Perturbative coefficients for improved actions by Monte Carlo at large β\beta

Perturbative estimates of operator coefficients for improved lattice actions are becoming increasingly important for precision simulations of many hadronic observables. Following previous work by Dimm, Lepage, and Mackenzie, we consider the feasibility of computing operator coefficients from numerical simulations deep in the perturbative region of lattice theories. Here we introduce a background field technique that may allow for the computation of the coefficients of clover-field operators in a variety of theories. This method is tested by calculations of the renormalized quark mass in lattice NRQCD, and of the $O(\alpha_s)$ clover coefficient for Sheikholeslami-Wohlert fermions. First results for the coefficient of the magnetic moment operator in NRQCD are also presented.Comment: 3 Pages, LaTeX (espcrc2.sty, uses \psfig), 3 Postscript figures, Talk presented at LATTICE'97, Edinburg

Perturbative Improvement for Lattice QCD: An Update

Recent developments in the Symanzik improvement program for lattice QCD are reviewed.Comment: Invited talk at the workshop on "Lattice QCD on Parallel Computers" (Tsukuba, March 1997). One file producing 12 pages; LaTe

Nonperturbative ``Lattice Perturbation Theory''

We discuss a program for replacing standard perturbative methods with Monte Carlo simulations in short distance lattice gauge theory calculations.Comment: 3 pages, uuencoded Latex file, two embedded figures and .sty file include

QCD on Coarse Lattices

We show that the perturbatively-improved gluon action for QCD, once it is tadpole-improved, gives accurate results even with lattice spacings as large as 0.4~fm. {\em No\/} tuning of the couplings is required. Using this action and lattice spacing, we obtain a static potential that is rotationally invariant to within a few percent, the spin-averaged charmonium spectrum accurate to within 30--40~MeV, and scaling to within 5--10\%. We demonstrate that simulations on coarse lattices are several orders of magnitude less costly than simulations using current methods.Comment: 4 page

Two-loop Perturbative Quark Mass Renormalization from Large Beta Monte Carlo

We present the calculation of heavy Wilson quark mass renormalization constants from large beta Monte Carlo simulations. Simulations were performed at various beta larger than 9, each on several spatial lattice sizes to allow for an infinite volume extrapolation. We use twisted boundary conditions to suppress tunneling and work in Coulomb gauge with appropriate adjustments for the temporal links. The one-loop coefficient obtained from this method is in agreement with the analytical result and a preliminary result for the second order coefficient is reported.Comment: Lattice 2000 (Perturbation Theory), 4 pages,4 figures, uses espcrc2.st

Perturbative expansions from Monte Carlo simulations at weak coupling: Wilson loops and the static-quark self-energy

Perturbative coefficients for Wilson loops and the static-quark self-energy are extracted from Monte Carlo simulations at weak coupling. The lattice volumes and couplings are chosen to ensure that the lattice momenta are all perturbative. Twisted boundary conditions are used to eliminate the effects of lattice zero modes and to suppress nonperturbative finite-volume effects due to Z(3) phases. Simulations of the Wilson gluon action are done with both periodic and twisted boundary conditions, and over a wide range of lattice volumes (from $3^4$ to $16^4$) and couplings (from $\beta \approx 9$ to $\beta \approx 60$). A high precision comparison is made between the simulation data and results from finite-volume lattice perturbation theory. The Monte Carlo results are shown to be in excellent agreement with perturbation theory through second order. New results for third-order coefficients for a number of Wilson loops and the static-quark self-energy are reported.Comment: 36 pages, 15 figures, REVTEX documen

Perturbative two- and three-loop coefficients from large beta Monte Carlo

Perturbative coefficients for Wilson loops and the static quark self-energy are extracted from Monte Carlo simulations at large beta on finite volumes, where all the lattice momenta are large. The Monte Carlo results are in excellent agreement with perturbation theory through second order. New results for third order coefficients are reported. Twisted boundary conditions are used to eliminate zero modes and to suppress Z_3 tunneling.Comment: 6 pages, 5 figures. Contributions of Howard Trottier and Paul Mackenzie to Lattice '9

Screening Masses of Hot SU(2) Gauge Theory from the 3D Adjoint Higgs Model

We study the Landau gauge propagators of the lattice SU(2) 3d adjoint Higgs model, considered as an effective theory of high temperature 4d SU(2) gauge theory. From the long distance behaviour of the propagators we extract the screening masses. It is shown that the pole masses extracted from the propagators agree well with the screening masses obtained recently in finite temperature SU(2) theory. The relation of the propagator masses to the masses extracted from gauge invariant correlators is also discussed. In so-called lambda gauges non-perturbative evidence is given for the gauge independence of pole masses within this class of gauges.Comment: Talk given at SEWM98 Conference, Copenhagen, December 199

Lattice QCD on Small Computers

We demonstrate that lattice QCD calculations can be made $10^3$--$10^6$ times faster by using very coarse lattices. To obtain accurate results, we replace the standard lattice actions by perturbatively-improved actions with tadpole-improved correction terms that remove the leading errors due to the lattice. To illustrate the power of this approach, we calculate the static-quark potential, and the charmonium spectrum and wavefunctions using a desktop computer. We obtain accurate results that are independent of the lattice spacing and agree well with experiment.Comment: 15 pages, 3 figs incl as LaTex pictures Minor additions to tables and tex