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 1-loop boundary improvement coefficients for the Schr"odinger Functional coupling with improved gauge actions, enhancing the precision of lattice QCD simulations and understanding of lattice artifacts.

Contribution

It provides the first 1-loop level determination of O(a) boundary improvement coefficients for various improved gauge actions in the Schr"odinger Functional scheme.

Findings

Calculated O(a) boundary improvement coefficients for improved gauge actions.

Analyzed lattice artifacts of step scaling functions for these actions.

Estimated the ratio of b3b1-parameters between improved and plaquette actions.

Abstract

We determine O($a$) boundary improvement coefficients up to 1-loop level for the Schr\"odinger Functional coupling with improved gauge actions including plaquette and rectangle loops. These coefficients are required to implement 1-loop O($a$) improvement in full QCD simulations for the coupling with the improved gauge actions. To this order, lattice artifacts of step scaling function for each improved gauge action are also investigated. In addition, passing through the SF scheme, we estimate the ratio of $\Lambda$-parameters between the improved gauge actions and the plaquette action more accurately.