Spectrum and Bethe-Salpeter amplitudes of $\Omega$ baryons from lattice QCD

Abstract

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 $SU(6)⨂O(3)$ quark model description. Our results are helpful for identifying the quantum number of experimentally observed $\Omega$ states.

Comments: 7 pages, 5 figures, submitted to Chinese Physics C