helpful for identifying the quantum number of experimentally observed $\Omega$ states.
Categories: hep-lat