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

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