Quantum Operator Design for Lattice Baryon Spectroscopy

Abstract

A previously-proposed method of constructing spatially-extended gauge-invariant three-quark operators for use in Monte Carlo lattice QCD calculations is tested, and a methodology for using these operators to extract the energies of a large number of baryon states is developed. This work is part of a long-term project undertaken by the Lattice Hadron Physics Collaboration to carry out a first-principles calculation of the low-lying spectrum of QCD. These techniques are then applied in the construction of nucleon operators. Correlation matrix elements between these operators are estimated using 200 configurations on a $12^3 \times 48$ anisotropic lattice in the quenched approximation with unphysically heavy u, d quark masses (the pion mass is approximately 700 MeV). After a change of basis operators using a variational method is applied, the energies of up to eight states are extracted in each symmetry channel. Although comparison with experiment is not justified, the pattern of levels obtained qualitatively agrees with the observed spectrum. A comparison with quark model predictions is also made; the quark model predicts more low-lying even-parity states than this study yields, but both the quark model and this study predict more odd-parity states near 2 GeV than currently observed in experiments.