On O($a^2$) effects in gradient flow observables

Abstract

In lattice gauge theories, the gradient flow has been used extensively both, for scale setting and for defining finite volume renormalization schemes for the gauge coupling. Unfortunately, rather large cutoff effects have been observed in some cases. We here investigate these effects to leading order in perturbation theory, considering various definitions of the lattice observable, the lattice flow equation and the Yang Mills lattice action. These considerations suggest an improved set- up for which we perform a scaling test in the pure SU(3) gauge theory, demonstrating strongly reduced cutoff effects. We then attempt to obtain a more complete understanding of the structure of O($a^2$) effects by applying Symanzik's effective theory approach to the 4+1 dimensional local field theory with flow time as the fifth dimension. From these considerations we are led to a fully O($a^2$) improved set-up the study of which is left to future work.

7 pages 2 figures, contribution to Lattice 2014; a few typos eliminated, TCD preprint number added

References in corpus (6)

• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Chiral symmetry and the Yang--Mills gradient flow
• Studying the gradient flow coupling in the Schrödinger functional
• The gradient flow coupling in the Schrödinger Functional
• The Yang-Mills gradient flow in finite volume
• Scale setting in lattice QCD

Cited by in corpus (9)

• Lattice tests of beyond Standard Model dynamics
• Symanzik improvement of the gradient flow in lattice gauge theories
• Nonperturbative beta function of twelve-flavor SU(3) gauge theory
• Determination of Reference Scales for Wilson Gauge Action from Yang--Mills Gradient Flow
• The Yang-Mills gradient flow and renormalization
• Nonperturbative determination of $\beta$ functions for SU(3) gauge theories with 10 and 12 fundamental flavors using domain wall fermions
• The $SU(\infty )$ twisted gradient flow running coupling
• Lattice gradient flow with tree-level $\mathcal{O}(a^4)$ improvement in pure Yang-Mills theory
• Running coupling of the sextet composite Higgs model