English

The perturbative QCD gradient flow to three loops

High Energy Physics - Phenomenology 2016-07-20 v2 High Energy Physics - Lattice

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.

Keywords

Cite

@article{arxiv.1606.03756,
  title  = {The perturbative QCD gradient flow to three loops},
  author = {Robert V. Harlander and Tobias Neumann},
  journal= {arXiv preprint arXiv:1606.03756},
  year   = {2016}
}

Comments

25 pages, 6 figures, 3 tables. v2: typos fixed; matches published version

R2 v1 2026-06-22T14:23:31.715Z