Tadpole-improved SU(2) lattice gauge theory

Abstract

A comprehensive analysis of tadpole-improved SU(2) lattice gauge theory is made. Simulations are done on isotropic and anisotropic lattices, with and without improvement. Two tadpole renormalization schemes are employed, one using average plaquettes, the other using mean links in Landau gauge. Simulations are done with spatial lattice spacings $a_s$ in the range of about 0.1--0.4 fm. Results are presented for the static quark potential, the renormalized lattice anisotropy $a_t/a_s$ (where $a_t$ is the ``temporal'' lattice spacing), and for the scalar and tensor glueball masses. Tadpole improvement significantly reduces discretization errors in the static quark potential and in the scalar glueball mass, and results in very little renormalization of the bare anisotropy that is input to the action. We also find that tadpole improvement using mean links in Landau gauge results in smaller discretization errors in the scalar glueball mass (as well as in the static quark potential), compared to when average plaquettes are used. The possibility is also raised that further improvement in the scalar glueball mass may result when the coefficients of the operators which correct for discretization errors in the action are computed beyond tree level.Comment: 14 pages, 7 figures (minor changes to overall scales in Fig.1; typos removed from Eqs. (3),(4),(15); some rewording of Introduction

Adjoint “quarks” on coarse anisotropic lattices: Implications for string breaking in full QCD

“…The renormalization of the anisotropy is fairly small in all cases, especially as compared to the very large renormalizations for unimproved actions on lattices with comparable spacings [32].…”

“…Unimproved actions exhibit much larger rotational symmetry breaking effects on such coarse lattices [32].…”

“…Refs. [38,34,32]). Using the lattice with a s = 0.36 fm here provides an increase in computational efficiency of some two orders of magnitude compared to the simulations of adjoint quarks done on lattices with "fine" spacings in Ref.…”

“…The renormalized anisotropy is determined by comparing the static potential a t V xt , computed in units of a t from Wilson loops W xt where the time axis is taken in the direction of small lattice spacings, with the potential a s V xy computed from Wilson loops W xy with both axes taken in the direction of large lattice spacings [32][33][34]39]. The anisotropy is determined after an unphysical constant is removed from the potentials, by subtraction of the simulation results at two different radii…”

“…Here we define the mean fields using the measured values of the average plaquettes. Since the lattice spacings a t in our simulations are small, we adopt the following prescription [32][33][34] for the mean fields…”