The hadronic vacuum polarization contribution to $a_{\mu}$ from full lattice QCD

TL;DR

This paper presents a lattice QCD calculation of the hadronic vacuum polarization contribution to the muon's anomalous magnetic moment, achieving a precise result that suggests a 3-sigma deviation from the Standard Model.

Contribution

First full lattice QCD calculation including $u/d$ quarks with physical masses and multiple sea quark flavors to determine $a_{}^{ ext{HVP,LO}}$ with systematic error analysis.

Findings

Calculated $a_{}^{ ext{HVP,LO}}$ as 667(6)(12)

Discrepancy of 3$$ sigma with experimental $a_{}$

Includes analysis of finite-volume effects and systematic errors

Abstract

We determine the contribution to the anomalous magnetic moment of the muon from the $\alpha^2_{\mathrm{QED}}$ 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 $a_{\mu}^{\mathrm{HVP,LO}}$ 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 $a_{\mu}$ and the Standard Model of 3$\sigma$.