Slow running of the Gradient Flow coupling from 200 MeV to 4 GeV in $N_{\mathrm{f}}=3$ QCD

Abstract

Using a finite volume Gradient Flow (GF) renormalization scheme with Schrödinger Functional (SF) boundary conditions, we compute the non-perturbative running coupling in the range $2.2\lesssim {\bar{g}}_{\mathrm{GF}}^2(L)\lesssim 13$. Careful continuum extrapolations turn out to be crucial to reach our high accuracy. The running of the coupling is always between one-loop and two-loop and very close to one-loop in the region of $200\mathrm{MeV}\lesssim \mu =1/L\lesssim 4\mathrm{GeV}$. While there is no convincing contact to two-loop running, we match non-perturbatively to the SF coupling with background field. In this case we know the $\mu$ dependence up to $\sim 100\mathrm{GeV}$ and can thus connect to the $\Lambda$-parameter.

34 pages, LaTeX

References in corpus (7)

• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Infinite N phase transitions in continuum Wilson loop operators
• Simulation of QCD with N_f=2+1 flavors of non-perturbatively improved Wilson fermions
• Critical slowing down and error analysis in lattice QCD simulations
• Accelerating Dynamical Fermion Computations using the Rational Hybrid Monte Carlo (RHMC) Algorithm with Multiple Pseudofermion Fields
• Step scaling and the Yang-Mills gradient flow
• The gradient flow running coupling with twisted boundary conditions

Cited by in corpus (22)

• FLAG Review 2021
• 50 Years of Quantum Chromodynamics
• An analysis of systematic effects in finite size scaling studies using the gradient flow
• The strong coupling from a nonperturbative determination of the $\Lambda$ parameter in three-flavor QCD
• FLAG Review 2024
• Toward scalable simulations of Lattice Gauge Theories on quantum computers
• Short flow-time coefficients of CP-violating operators
• Lattice determinations of the strong coupling
• Determination of ${\alpha }_s(m_Z)$ by the non-perturbative decoupling method
• Past, present, and future of precision determinations of the QCD coupling from lattice QCD
• Light quark masses in N_f = 2+1 lattice QCD with Wilson fermions
• Strong coupling from non-equilibrium Monte Carlo simulations
• The twisted gradient flow coupling at one loop
• Determination of the charm quark mass in lattice QCD with $2+1$ flavours on fine lattices
• The renormalised $\mathrm{O}(a)$ improved vector current in three-flavour lattice QCD with Wilson quarks
• Gradient flow step-scaling function for SU(3) with $N_f=8$ fundamental flavors
• Dislocations under gradient flow and their effect on the renormalized coupling
• Gradient flow step-scaling function for SU(3) with $N_f$ = 6 or 4 fundamental flavors
• Precision Determination of ${\alpha }_s$ from Lattice QCD
• Perturbative O($a^2$) effects in gradient flow couplings with SF and SF-open boundary conditions
• Memory efficient finite volume schemes with twisted boundary conditions
• The energy-momentum tensor in lattice QCD and the Equation of State