On the Viability of Lattice Perturbation Theory

TL;DR

This paper demonstrates that using renormalized coupling constants instead of bare ones significantly improves the accuracy of lattice perturbation theory in QCD, enabling reliable predictions at lower coupling strengths.

Contribution

It introduces a method to enhance lattice perturbation theory by employing physical quantity-based renormalized couplings and provides a mean-field analysis explaining large renormalizations.

Findings

Renormalized couplings improve predictive power.

Scaling is asymptotic at low β values.

Reliable quenched QCD simulations possible at β as low as 5.7.

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, like 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, like the coupling constant, to their continuum analogues. This suggests a new prescription for designing lattice operators that are more continuum-like than conventional operators. Finally, we provide evidence that the scaling of physical quantities is asymptotic or perturbative already at $\beta$'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 (quenched) QCD are possible at these same low $\beta$'s.