Lattice QCD yields the NLO HVP contribution to muon g-2 as -101.57(26)stat(54)syst ×10^{-11}, 1.4σ below the 2025 White Paper estimate and twice as precise.
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Properties and uses of the Wilson flow in lattice QCD
Mixed citation behavior. Most common role is background (57%).
25
Pith papers citing it
Background
57% of classified citations
abstract
Theoretical and numerical studies of the Wilson flow in lattice QCD suggest that the gauge field obtained at flow time t>0 is a smooth renormalized field. The expectation values of local gauge-invariant expressions in this field are thus well-defined physical quantities that probe the theory at length scales on the order of sqrt(t). Moreover, by transforming the QCD functional integral to an integral over the gauge field at a specified flow time, the emergence of the topological (instanton) sectors in the continuum limit becomes transparent and is seen to be caused by a dynamical effect that rapidly separates the sectors when the lattice spacing is reduced from 0.1 fm to smaller values.
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representative citing papers
First non-perturbative lattice determination of the Yang-Mills topological susceptibility slope χ' in the large-N limit using a novel algorithm to avoid topological freezing.
A perturbative Ricci-flow formulation in gravity yields a renormalization scheme for Newton's constant that exhibits a non-Gaussian fixed point at two-loop order.
Lattice simulations in Rindler spacetime show that acceleration turns the confinement-deconfinement transition in gluodynamics into a spatial crossover that approximately follows the Tolman-Ehrenfest law, while the critical temperature stays unchanged.
First non-asymptotic-scaling determination of the large-N Yang-Mills Λ-parameter yields √(8t₀)Λ_MS(N=∞) = 0.639(36).
New A and V gradient flow schemes enable nonperturbative renormalization of composite fermion operators via conserved currents and ratios of correlation functions, demonstrated on domain-wall ensembles for Z_V/Z_A and strange quark mass.
Lattice computation of Wilson-'t Hooft loops supplies numerical evidence for dyon condensation at theta=2pi in SU(2) Yang-Mills.
In the continuum limit, κ_PS, κ_VA and κ_TX are all consistent with zero and with each other down to 164 MeV, implying concurrent chiral and U(1)_A restoration in the quark-connected nonsinglet sector.
Lattice QCD results show the shear viscosity to entropy density ratio of gluon plasma reaches a minimum near the transition temperature Tc while the bulk viscosity to entropy density ratio decreases monotonically from 0.76 to 2.25 Tc.
Out-of-equilibrium simulations with open-to-periodic boundary switching plus a tailored stochastic normalizing flow enable efficient topology sampling in the continuum limit of four-dimensional SU(3) Yang-Mills theory.
Derives α_S(μ) ≃ Λ_S²/μ² from a scale-invariant gluon condensate via gradient flow, reaching an infrared fixed point consistent with confinement.
Continuum-extrapolated lattice QCD simulations with complex Langevin produce the equation of state at high baryon chemical potentials above the crossover temperature at the physical point.
Tuning study of aHISQ action on anisotropic lattices from 1 to 8, with comparison of fermion anisotropy tuning and an empirical model for pion taste splittings showing qualitatively different behavior versus naive staggered quarks.
Non-perturbative renormalization constants for gluonic and fermionic components of the traceless energy-momentum tensor in Nf=3 lattice QCD are computed to few-percent accuracy using discretized Ward identities with shifted boundary conditions.
Extends the RI/SMOM scheme to semi-leptonic operators via Ward-identity-protected vector currents and demonstrates equivalence to the Gorbahn et al. 2023 projectors for Wilson coefficient calculations.
The paradox in the canonical approach at high temperature with the Roberge-Weiss transition originates from infinite-size effects and vanishes in finite-size systems due to smearing, validating the approach for lattice QCD.
Gradient-flow scales are set for SU(3), SU(5), SU(8) and large-N Yang-Mills down to 0.025 fm using twisted volume reduction and topology-taming algorithms.
Introduces bounds-based stopping criteria and automatic windowing for autocorrelation integrals to estimate statistical errors in lattice field theory Monte Carlo simulations.
Extended lattice simulations yield continuum-limit anomalous dimensions γ* = 0.170(6) for Nf=1 and γ* = 0.291(9) for Nf=2 adjoint SU(2), with chiral perturbation theory ruling out spontaneous chiral symmetry breaking.
New four-flavor smeared Möbius Domain Wall Fermion ensembles yield F_K/F_pi = 1.1962(34) as a precision test for inexpensive chiral fermion calculations in lattice QCD.
Lattice QCD result for f_K/f_π in isoQCD gives |V_us|/|V_ud| consistent with CKM unitarity once isospin and QED effects are included.
High-precision lattice computation yields χ_top^{1/4} = 198.1(0.7)(2.7) MeV for SU(3) Yang-Mills after continuum and infinite-volume extrapolation from seven spacings and volumes.
Energy-momentum tensor correlator is reduced to fewer spectral functions via rotational symmetry decomposition and conservation-derived differential relations at zero and finite temperature.
Machine learning generative models and renormalization-group neural networks are used to enhance gauge field sampling and learn fixed-point actions in 4D SU(3) lattice gauge theories, with presented scaling results toward the continuum limit using gradient-flow and potential observables.
citing papers explorer
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Higher-order hadronic vacuum polarization contribution to the muon $g-2$ from lattice QCD
Lattice QCD yields the NLO HVP contribution to muon g-2 as -101.57(26)stat(54)syst ×10^{-11}, 1.4σ below the 2025 White Paper estimate and twice as precise.
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The topological susceptibility slope $\chi^\prime$ in the large-$N$ limit
First non-perturbative lattice determination of the Yang-Mills topological susceptibility slope χ' in the large-N limit using a novel algorithm to avoid topological freezing.
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The perturbative Ricci flow in gravity
A perturbative Ricci-flow formulation in gravity yields a renormalization scheme for Newton's constant that exhibits a non-Gaussian fixed point at two-loop order.
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Spatial confinement-deconfinement transition in accelerated gluodynamics within lattice simulation
Lattice simulations in Rindler spacetime show that acceleration turns the confinement-deconfinement transition in gluodynamics into a spatial crossover that approximately follows the Tolman-Ehrenfest law, while the critical temperature stays unchanged.
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The large-$N$ Yang--Mills $\Lambda$-parameter from step scaling
First non-asymptotic-scaling determination of the large-N Yang-Mills Λ-parameter yields √(8t₀)Λ_MS(N=∞) = 0.639(36).
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Gradient Flow Renormalization Schemes for Composite Fermion Operators
New A and V gradient flow schemes enable nonperturbative renormalization of composite fermion operators via conserved currents and ratios of correlation functions, demonstrated on domain-wall ensembles for Z_V/Z_A and strange quark mass.
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Numerical Hints for Dyon Condensation at $\theta=2\pi$ via Wilson-'t Hooft Loops in $SU(2)$ Yang-Mills Theory
Lattice computation of Wilson-'t Hooft loops supplies numerical evidence for dyon condensation at theta=2pi in SU(2) Yang-Mills.
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RG-Invariant Symmetry Ratio for QCD: A Study of $U(1)_A$ and Chiral Symmetry Restoration
In the continuum limit, κ_PS, κ_VA and κ_TX are all consistent with zero and with each other down to 164 MeV, implying concurrent chiral and U(1)_A restoration in the quark-connected nonsinglet sector.
-
Shear and bulk viscosities of the gluon plasma across the transition temperature from lattice QCD
Lattice QCD results show the shear viscosity to entropy density ratio of gluon plasma reaches a minimum near the transition temperature Tc while the bulk viscosity to entropy density ratio decreases monotonically from 0.76 to 2.25 Tc.
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Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
Out-of-equilibrium simulations with open-to-periodic boundary switching plus a tailored stochastic normalizing flow enable efficient topology sampling in the continuum limit of four-dimensional SU(3) Yang-Mills theory.
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Renormalization Group Approach to Confinement
Derives α_S(μ) ≃ Λ_S²/μ² from a scale-invariant gluon condensate via gradient flow, reaching an infrared fixed point consistent with confinement.
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Finite-density equation of state of hot QCD using the complex Langevin equation
Continuum-extrapolated lattice QCD simulations with complex Langevin produce the equation of state at high baryon chemical potentials above the crossover temperature at the physical point.
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Highly improved staggered quarks on anisotropic lattices
Tuning study of aHISQ action on anisotropic lattices from 1 to 8, with comparison of fermion anisotropy tuning and an empirical model for pion taste splittings showing qualitatively different behavior versus naive staggered quarks.
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The QCD energy-momentum tensor on the lattice: non-perturbative renormalization with $N_f=3$
Non-perturbative renormalization constants for gluonic and fermionic components of the traceless energy-momentum tensor in Nf=3 lattice QCD are computed to few-percent accuracy using discretized Ward identities with shifted boundary conditions.
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A note on momentum subtraction schemes for quark bilinears and semileptonic operators
Extends the RI/SMOM scheme to semi-leptonic operators via Ward-identity-protected vector currents and demonstrates equivalence to the Gorbahn et al. 2023 projectors for Wilson coefficient calculations.
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The canonical approach at high temperature revisited
The paradox in the canonical approach at high temperature with the Roberge-Weiss transition originates from infinite-size effects and vanishes in finite-size systems due to smearing, validating the approach for lattice QCD.
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Scale setting of SU($N$) Yang--Mills theory, topology and large-$N$ volume independence
Gradient-flow scales are set for SU(3), SU(5), SU(8) and large-N Yang-Mills down to 0.025 fm using twisted volume reduction and topology-taming algorithms.
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Bounding statistical errors in lattice field theory simulations
Introduces bounds-based stopping criteria and automatic windowing for autocorrelation integrals to estimate statistical errors in lattice field theory Monte Carlo simulations.
-
SU(2) gauge theory with one and two adjoint fermions towards the continuum limit
Extended lattice simulations yield continuum-limit anomalous dimensions γ* = 0.170(6) for Nf=1 and γ* = 0.291(9) for Nf=2 adjoint SU(2), with chiral perturbation theory ruling out spontaneous chiral symmetry breaking.
-
$F_K/F_\pi$ as a precision test of a new four flavor Domain Wall Fermion action
New four-flavor smeared Möbius Domain Wall Fermion ensembles yield F_K/F_pi = 1.1962(34) as a precision test for inexpensive chiral fermion calculations in lattice QCD.
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$f_K/f_{\pi}$ in iso-symmetric QCD and the CKM matrix unitarity
Lattice QCD result for f_K/f_π in isoQCD gives |V_us|/|V_ud| consistent with CKM unitarity once isospin and QED effects are included.
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Topological susceptibility and excess kurtosis in SU(3) Yang-Mills theory
High-precision lattice computation yields χ_top^{1/4} = 198.1(0.7)(2.7) MeV for SU(3) Yang-Mills after continuum and infinite-volume extrapolation from seven spacings and volumes.
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Tensor Decomposition for Energy-Momentum Correlation Functions
Energy-momentum tensor correlator is reduced to fewer spectral functions via rotational symmetry decomposition and conservation-derived differential relations at zero and finite temperature.
-
Machine learning for four-dimensional SU(3) lattice gauge theories
Machine learning generative models and renormalization-group neural networks are used to enhance gauge field sampling and learn fixed-point actions in 4D SU(3) lattice gauge theories, with presented scaling results toward the continuum limit using gradient-flow and potential observables.
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The theory of electric dipole moments: the view from below
A bottom-up review organizing the theory of EDMs from quark-gluon CP violation via chiral perturbation theory and structure calculations, with emphasis on paramagnetic system sensitivity to hadronic sources.