Computation of the relation between the bare lattice coupling and the MSbar coupling in SU(N) gauge theories to two loops

TL;DR

This paper extends the perturbation expansion of the MSbar coupling in SU(N) gauge theories to two-loop order using lattice calculations, background field technique, and coordinate space methods.

Contribution

It provides a detailed calculation of the relation between the bare lattice coupling and the MSbar coupling at two loops in SU(N) gauge theories, employing novel computational techniques.

Findings

Two-loop relation between lattice and MSbar couplings derived.

Application of background field technique in lattice perturbation theory.

Use of coordinate space method for evaluating lattice Feynman integrals.

Abstract

The perturbation expansion of the MSbar coupling in the SU(N) gauge theory in powers of the bare lattice coupling is extended to two-loop order. A discussion of our results has already been published elsewhere. We here describe the calculation in some detail. It relies on the background field technique and a recently introduced coordinate space method to evaluate lattice Feynman integrals.