Results and techniques for higher order calculations within the gradient-flow formalism
Johannes Artz, Robert V. Harlander, Fabian Lange, Tobias Neumann, and, Mario Prausa
TL;DR
This paper develops a systematic perturbative method within the QCD gradient-flow formalism, providing higher-order calculations for observables, including three-loop results for quark and gluon condensates, and tools for accurate scheme conversions.
Contribution
It introduces a comprehensive perturbative framework for the gradient-flow formalism, including Feynman rules and higher-order calculations, enhancing precision in QCD observable evaluations.
Findings
Three-loop results for the quark condensate at finite flow time.
Conversion factor for ringed quark fields to the MS scheme.
Re-evaluation and improved accuracy of the three-loop gluon condensate.
Abstract
We describe in detail the implementation of a systematic perturbative approach to observables in the QCD gradient-flow formalism. This includes a collection of all relevant Feynman rules of the five-dimensional field theory and the composite operators considered in this paper. Tools from standard perturbative calculations are used to obtain Green's functions at finite flow time at higher orders in perturbation theory. The three-loop results for the quark condensate at finite and the conversion factor for the "ringed" quark fields to the scheme are presented as applications. We also re-evaluate an earlier result for the three-loop gluon condensate, improving on its accuracy.
Click any figure to enlarge with its caption.
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15
Figure 16
Figure 17
Figure 18
Figure 19
Figure 20
Figure 21
Figure 22
Figure 23
Figure 24
Figure 25
Figure 26
Figure 27
Figure 28
Figure 29
Figure 30
Figure 31
Figure 32
Figure 33
Figure 34
Figure 35
Figure 36
Figure 37
Figure 38
Figure 39
Figure 40Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.