Two-loop computation of a finite volume running coupling on the lattice

TL;DR

This paper calculates the two-loop coefficient relating lattice bare coupling to the Schrödinger functional coupling in SU(2) gauge theory, enabling precise connection to the MSbar scheme and O(a) improvement.

Contribution

It provides the two-loop relation between lattice and Schrödinger functional couplings and verifies the two-loop beta-function on the lattice.

Findings

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

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

Analysis of coupling expansion behaviors beyond one loop

Abstract

In pure SU(2) gauge theory we compute the two-loop coefficient in the relation between the lattice bare coupling and the running coupling defined through the Schroedinger functional. This result is required to relate the latter to the MSbar-coupling in our programme to compute alpha_s. In addition it allows us to implement O(a) improvement of the Schroedinger functional to two-loop order. The two-loop beta-function is verified in a perturbative computation on the lattice, and the behavior of expansions in the standard and in the Parisi-improved bare couplings are investigated beyond one loop.