The hadronic vacuum polarization contribution to $a_{\hat{I}}¼$ from full lattice QCD

Abstract

We determine the contribution to the anomalous magnetic moment of the muon from the $\hat{I}{\pm }_{\mathrm{QED}}^2$ hadronic vacuum polarization diagram using full lattice QCD and including $u/d$ quarks with physical masses for the first time. We use gluon field configurations that include $u$, $d$, $s$ and $c$ quarks in the sea at multiple values of the lattice spacing, multiple $u/d$ masses and multiple volumes that allow us to include an analysis of finite-volume effects. We obtain a result for $a_{\hat{I}}{¼}^{\mathrm{HVP},\mathrm{LO}}$ of $667(6)(12)$, where the first error is from the lattice calculation and the second includes systematic errors from missing QED and isospin-breaking effects and from quark-line disconnected diagrams. Our result implies a discrepancy between the experimental determination of $a_{\hat{I}}¼$ and the Standard Model of 3$\ddot{I}ƒ$.

14 pages, 10 figures. Discussion of method extended with additional tests and figures added. Typographical errors corrected