The perturbative QCD gradient flow to three loops

TL;DR

This paper computes the gradient flow in QCD perturbatively up to three loops, providing precise results for the action density and reducing theoretical uncertainties in lattice calculations.

Contribution

It extends the perturbative calculation of the gradient flow in QCD to NNLO, including quark mass effects at NLO, and improves the precision of theoretical predictions.

Findings

Perturbative series for the action density is well-behaved up to NNLO.

Theoretical uncertainty is significantly reduced at small flow times.

Quark mass effects are incorporated at NLO.

Abstract

The gradient flow in QCD is treated perturbatively through next-to-next-to-leading order in the strong coupling constant. The evaluation of the relevant momentum and flow-time integrals is described, including various means of validation. For the vacuum expectation value of the action density, which turns out to be a useful quantity in lattice calculations, we find a very well-behaved perturbative series through NNLO. Quark mass effects are taken into account through NLO. The theoretical uncertainty due to renormalization scale variation is significantly reduced with respect to LO and NLO, as long as the flow time is smaller than about 0.1 fm.