Two Loop Computation of a Running Coupling in Lattice Yang-Mills Theory

TL;DR

This paper calculates the two-loop relation between lattice and running couplings in SU(2) gauge theory, enabling improved precision in lattice QCD computations and verifying the two-loop beta-function on the lattice.

Contribution

It provides the two-loop coefficient for the relation between lattice and Schroedinger functional couplings in pure SU(2) gauge theory, and verifies the two-loop beta-function on the lattice.

Findings

Two-loop coefficient computed for SU(2) lattice gauge theory

Verification of the two-loop beta-function on the lattice

Implementation of O(a) improvement at two-loop order

Abstract

We compute the two loop coefficient in the relation between the lattice bare coupling and the running coupling defined through the Schroedinger functional for the case of pure SU(2) gauge theory. This result is needed as one computational component to relate the latter to the MSbar-coupling, and it allows us to implement O(a) improvement of the Schroedinger functional to two-loop order. In addition, the two-loop beta-function is verified in a perturbative computation on the lattice, and the behavior of an improved bare coupling is investigated beyond one loop.