https://doi.org/10.1140/epjc/s10052-019-7228-z
Regular Article - Theoretical Physics
The gradient flow coupling at high-energy and the scale of SU(3) Yang–Mills theory
1
Dipartimento di Fisica, Università di Milano-Bicocca and INFN, sezione di Milano-Bicocca, Piazza della Scienza 3, 20126, Milan, Italy
2
School of Mathematics and Hamilton Mathematics Institute, Trinity College Dublin, Dublin 2, Ireland
* e-mail: alberto.ramos@maths.tcd.ie
Received:
4
June
2019
Accepted:
18
August
2019
Published online:
28
August
2019
Using finite size scaling techniques and a renormalization scheme based on the Gradient Flow, we determine non-perturbatively the 
-function of the SU(3) Yang–Mills theory for a range of renormalized couplings 
1–12. We perform a detailed study of the matching with the asymptotic NNLO perturbative behavior at high-energy, with our non-perturbative data showing a significant deviation from the perturbative prediction down to 
. We conclude that schemes based on the Gradient Flow are not competitive to match with the asymptotic perturbative behavior, even when the NNLO expansion of the -function is known. On the other hand, we show that matching non-perturbatively the Gradient Flow to the Schrödinger Functional scheme allows us to make safe contact with perturbation theory with full control on truncation errors. This strategy allows us to obtain a precise determination of the 
-parameter of the SU(3) Yang–Mills theory in units of a reference hadronic scale (
), showing that a precision on the QCD coupling below 0.5% per-cent can be achieved using these techniques.
© The Author(s), 2019
