The lattice gradient flow at tree-level and its improvement

Abstract

The Yang-Mills gradient flow and the observable E(t), defined by the square of the field strength tensor at t>0, are calculated at finite lattice spacing and tree-level in the gauge coupling. Improvement of the flow, the gauge action and the observable are all considered. The results are relevant for two purposes. First, the discretization of the flow, gauge action and observable can be chosen in such a way that $O(a^2)$, $O(a^4)$ or even $O(a^6)$ improvement is achieved. Second, simulation results using arbitrary discretizations can be tree-level improved by the perturbatively calculated correction factor normalized to one in the continuum limit.

14 pages, 8 figures, references added, published version

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Cited by in corpus (72)

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• Nonperturbative investigations of SU(3) gauge theory with eight dynamical flavors
• Sp(4) gauge theory on the lattice: towards SU(4)/Sp(4) composite Higgs (and beyond)
• 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
• FLAG Review 2024
• Search for a new resonance decaying to a $W$ or $Z$ boson and a Higgs boson in the $\ell \ell /\ell \nu /\nu \nu +b\bar{b}$ final states with the ATLAS Detector
• Gradient flow and scale setting on MILC HISQ ensembles
• Nonperturbative beta function of twelve-flavor SU(3) gauge theory
• The infrared regime of SU(2) with one adjoint Dirac flavour
• Sp(4) gauge theories on the lattice: Quenched fundamental and antisymmetric fermions
• Nonperturbative beta function of eight-flavor SU(3) gauge theory
• Locally smeared operator product expansions in scalar field theory
• Anisotropic pressure induced by finite-size effects in SU(3) Yang-Mills theory
• Wilson flow and scale setting from lattice QCD
• The twelve-flavor $\mathbf{\beta }$-function and dilaton tests of the sextet scalar
• Renormalization of the Polyakov loop with gradient flow
• The gradient flow running coupling with twisted boundary conditions
• Gradient flow step-scaling function for SU(3) with twelve flavors
• Continuous renormalization group $\beta$ function from lattice simulations
• The gradient flow coupling at high-energy and the scale of SU(3) Yang-Mills theory
• Gradient Flow of O(N) nonlinear sigma model at large N
• Short flow-time coefficients of CP-violating operators
• Scale setting the Möbius Domain Wall Fermion on gradient-flowed HISQ action using the omega baryon mass and the gradient-flow scales $t_0$ and $w_0$
• Gradient flow step-scaling function for SU(3) with ten fundamental flavors
• The renormalization group step scaling function of the 2-flavor SU(3) sextet model
• Large $N_c$ scaling of meson masses and decay constants
• Improved study of the $\beta$-function of $SU(3)$ gauge theory with $N_f=10$ massless domain-wall fermions
• Latent heat and pressure gap at the first-order deconfining phase transition of SU(3) Yang-Mills theory using the small flow-time expansion method
• Determination of Reference Scales for Wilson Gauge Action from Yang--Mills Gradient Flow
• The Yang-Mills gradient flow and SU(3) gauge theory with 12 massless fundamental fermions in a colour-twisted box
• Gradient Flow Coupling in the SU(2) gauge theory with two adjoint fermions
• Distribution of Energy-Momentum Tensor around a Static Quark in the Deconfined Phase of SU(3) Yang-Mills Theory
• Scale setting for large-$N$ SUSY Yang-Mills on the lattice
• The flavor dependence of $m_{\varrho }/f_{\pi }$
• Themodynamics for pure SU($2$) gauge theory using gradient flow
• The Yang-Mills gradient flow and renormalization
• The static force from generalized Wilson loops using gradient flow
• $\Lambda$ parameter of the SU(3) Yang-Mills theory from the continuous $\beta$ function
• Efficient integration of gradient flow in lattice gauge theory and properties of low-storage commutator-free Lie group methods
• Numerical study of tree-level improved lattice gradient flows in pure Yang-Mills theory
• Gradient flow step-scaling function for SU(3) with $N_f=8$ fundamental flavors
• Nonperturbative determination of $\beta$ functions for SU(3) gauge theories with 10 and 12 fundamental flavors using domain wall fermions
• On the equivalence between the Wilson flow and stout-link smearing
• Slope of the beta function at the fixed point of SU(2) gauge theory with six or eight flavors
• Numerical results for gauge theories near the conformal window
• Energy--momentum tensor on the lattice: recent developments
• Toward the minimal realization of a light composite Higgs
• Dislocations under gradient flow and their effect on the renormalized coupling
• The lattice gradient flow at tree level
• Measurement of thermodynamics using gradient flow
• Spectroscopy of the BSM sextet model
• The $SU(\infty )$ twisted gradient flow running coupling
• Static force from generalized Wilson loops on the lattice using the gradient flow
• Machine-learned RG-improved gauge actions and classically perfect gradient flows
• Wilson flow with naive staggered quarks
• Gradient flow step-scaling function for SU(3) with $N_f$ = 6 or 4 fundamental flavors
• Determination of the Strong Coupling Constant by the ALPHA Collaboration
• Gradient Flow: Perturbative and Non-Perturbative Renormalization
• The gradient flow of the Dirac spectrum
• Axial $U(1)$ anomaly in a gravitational field via the gradient flow
• Latent heat and pressure gap at the first-order deconfining phase transition of SU(3) Yang-Mills theory using the small flow-time expansion method
• Status of a minimal composite Higgs theory
• Gradient Flow Analysis on MILC HISQ Ensembles
• Bulk-preventing actions for SU(N) gauge theories
• Lattice gradient flow with tree-level $\mathcal{O}(a^4)$ improvement in pure Yang-Mills theory
• Weakly coupled conformal gauge theories on the lattice
• Running coupling of the sextet composite Higgs model