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

We introduce a new method for calculating the ${rm O}(alpha^3)$ 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 $hatPi(q^2)$, 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 $hatPi(q^2)$ that were obtained on four-flavor QCD gauge-field configurations with 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.