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

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 currentcurrent correlator at zero spatial momentum. Our results lead to a total (including u, d and s quarks) quarkline disconnected contribution to aμ of −0.15% of the u=d hadronic vacuum polarization contribution with an uncertainty which is 1% of that contribution.