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

• Main Authors: Mattia Dalla Brida, Alberto Ramos
• Format: Article
• Language: English
• Published: SpringerOpen 2019-08-01
• Series: European Physical Journal C: Particles and Fields
• Online Access: http://link.springer.com/article/10.1140/epjc/s10052-019-7228-z

Abstract Using finite size scaling techniques and a renormalization scheme based on the Gradient Flow, we determine non-perturbatively the $$\beta $$ β -function of the SU(3) Yang–Mills theory for a range of renormalized couplings $${\bar{g}}^2\sim $$ g¯2∼ 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 $$\bar{g}^2\sim 1$$ g¯2∼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 $$\beta $$ β -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 $$\Lambda $$ Λ -parameter of the SU(3) Yang–Mills theory in units of a reference hadronic scale ($$\sqrt{8t_0}\, \Lambda _{\overline{\mathrm{MS}}} = 0.6227(98)$$ 8t0ΛMS¯=0.6227(98) ), showing that a precision on the QCD coupling below 0.5% per-cent can be achieved using these techniques.