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

An accurate determination of the leading-order hadronic vacuum polarization (HVP) contribution to the
anomalous magnetic moment of the muon is critical to understanding the size and significance of any
discrepancy between the Standard Model prediction and experimental results being obtained by the Muon
g-2 experiment at Fermilab. The Standard Model prediction is currently based on a data-driven approach to
the HVP using experimental results for σðeþe− → hadronsÞ. Lattice QCD aims to provide a result with
similar uncertainty from calculated vector-vector correlation functions, but the growth of statistical and
systematic errors in the u=d quark correlation functions at large Euclidean time has made this difficult to
achieve. We show that restricting the lattice contributions to a one-sided window 0 <t<t1 can greatly
improve lattice results while still capturing a large fraction of the total HVP. We illustrate this by comparing
windowed lattice results based on the 2019 Fermilab Lattice/HPQCD/MILC HVP analysis with
corresponding results obtained from the KNT19 analysis of Reþe− data. For t1 ¼ 1.5 fm, 70% of the
total HVP is contained within the window and our lattice result has an error of 0.7%, only about twice as big
as the error from the eþe− analysis. We see a tension of 2.7σ between the two results. With increased
statistics in the lattice data the one-sided windows will allow stringent tests of lattice and Reþe− results that
include a large fraction of the total HVP contribution.