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

Abstract

Using finite size scaling techniques and a renormalization scheme based on the Gradient Flow, we determine non-perturbatively the $\beta$-function of the $SU(3)$ Yang-Mills theory for a range of renormalized couplings ${\bar{g}}^2\sim 1-12$. 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 ${\bar{g}}^2\sim 1$. 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 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 $\Lambda$-parameter of the $SU(3)$ Yang-Mills theory in units of a reference hadronic scale ($\sqrt{8t_0}{\Lambda }_{\overline{\mathrm{MS}}}=0.6227(98)$), showing that a precision on the QCD coupling below 0.5\% per-cent can be achieved using these techniques.

arXiv commentLaTeX, 55 pages

References in corpus (36)

• The four-loop beta-function in Quantum Chromodynamics
• A New Way to Set the Energy Scale in Lattice Gauge Theories and its Application to the Static Force and ${\alpha }_s$ in SU(2) Yang--Mills Theory
• Properties and uses of the Wilson flow in lattice QCD
• The three-loop QCD $\beta$-function and anomalous dimensions
• Five-Loop Running of the QCD coupling constant
• The Four-Loop QCD Beta-Function and Anomalous Dimensions
• The Schrödinger Functional - a Renormalizable Probe for Non-Abelian Gauge Theories
• Perturbative analysis of the gradient flow in non-abelian gauge theories
• The Nf=0 heavy quark potential from short to intermediate distances
• Infinite N phase transitions in continuum Wilson loop operators
• The five-loop beta function of Yang-Mills theory with fermions
• A Precise Determination of the Running Coupling in the SU(3) Yang-Mills Theory
• Computation of the strong coupling in QCD with two dynamical flavours
• Computation of the Running Coupling in the SU(2) Yang-Mills Theory
• The gradient flow coupling in the Schrödinger Functional
• Studying the gradient flow coupling in the Schrödinger functional
• The strong coupling from a nonperturbative determination of the $\Lambda$ parameter in three-flavor QCD
• The running coupling from the QCD Schrödinger functional -- a one-loop analysis
• A Determination of the Lambda Parameter from Full Lattice QCD
• The lattice gradient flow at tree-level and its improvement
• Critical slowing down of topological modes
• Symanzik improvement of the gradient flow in lattice gauge theories
• Equation of State for SU(3) Gauge Theory via the Energy-Momentum Tensor under Gradient Flow
• Towards the five-loop Beta function for a general gauge group
• Automatic differentiation for error analysis of Monte Carlo data
• Slow running of the Gradient Flow coupling from 200 MeV to 4 GeV in $N_{\mathrm{f}}=3$ QCD
• Determination of the QCD $\Lambda$-parameter and the accuracy of perturbation theory at high energies
• The perturbative QCD gradient flow to three loops
• Step scaling and the Yang-Mills gradient flow
• The gradient flow running coupling with twisted boundary conditions
• SMD-based numerical stochastic perturbation theory
• A non-perturbative exploration of the high energy regime in $N_{\text{f}}=3$ QCD
• Non-perturbative determination of the $\Lambda$-parameter in the pure SU(3) gauge theory from the twisted gradient flow coupling
• Investigation of New Methods for Numerical Stochastic Perturbation Theory in ${\phi }^4$ Theory
• Precision Determination of ${\alpha }_s$ from Lattice QCD
• Determination of the Strong Coupling Constant by the ALPHA Collaboration

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• Logarithmic corrections to O($a$) and O($a^2$) effects in lattice QCD with Wilson or Ginsparg-Wilson quarks
• $\Lambda$ parameter of the SU(3) Yang-Mills theory from the continuous $\beta$ function
• Temperature Dependence of Heavy Quark Diffusion from (2+1)-flavor Lattice QCD
• Machine-learned RG-improved gauge actions and classically perfect gradient flows
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