Stout-smearing, gradient flow and $c_{\text{SW}}$ at one loop order

TL;DR

This paper calculates the one-loop correction to the clover coefficient $c_{SW}$ for stout-smeared Wilson fermions, improving understanding of lattice artifacts in smearing-enhanced fermion actions.

Contribution

It introduces techniques for one-loop calculations in lattice perturbation theory applicable to smeared-link fermion actions, specifically determining $c_{SW}^{(1)}$ for stout smearing.

Findings

Computed the one-loop correction $c_{SW}^{(1)}$ for stout-smeared Wilson fermions.

Provided methods applicable to perturbative calculations with smeared links.

Enhanced precision in lattice QCD simulations with smeared fermion actions.

Abstract

The one-loop determination of the coefficient $c_\text{SW}$ of the Wilson quark action has been useful to push the leading cut-off effects for on-shell quantities to $\mathcal{O}(\alpha^2 a)$ and, in conjunction with non-perturbative determinations of $c_\text{SW}$, to $\mathcal{O}(a^2)$, as long as no link-smearing is employed. These days it is common practice to include some overall link-smearing into the definition of the fermion action. Unfortunately, in this situation only the tree-level value $c_\text{SW}^{(0)}=1$ is known, and cut-off effects start at $\mathcal{O}(\alpha a)$. We present some general techniques for calculating one loop quantities in lattice perturbation theory which continue to be useful for smeared-link fermion actions. Specifically, we discuss the application to the 1-loop improvement coefficient $c_\text{SW}^{(1)}$ for overall stout-smeared Wilson fermions.