Lattice QCD determination of patterns of excited baryon states

Energies for excited isospin $I=\frac{1}{2}$ and $I=\frac{3}{2}$ states that include the nucleon and $\Delta$ families of baryons are computed using quenched, anisotropic lattices. Baryon interpolating field operators that are used include nonlocal operators that provide $G_2$ irreducible representations of the octahedral group. The decomposition of spin $\frac{5}{2}$ or higher spin states is realized for the first time in a lattice QCD calculation. We observe patterns of degenerate energies in the irreducible representations of the octahedral group that correspond to the subduction of the continuum spin $\frac{5}{2}$ or higher. The overall pattern of low-lying excited states corresponds well to the pattern of physical states subduced to the irreducible representations of the octahedral group.