A perturbative determination of O($a$) boundary improvement coefficients for the Schr\"odinger Functional coupling at 1-loop with improved gauge actions

TL;DR

This paper calculates boundary improvement coefficients at 1-loop for the Schr"odinger Functional coupling using improved gauge actions, aiming to reduce lattice artifacts in QCD simulations.

Contribution

It provides the first perturbative determination of O($a$) boundary coefficients at 1-loop for improved gauge actions in the Schr"odinger Functional framework.

Findings

Boundary coefficients are computed for various improved gauge actions.

Lattice artifacts of the step scaling function are analyzed at 1-loop.

Numerical simulations show the impact of 1-loop O($a$) improvement on the SSF.

Abstract

We perturbatively determine O($a$) boundary improvement coefficients at 1-loop for the Schr\"odinger Functional coupling with improved gauge actions. These coefficients are required to implement the 1-loop O($a$) improvement in full QCD simulations for the coupling with the improved gauge actions. To this order, lattice artifacts of the step scaling function (SSF) for each improved gauge action are also investigated. Furthermore, we investigate the effect of the 1-loop O($a$) improvement to the SSF in numerical simulations of the pure SU(3) gauge theory.