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 o-(e+e- -> hadrons). 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 Re+e- data. For t1 = 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 e+e- analysis. We see a tension of 2.7o-between the two results. With increased statistics in the lattice data the one-sided windows will allow stringent tests of lattice and Re+e- results that include a large fraction of the total HVP contribution.

Automated summary

Accurately determining the contribution of hadronic vacuum polarization (HVP) to the muon's anomalous magnetic moment is crucial for understanding any discrepancies between the Standard Model prediction and experimental results. This study investigates the use of lattice QCD to calculate HVP, but faces challenges due to increasing statistical and systematic errors. By limiting the lattice contributions to a specific time window, the results can be significantly improved while still capturing a large fraction of the HVP. The findings suggest that this approach could allow for rigorous tests of lattice and experimental results in the future.