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.
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Harlander, R.V., Neumann, T. The perturbative QCD gradient flow to three loops. J. High Energ. Phys. 2016, 161 (2016). https://doi.org/10.1007/JHEP06(2016)161
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DOI: https://doi.org/10.1007/JHEP06(2016)161