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

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.

Comments: 7 pages, 1 figure, talk given at the 38th International Symposium on Lattice Field Theory (LATTICE2021), 26th-30th July 2021, Zoom/Gather@Massachusetts Institute of Technology Version 3: Corrected some equations in section 3.2