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

Abstract

A systematic treatment of O(a)-improvement in lattice theories with static quarks is presented. The Schrödinger 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.

Comments: 42 pages, 19 eps figures; Improved notation and discussion for the case of finite delta m; corrected and added one reference