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An accurate determination of the leading-order hadronic vacuum polarisation(HVP) contribution to the anomalous magnetic moment of the muon is critical tounderstanding the size and significance of any discrepancy between the StandardModel prediction and experimental results being obtained by the Muon g-2experiment at Fermilab. The Standard Model prediction is currently based on adata-driven approach to the HVP using experimental results for$\sigma(e^+e^-\rightarrow\,\mathrm{hadrons})$. Lattice QCD aims to provide aresult with similar uncertainty from calculated vector-vector correlationfunctions, but the growth of statistical and systematic errors in the $u/d$quark correlation functions at large Euclidean time has made this difficult toachieve. We show that restricting the lattice contributions to a one-sidedwindow $0<t<t_1$ can greatly improve lattice results while still capturing alarge fraction of the total HVP. We illustrate this by comparing windowedlattice results based on the 2019 Fermilab Lattice/HPQCD/MILC HVP analysis withcorresponding results obtained from the KNT19 analysis of $R_{e^+e^-}$ data.For $t_1=1.5$ fm, 70% of the total HVP is contained within the window and ourlattice result has an error of~0.7%, only about twice as big as the error fromthe $e^+e^-$~analysis. We see a tension of 2.7$\sigma$ between the two results.With increased statistics in the lattice data the one-sided windows will allowstringent tests of lattice and $R_{e^+e^-}$ results that include a largefraction of the total HVP contribution.

Windows on the hadronic vacuum polarisation contribution to the muon anomalous magnetic moment