An estimate of the hadronic vacuum polarization disconnected contribution to the anomalous magnetic moment of the muon from lattice QCD

TL;DR

This paper estimates the disconnected quark-line contribution to the muon's anomalous magnetic moment from lattice QCD, providing the first such estimate with significant statistical signal, albeit at a single lattice spacing and unphysical quark mass.

Contribution

It introduces the first lattice QCD-based estimate of the disconnected contribution to the muon g-2, using a novel reconstruction of the Adler function from time-moments.

Findings

Disconnected contribution is about -0.15% of the u/d hadronic vacuum polarization.

Uncertainty in the estimate is approximately 1% of the total contribution.

Results are based on lattice QCD at one lattice spacing and unphysical quark masses.

Abstract

The quark-line disconnected diagram is a potentially important ingredient in lattice QCD calculations of the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon. It is also a notoriously difficult one to evaluate. Here, for the first time, we give an estimate of this contribution based on lattice QCD results that have a statistically significant signal, albeit at one value of the lattice spacing and an unphysically heavy value of the $u/d$ quark mass. We use HPQCD's method of determining the anomalous magnetic moment by reconstructing the Adler function from time-moments of the current-current correlator at zero spatial momentum. Our results lead to a total (including $u$, $d$ and $s$ quarks) quark-line disconnected contribution to $a_{\mu}$ of $-0.15\%$ of the $u/d$ hadronic vacuum polarization contribution with an uncertainty which is 1\% of that contribution.