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

TL;DR

This paper presents a novel lattice QCD method to compute higher-order hadronic vacuum polarization contributions to the muon g-2, providing an ab initio approach that aligns with existing data-driven results.

Contribution

The authors develop a new lattice QCD-based method to calculate the ${ m O}( ext{alpha}^3)$ hadronic vacuum polarization contribution to muon g-2, enabling direct ab initio computations.

Findings

Calculated $a_^{ m HVP,HO}$ as -9.3(1.3) x 10^{-10}

Method agrees with existing $e^+e^-$ data results within uncertainties

Demonstrated approach using four-flavor QCD gauge-field configurations.

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.