Abstract
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 $\hat\Pi(q^2)$, 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 $10^{10} a_\mu^{\rm HVP,HO} = -9.3(1.3)$, in agreement with, but with a larger uncertainty than, determinations from $e^+e^- \to {\rm hadrons}$ data plus dispersion relations.
Highlights
The anomalous magnetic moment of the muon is one of the most precisely determined observables in particle physics, having been measured with an uncertainty of 0.54 parts per million by BNL Experiment E821 [1]
We introduce a new method for calculating the Oðα3Þ hadronic-vacuum-polarization contribution to the muon anomalous magnetic moment from ab initio lattice QCD
We demonstrate the approach using previously published results for the Taylor coefficients of Πðq2Þ that were obtained on four-flavor QCD gauge-field configurations with physical light-quark masses
Summary
The anomalous magnetic moment of the muon (gμ − 2) is one of the most precisely determined observables in particle physics, having been measured with an uncertainty of 0.54 parts per million by BNL Experiment E821 [1]. The largest source of uncertainty in the standard model gμ − 2 is from the Oðα2Þ hadronic vacuum-polarization (HVP) contribution [2], aHμ VP, which is shown in Fig. 1.1 This contribution can be obtained by combining experimental measurements of electron-positron inclusive scattering into hadrons with dispersion relations, and recent determinations from this approach quote errors of 0.4– 0.6% [14,15,16]. Appendix A provides expressions suitable for computing the Oðα3Þ hadronic vacuumpolarization contribution to aHμ VP directly from lattice-QCD simulations, while App. B provides the definition of the N 1⁄4 2 þ 1 þ 1 Mellin-Barnes approximant for the ΠðQ2Þ used in this paper. C gives the values of the quark-connected Taylor coefficients employed in our analysis
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