Logarithmic corrections to $\mathbf{a^2}$ scaling in lattice Yang Mills theory

TL;DR

This paper investigates the leading logarithmic corrections to the $a^2$ scaling of lattice artifacts in SU(N) pure gauge theory, showing that these corrections reduce cutoff effects and paving the way for more comprehensive lattice QCD studies.

Contribution

It provides the first calculation of logarithmic corrections to $a^2$ scaling in lattice SU(N) gauge theory based on anomalous dimensions of specific operators.

Findings

Logarithmic corrections decrease cutoff effects in SU(N) gauge theory.

Results are a foundational step for full lattice QCD at $O(a^2)$.

First explicit computation of these corrections in this context.

Abstract

We analyse the leading logarithmic corrections to the $a^2$ scaling of lattice artefacts in QCD, following the seminal work of Balog, Niedermayer and Weisz in the O(n) non-linear sigma model. Restricting our attention to contributions from the action, the leading logarithmic corrections can be determined by the anomalous dimensions of a minimal on-shell basis of mass-dimension 6 operators. We present results for the SU(N) pure gauge theory. In this theory the logarithmic corrections reduce the cutoff effects. These computations are the first step towards a study of full lattice QCD at O($a^2$), which is in progress.