Stout smearing and Wilson flow in lattice perturbation theory

TL;DR

This paper develops a perturbative expansion for stout smearing and Wilson flow in lattice gauge theory to facilitate one-loop calculations, linking the two methods and applying them to fermion self-energy computations.

Contribution

It provides the first systematic perturbative expansion of stout smearing and Wilson flow up to order g_0^3, enabling their use in lattice perturbation theory.

Findings

Derived the expansion of stout smearing and Wilson flow to order g_0^3.

Showed how to incorporate these methods into Feynman rules for lattice fermions.

Calculated the self-energy of clover-improved Wilson fermions using the developed framework.

Abstract

We present the expansion of stout smearing and the Wilson flow in lattice perturbation theory to order $g_0^3$, which is suitable for one-loop calculations. As the Wilson flow is generated by infinitesimal stout smearing steps, the results are related to each other by taking the appropriate limits. We show how to apply perturbative stout smearing or Wilson flow to the Feynman rules of any lattice fermion action and and illustrate them by calculating the self-energy of the clover-improved Wilson fermion.