Hadronic vacuum polarization using gradient flow

Abstract

The gradient-flow operator product expansion for QCD current correlators including operators up to mass dimension four is calculated through NNLO. This paves an alternative way for efficient lattice evaluations of hadronic vacuum polarization functions. In addition, flow-time evolution equations for flowed composite operators are derived. Their explicit form for the non-trivial dimension-four operators of QCD is given through order ${\alpha }_s^3$.

30 pages, 1 ancillary file. v2: Added minor clarifications and references; fixed some typos, most notably in Eq. (4.12)

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• The hadronic light-by-light scattering contribution to the muon anomalous magnetic moment from lattice QCD
• Perturbative analysis of the gradient flow in non-abelian gauge theories
• High-precision scale setting in lattice QCD
• Infinite N phase transitions in continuum Wilson loop operators
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• Reconstruction of heavy quark current correlators at O(α_s^3)
• FeynGame
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• The perturbative QCD gradient flow to three loops
• Resummation of Threshold, Low- and High-Energy Expansions for Heavy-Quark Correlators
• Analytical determination of the QCD quark masses

Cited by in corpus (9)

• Effective electroweak Hamiltonian in the gradient-flow formalism
• Off-lightcone Wilson-line operators in gradient flow
• Short-flow-time expansion of quark bilinears through next-to-next-to-leading order QCD
• Three-Loop OPE Wilson Coefficients of Dimension-Four Operators for (Axial-)Vector and (Pseudo-)Scalar Current Correlators
• Gradient Flow: Perturbative and Non-Perturbative Renormalization
• Stout smearing and Wilson flow in lattice perturbation theory
• Two-loop gradient-flow renormalization of scalar QCD
• Applications of the Perturbative Gradient Flow
• One-loop matching of the LEFT to the QCD gradient flow