Higher-order hadronic-vacuum-polarization contribution to the muon g-2 from lattice QCD

Abstract

We introduce a new method for calculating the $\mathrm{O}({\alpha }^3)$ hadronic-vacuum-polarization contribution to the muon anomalous magnetic moment from $ab-initio$ lattice QCD. We first derive expressions suitable for computing the higher-order contributions either from the renormalized vacuum polarization function $\hat{\Pi }(q^2)$, or directly from the lattice vector-current correlator in Euclidean space. We then demonstrate the approach using previously-published results for the Taylor coefficients of $\hat{\Pi }(q^2)$ that were obtained on four-flavor QCD gauge-field configurations with physical light-quark masses. We obtain $10^{10}{a}_{\mu }^{\mathrm{HVP},\mathrm{HO}}=-9.3(1.3)$, in agreement with, but with a larger uncertainty than, determinations from $e^{+}{e}^{-}\to \mathrm{hadrons}$ data plus dispersion relations.

Expanded and clarified discussion and revised Figure 4. Results unchanged. 11 pages, 5 tables, 5 figures. Version accepted to Physical Review D

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• Leading hadronic contribution to the muon magnetic moment from lattice QCD
• The hadronic light-by-light scattering contribution to the muon anomalous magnetic moment from lattice QCD
• The light-quark contribution to the leading HVP term of the muon $g-2$ from twisted-mass fermions
• Electron and muon magnetic moments and implications for dark matter and model characterisation in non-universal $U(1{)}^{\prime }$ supersymmetric models
• Electromagnetic finite-size effects to the hadronic vacuum polarization
• Disconnected Loop Subtraction Methods in Lattice QCD
• Recent Developments of Muon g-2 from Lattice QCD
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