Flavor structure of the excited baryon spectra from lattice QCD

TLDR

Lattice QCD calculations of excited baryon spectra for the N, Δ, Λ, Σ, Ξ, and Ω families are performed using operators built from SU(3)$_F$, SU(4) Dirac, and O(3) orbital symmetries, with covariant derivatives to realize orbital angular momenta, and correlation‑function matrices to extract excited states. The resulting spectra exhibit bands of states with total spins up to $J=7/2$, each assigned a dominant flavor symmetry that matches $SU(6)\!\times\!O(3)$ counting for the lowest parity bands, and hybrid states are identified by the dominance of chromo‑magnetic operators.

Abstract

Excited state spectra are calculated using lattice QCD for baryons that can be formed from $u$, $d$ and $s$ quarks, namely the $N$, $\Delta$, $\Lambda$, $\Sigma$, $\Xi$ and $\Omega$ families of baryons. Baryonic operators are constructed from continuum operators that transform as irreducible representations of SU(3)$_F$ symmetry for flavor, SU(4) symmetry for Dirac spins of quarks and O(3) symmetry for orbital angular momenta. Covariant derivatives are used to realize orbital angular momenta. Using the operators, we calculate matrices of correlation functions in order to extract excited states. The resulting lattice spectra have bands of baryonic states with well-defined total spins up to $J=7/2$. Each state can be assigned a dominant flavor symmetry and the counting of states of each flavor and spin reflects $SU(6) \times O(3)$ symmetry for the lowest negative-parity and positive-parity bands. States with strong hybrid content are identified through the dominance of chromo-magnetic operators.