Renormalization and O(a)-improvement of the static-light axial current

TL;DR

This paper develops a systematic approach for O(a)-improvement of static-light axial currents in lattice QCD, introducing a renormalization condition in the Schrödinger functional scheme and analyzing scale dependence and lattice effects.

Contribution

It provides a comprehensive treatment of O(a)-improvement, defines a renormalization condition in the SF-scheme, and computes the 2-loop anomalous dimension for static axial currents.

Findings

Derived the 2-loop anomalous dimension.

Computed the relation between schemes to 1-loop order.

Evaluated lattice spacing effects in perturbation theory.

Abstract

A systematic treatment of O(a)-improvement in lattice theories with static quarks is presented. The Schr\"odinger functional is discussed and a renormalization condition for the static axial current in the SF-scheme is introduced. Its relation to other schemes is computed to 1-loop order and the 2-loop anomalous dimension is derived. In finite volume renormalization schemes such as the SF-scheme, the renormalization scale dependence of the renormalized quantities is described by the step scaling function which can be computed by MC- simulations. We evaluate its lattice spacing effects in perturbation theory.