Logarithmic corrections to O(a^2) lattice artifacts

TL;DR

This paper calculates logarithmic corrections to lattice artifacts in the O(n) sigma-model, providing insights that could improve precision in lattice QCD simulations by understanding cutoff effects.

Contribution

It derives the form of logarithmic corrections to O(a^2) lattice artifacts and computes next-to-leading terms, relevant for lattice QCD precision measurements.

Findings

Leading artifacts are of the form a^2[ln(a^2)]^{n/(n-2)}

Next-to-leading corrections are computed explicitly

Results match lattice artifacts in the step scaling function for n=3

Abstract

We compute logarithmic corrections to the O(a^2) lattice artifacts for a class of lattice actions for the non-linear O(n) sigma-model in two dimensions. The generic leading artifacts are of the form $a^2[\ln(a^2)]^{(n/(n-2))}$. We also compute the next-to-leading corrections and show that for the case n=3 the resulting expressions describe well the lattice artifacts in the step scaling function, which are in a large range of the cutoff apparently of the form O(a). An analogous computation should, if technically possible, accompany any precision measurements in lattice QCD.