The Running Coupling from Lattice Gauge Theory

From an accurate determination of the inter-quark potential, one can study the running coupling constant for a range of $R$-values and hence estimate the scale \Lambda_{\msbar} . Detailed results are presented for $SU(2)$ pure gauge theory to illustrate the method.Comment: 8 pages Liverpool preprint LTH279, 24 Jan 1992 (1 figure not enclosed) (Accepted for publication in Phys Lett B

Non-perturbative determination of beta-functions and excited string states from lattices

We use lattice sum rules for the static quark potential to determine the beta-function for symmetric and asymmetric lattices non-perturbatively. We also study the colour field distributions in excited gluonic states.Comment: 9 pages, LATEX, 1 postscript figur

Approximate actions for dynamical fermions

Recent developments and applications of approximate actions for full lattice QCD are described. We present first results based on the stochastic estimation of the fermion determinant on $12^3\times 24$ configurations at $\beta=5.2$.Comment: 3 pages, Latex, no figures, Contribution to Lattice 97, The XV International Symposium on Lattice Field Theory, Edinburgh 22-26 July 199

The Heavy Hybrid Spectrum from NRQCD and the Born-Oppenheimer Approximation

The spectrum of heavy-quark hybrids is studied in the leading Born-Oppenheimer (LBO) approximation and using leading-order NRQCD simulations with an improved gluon action on anisotropic lattices. The masses of four hybrid states are obtained from our simulations for lattice spacings 0.1 fm and 0.2 fm and are compared to the LBO predictions obtained using previously-determined glue-excited static potentials. The consistency of results from the two approaches reveals a compelling physical picture for heavy-quark hybrid states.Comment: LATTICE99(Heavy Quarks),3 pages,2 figures,uses espcrc2.st

A Study of Degenerate Four-quark states in SU(2) Lattice Monte Carlo

The energies of four-quark states are calculated for geometries in which the quarks are situated on the corners of a series of tetrahedra and also for geometries that correspond to gradually distorting these tetrahedra into a plane. The interest in tetrahedra arises because they are composed of {\bf three } degenerate partitions of the four quarks into two two-quark colour singlets. This is an extension of earlier work showing that geometries with {\bf two} degenerate partitions (e.g.\ squares) experience a large binding energy. It is now found that even larger binding energies do not result, but that for the tetrahedra the ground and first excited states become degenerate in energy. The calculation is carried out using SU(2) for static quarks in the quenched approximation with $\beta=2.4$ on a $16^3\times 32$ lattice. The results are analysed using the correlation matrix between different euclidean times and the implications of these results are discussed for a model based on two-quark potentials.Comment: Original Raw PS file replace by a tarred, compressed and uuencoded PS fil

Hybrid Quarkonia with High Statistics from NRQCD

We have studied the O(mv^6) effects in NRQCD on the spectrum of heavy quarkonia and compare our results for different lattices (quenched and dynamical). We also report on an investigation into hybrid states within the framework of NRQCD. This suggests that the lowest lying hybrid is around the B^* \bar B threshold and 3 standard deviations above the B \bar B.Comment: 3 pages, LaTeX2e, 4 figures, uses styles [espcrc2, epsf], talk presented at Lattice 9

Effects of Dynamical Quarks in UKQCD Simulations

Recent results from the UKQCD Collaboration's dynamical simulations are presented. The main feature of these ensembles is that they have a fixed lattice spacing and volume, but varying sea quark mass from infinite (corresponding to the quenched simulation) down to roughly that of the strange quark mass. The main aim of this work is to uncover dynamical quark effects from these ``matched'' ensembles. We obtain some evidence of dynamical quark effects in the static quark potential with less effects in the hadronic spectrum.Comment: Invited paper presented at the Workshop on Lattice Hadron Physics, July 2001, Cairns, Australia. 7 pages. Uses espcrc2.sty (included

Non-Relativistic QCD for Heavy Quark Systems

We employ a nonrelativistic version of QCD (NRQCD) to study heavy quark-antiquark bound states in the lowest approximation without fine structure. We use gluon configurations on a 16^3 by 48 lattice at beta=6.2 from the UKQCD collaboration. For quark masses in the vicinity of the b we obtain bound state masses for S, P and both types of D wave. We also detect signals for two types of hybrids (quark,antiquark,gluon states). The results are sufficiently accurate to confirm that the values of the D wave mass from both lattice D waves coincide indicating that the cubical invariance of the lattice is restored to full rotational invariance at large distance. Our results also show that the S-P splitting is indeed insensitive to variations in the bare quark mass from Ma=1.0 to Ma=1.9.Comment: 13 pages, DAMTP-92-7