We give results for the B and the D meson spectrum using NRQCD on the lattice in the quenched approximation. The masses of radially and orbitally excited states are calculated as well as S-wave hyperfine and P-wave fine structure. Radially excited P states are observed for the first time. Radial and orbital excitation energies match well to experiment, as does the strange-nonstrange S-wave splitting. We compare the light and heavy quark mass dependence of various splittings to experiment. Our B results cover a range in lattice spacings of more than a factor of two. Our D results are from a single lattice spacing and we compare them to numbers in the literature from finer lattices using other methods. We see no significant dependence of physical results on the lattice spacing.

We report on a study of heavy quark bound states containing an additional excitation of the gluonic degrees of freedom. To this end we employ the nonrelativistic QCD approach on coarse and asymmetric lattices, where we discard vacuum polarization effects and neglect all spin-correction terms. We find a clear hybrid signal on all our lattices (a s 0.15, . . . , 0.47 fm). We have studied in detail the lattice spacing artifacts, finite volume effects, and mass dependence. Within the above approximations we predict the lowest lying hybrid excitation in charmonium to be 1.323(13) GeV above the ground state, where we use the 1P-1S splitting to set the scale. The bottomonium hybrid was found to be 1.542(8) GeV above its ground state. [S0031-9007(99)

We present data for the axial coupling constant g A of the nucleon obtained in lattice QCD with two degenerate flavors of dynamical non-perturbatively improved Wilson quarks. The renormalization is also performed non-perturbatively. For the analysis we give a chiral extrapolation formula for g A based on the small scale expansion scheme of chiral effective field theory for two degenerate quark flavors. Applying this formalism in a finite volume we derive a formula that allows us to extrapolate our data simultaneously to the infinite volume and to the chiral limit. Using the additional lattice data in finite volume we are able to determine the axial coupling of the nucleon in the chiral limit without imposing the known value at the physical point.

A lattice study of the equation of state for pure SU͑3͒ gauge theory using a renormalization-group ͑RG͒ improved action is presented. The energy density and pressure are calculated on a 16 3 ϫ4 and a 32 3 ϫ8 lattice employing the integral method. Extrapolating the results to the continuum limit, we find the energy density and pressure to be in good agreement with those obtained with the standard plaquette action within the error of 3-4 %. ͓S0556-2821͑99͒07819-4͔

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