We present a study of the SU (3) glueball spectrum for all J P C values at lattice spacings down to a −1 = 3.73(6) GeV (β = 6.4) using lattices of size up to 32 4 . We extend previous studies and show that the continuum limit has effectively been reached. The number of clearly identified J P C states has been substantially increased. There are no clear signals for spin-exotic glueballs below 3 GeV. A comparison with current experimental glueball candidates is made.Introduction The extraction of reliable predictions for the glueball spectrum of QCD remains an important challenge for lattice gauge theory. As part of a recent programme to study non-

We discuss renormalisation group improvement of the effective potential both in general and in the context of $O(N)$ scalar $\p^4$ and the Standard Model. In the latter case we find that absolute stability of the electroweak vacuum implies that $m_H\geq 1.95m_t-189~GeV$, for $\as (M_Z) = 0.11$. We point out that the lower bound on $m_H$ {\it decreases\/} if $\as (M_Z)$ is increased.Comment: 22 pages plus three PostScript figures (appended), Liverpool preprint LTH 288, University of Michigan preprint UM-TH-92-2

We compute the hadron mass spectrum, the quark masses and the meson decay constants in quenched lattice QCD with non-perturbatively O(a) improved Wilson fermions. The calculations are done for two values of the coupling constant, β = 6.0 and 6.2, and the results are compared with the predictions of ordinary Wilson fermions. We find that the improved action reduces lattice artifacts as expected.

We investigate the continuum limit of the gauge-ball spectrum in the four-dimensional pure U(1) lattice gauge theory. In the confinement phase we identify various states scaling with the correlation length exponent ν ≃ 0.35. The square root of the string tension also scales with this exponent, which agrees with the non-Gaussian fixed point exponent recently found in the finite size studies of this theory. Possible scenarios for constructing a non-Gaussian continuum theory with the observed gaugeball spectrum are discussed. The 0 ++ state, however, scales with a Gaussian value ν ≃ 0.5. This suggests the existence of a second, Gaussian continuum limit in the confinement phase and also the presence of a light or possibly massless scalar in the non-Gaussian continuum theory. In the Coulomb phase we find evidence for a few gauge-balls, being resonances in multi-photon channels; they seem to approach the continuum limit with as yet unknown critical exponents. The maximal value of the renormalized coupling in this phase is determined and its universality confirmed.

We propose the study of non-local gauge invariant operators to obtain an uncontaminated ground state for hadrons. The efficiency of the operators is shown by looking at the wave function of the first excited state, which has a node as a function of spatial extent of the operator.Liverpool Preprint LTH-339 (Nov. 1994); hep-lat/9411013