Dimensional regularization of Schrodinger Functional correlation functions

TL;DR

This paper introduces a method for directly matching Schrodinger Functional renormalization schemes with perturbative schemes using dimensional regularization, employing a technique to handle Euclidean time translational invariance issues.

Contribution

It proposes a novel direct matching approach and applies a specialized dimensional regularization technique to compute correlation functions in the Schrodinger Functional scheme.

Findings

Identified divergent parts of correlation functions.

Developed a technique to handle lack of translational invariance.

Finite parts computation is ongoing.

Abstract

The matching between Schrodinger Functional renormalization schemes and conventional perturbative schemes is usually done using an intermediate lattice scheme. We propose to do the matching directly. This requires the perturbative evaluation of Schrodinger Functional correlation functions in the continuum. We use dimensional regularization but due to the lack of translational invariance in the Euclidean time direction, we employ a general technique introduced by Luscher. In this talk I describe this technique and its application to the one-loop expansion of correlation functions used in the definition of the renormalized quark mass in the Schrodinger Functional scheme. The divergent parts are identified and the computation of finite parts is in progress.