Hadronic vacuum polarization function within dispersive approach to QCD

Abstract

The dispersive approach to quantum chromodynamics is applied to the study of the hadronic vacuum polarization function and associated quantities. This approach merges the intrinsically nonperturbative constraints, which originate in the kinematic restrictions on the respective physical processes, with corresponding perturbative input. The obtained hadronic vacuum polarization function agrees with pertinent lattice simulation data. The evaluated hadronic contributions to the muon anomalous magnetic moment and to the shift of the electromagnetic fine structure constant conform with recent assessments of these quantities.

16 pages, 4 figures

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• Hadronic corrections to $\mu$-$e$ scattering at NNLO with space-like data
• Nearly perturbative lattice-motivated QCD coupling with zero IR limit
• Bjorken polarized sum rule and infrared-safe QCD couplings
• Renormalon-motivated evaluation of QCD observables
• Electron-positron annihilation into hadrons at the higher-loop levels
• Lattice-motivated holomorphic nearly perturbative QCD
• Determination of perturbative QCD coupling from ALEPH $\tau$ decay data using pinched Borel-Laplace and Finite Energy Sum Rules
• Borel-Laplace Sum Rules with $\tau$ decay data, using OPE with improved anomalous dimensions
• Explicit form of the R-ratio of electron-positron annihilation into hadrons
• Timelike and spacelike kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment
• Lattice-motivated QCD coupling and hadronic contribution to muon $g-2$
• Infrared-suppressed QCD coupling and the hadronic contribution to muon g-2
• Evaluation of neutrinoless double beta decay: QCD running to sub-GeV scales
• Recurrent form of the renormalization group relations for the higher-order hadronic vacuum polarization function perturbative expansion coefficients
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• Effects of the quark flavour thresholds in the hadronic vacuum polarization contributions to the muon anomalous magnetic moment
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• Window quantities for the hadronic vacuum polarization contributions to the muon anomalous magnetic moment in spacelike and timelike domains