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.

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