Viability of lattice perturbation theory

TLDR

The paper demonstrates that QCD lattice perturbation theory fails to match Monte Carlo data because it uses the bare lattice coupling as the expansion parameter. The authors replace the bare coupling with renormalized couplings defined through physical observables, employ an automatic scale‑setting procedure, and provide a mean‑field analysis that explains the large renormalizations between lattice and continuum quantities, thereby improving predictions. The study proposes a new prescription for designing lattice operators that are more continuum‑like and shows that physical quantities scale perturbatively already at β as low as 5.7, indicating that reliable quenched QCD simulations are possible at these low β values.

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.