Lattice QCD determination of states with spin 5/2 or higher in the   spectrum of nucleons
  Energies for excited isospin 1/2 states that include the nucleon 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 5/2 or higher 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 5/2 or higher. 
S. Basak, R.G. Edwards, G. T. Fleming, A. Lichtl, C. Morningstar, D.   G. Ricards, I. Sato and S. J. Wallace