The spectrum of glueballs below 4 GeV in the SU͑3͒ pure-gauge theory is investigated using Monte Carlo simulations of gluons on several anisotropic lattices with spatial grid separations ranging from 0.1 to 0.4 fm. Systematic errors from discretization and finite volume are studied, and the continuum spin quantum numbers are identified. Care is taken to distinguish single glueball states from two-glueball and torelon-pair states. Our determination of the spectrum significantly improves upon previous Wilson action calculations. ͓S0556-2821͑99͒07013-7͔

An analytic method of smearing link variables in lattice QCD is proposed and tested. The differentiability of the smearing scheme with respect to the link variables permits the use of modern Monte Carlo updating methods based on molecular dynamics evolution for gauge-field actions constructed using such smeared links. In examining the smeared mean plaquette and the static quark-antiquark potential, no degradation in effectiveness is observed as compared to link smearing methods currently in use, although an increased sensitivity to the smearing parameter is found.

The glueball-to-vacuum matrix elements of local gluonic operators in scalar, tensor, and pseudoscalar channels are investigated numerically on several anisotropic lattices with the spatial lattice spacing ranging from 0.1fm -0.2fm. These matrix elements are needed to predict the glueball branching ratios in J/ψ radiative decays which will help identify the glueball states in experiments. Two types of improved local gluonic operators are constructed for a self-consistent check and the finite volume effects are studied. We find that lattice spacing dependence of our results is very weak and the continuum limits are reliably extrapolated, as a result of improvement of the lattice gauge action and local operators. We also give updated glueball masses with various quantum numbers.

We present a detailed description of the extraction of the highly excited isovector meson spectrum on dynamical anisotropic lattices using a new quark-field construction algorithm and a large variational basis of operators. With careful operator construction, the combination of these techniques is used to identify the continuum spin of extracted states reliably, overcoming the reduced rotational symmetry of the cubic lattice. Excited states, states with exotic quantum numbers (0 +− , 1 −+ and 2 +− ) and states of high spin are resolved, including, for the first time in a lattice QCD calculation, spin-four states. The determinations of the spectrum of isovector mesons and kaons are performed on dynamical lattices with two volumes and with pion masses down to ∼ 400 MeV, with statistical precision typically at or below 1% even for highly excited states.