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

References in corpus (5)

• Perturbative analysis of the gradient flow in non-abelian gauge theories
• High-precision scale setting in lattice QCD
• Improving the continuum limit of gradient flow step scaling
• Step scaling and the Yang-Mills gradient flow
• The gradient flow running coupling scheme

Cited by in corpus (24)

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• 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
• The gradient flow running coupling with twisted boundary conditions
• 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 $w_0$
• 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
• Distribution of Energy-Momentum Tensor around a Static Quark in the Deconfined Phase of SU(3) Yang-Mills Theory
• The flavor dependence of $m_{\varrho }/f_{\pi }$
• The Yang-Mills gradient flow and renormalization
• 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
• Toward the minimal realization of a light composite Higgs
• Energy--momentum tensor on the lattice: recent developments
• Measurement of thermodynamics using gradient flow
• The lattice gradient flow at tree level
• The $SU(\infty )$ twisted gradient flow running coupling
• The gradient flow of the Dirac spectrum
• Gradient Flow: Perturbative and Non-Perturbative Renormalization
• 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
• Gradient Flow Analysis on MILC HISQ Ensembles