Logarithmic corrections to $\mathbf{a^2}$ scaling in lattice QCD with Wilson and Ginsparg-Wilson quarks

TL;DR

This paper investigates the leading logarithmic corrections to the quadratic lattice spacing artifacts in QCD with Wilson and Ginsparg-Wilson quarks, extending previous sigma model analyses to lattice QCD.

Contribution

It provides a detailed calculation of the leading logarithmic corrections for $a^2$ scaling in lattice QCD, focusing on action contributions and anomalous dimensions of specific operators.

Findings

Derived the form of logarithmic corrections for Wilson and Ginsparg-Wilson quarks.

Identified the relevant operators in the Symanzik Effective Theory.

Extended sigma model results to lattice QCD 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. Limiting the discussion to contributions from the action, the leading logarithmic corrections can be determined by the anomalous dimensions of mass-dimension 6 operators. These operators form a minimal on-shell basis of the Symanzik Effective Theory. We present results for non-perturbatively O($a$) improved Wilson and Ginsparg-Wilson quarks.