The gradient flow coupling at high-energy and the scale of SU(3) Yang-Mills theory

Using finite size scaling techniques and a renormalization scheme based on theGradient Flow, we determine non-perturbatively the beta-function of the SU(3) Yang-Mills theory for a range of renormalized couplings (g) over bar (2) similar to 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 (g) over bar (2) similar to 1. 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 beta-function is known. On the other hand, we show that matching non-perturbatively the Gradient Flow to the Schrodinger 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 Lambda-parameter of the SU(3) Yang-Mills theory in units of a reference hadronic scale (root 8t(0) Lambda((MS) over bar) = 0.6227(98)), showing that a precision on the QCD coupling below 0.5% per-cent can be achieved using these techniques.