Perturbative determination of $c_{SW}$ with Symanzik improved gauge action and stout smearing

TL;DR

This paper calculates the one-loop correction to the clover coefficient $c_{SW}$ for improved gauge actions with stout smearing, providing essential data for lattice QCD simulations.

Contribution

It presents the first numerical determination of the one-loop $c_{SW}$ for Symanzik improved gauge actions with stout smearing and discusses mean field improvement effects.

Findings

Numerical value for one-loop $c_{SW}$ with Symanzik improved gauge action.

First estimate of one-loop $c_{NGI}$ for the quark field.

Analysis of mean field improvement implications.

Abstract

We determine the improvement factor $c_{SW}$ in one-loop lattice perturbation theory for the plaquette and Symanzik improved gauge actions. The fermionic action is ${\mathcal{O}(a)}$ clover improved with one-time stout smearing. $c_{SW}$ is derived from the one-loop correction to the quark-quark-gluon vertex in the off-shell regime. We give a first numerical value for the one-loop contribution to the non gauge-invariant improvement coefficient $c_{NGI}$ for the quark field using the plaquette action. A discussion of mean field improvement is included.