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

TL;DR

This study uses lattice QCD to analyze the spectrum and internal structure of $ ext{Omega}$ baryons, providing insights into their quantum numbers and confirming theoretical models with numerical data.

Contribution

First lattice QCD calculation of $ ext{Omega}$ baryon spectra and Bethe-Salpeter amplitudes, linking results to quark model classifications.

Findings

Mass ordering consistent with quark model predictions.

Bethe-Salpeter amplitude of $ ext{Omega}(1/2^+)$ shows a radial node.

Results support identification of $ ext{Omega}$ states' quantum numbers.

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