Viability of lattice perturbation theory

Abstract

In this paper we show that the apparent failure of QCD lattice perturbation theory to account for Monte Carlo measurements of perturbative quantities results from choosing the bare lattice coupling constant as the expansion parameter. Using instead "renormalized" coupling constants defined in terms of physical quantities, such as the heavy-quark potential, greatly enhances the predictive power of lattice perturbation theory. The quality of these predictions is further enhanced by a method for automatically determining the coupling-constant scale most appropriate to a particular quantity. We present a mean-field analysis that explains the large renormalizations relating lattice quantities, such as the coupling constant, to their continuum analogues. This suggests a new prescription for designing lattice operators that are more continuumlike than conventional operators. Finally, we provide evidence that the scaling of physical quantities can be asymptotic or perturbative already at (quenched) $\beta \text{'}\mathrm{s}$ as low as 5.7, provided the evolution from scale to scale is analyzed using renormalized perturbation theory. This result indicates that reliable simulations of QCD are possible at these same low $\beta \text{'}\mathrm{s}$.