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

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.

9 pages, 3 figures

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• Calculation of the hadronic vacuum polarization disconnected contribution to the muon anomalous magnetic moment
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• Finite-volume effects in $(g-2{)}_{\mu }^{\text{HVP,LO}}$
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• Electromagnetic finite-size effects to the hadronic vacuum polarization
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