Peturbative study of the Chirally Rotated Schrödinger Functionality in Lattice QCD

Abstract

In this thesis we study the renormalisation and O(a) improvement of the Chirally Rotated Schrödinger Functional (xSF) in perturbation theory. The xSF was originally proposed in [1] as a way of rehabiliting the mechanism of automatic O(a) improvement in the Schrödinger Functional formulation. In order to achieve this in the interacting theory, the finite coefficient of a dimension 3 boundary counterterm has to be tuned. After this, O(a) effects originating from the bulk action or from insertions of composite operators in the bulk will be absent in physical quantities. As in any lattice regularization with SF boundary conditions, extra O(a) effects arise from the boundaries and are cancelled by tuning two dimension 4 boundary coefficients.