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

C. T. H. Davies1,*, C. DeTar2, A. X. El-Khadra3,4, Steven Gottlieb5, D. Hatton1, A. S. Kronfeld6, S. Lahert3, G. P. Lepage7,†, C. McNeile8 et al. (Fermilab Lattice, HPQCD, and MILC Collaborations)

C. McNeile8, E. T. Neil9, C. T. Peterson9, G. S. Ray8, R. S. Van de Water6, and A. Vaquero2 (Fermilab Lattice, HPQCD, and MILC Collaborations)

  • 1SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom
  • 2Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah 84112, USA
  • 3Department of Physics, University of Illinois, Urbana, Illinois 61801, USA
  • 4Illinois Centre for Advanced Studies of the Universe, University of Illinois, Urbana, Illinois 61801, USA
  • 5Department of Physics, Indiana University, Bloomington, Indiana 47405, USA
  • 6Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
  • 7Laboratory for Elementary-Particle Physics, Cornell University, Ithaca, New York 14853, USA
  • 8Centre for Mathematical Sciences, University of Plymouth PL4 8AA, United Kingdom
  • 9Department of Physics, University of Colorado, Boulder, Colorado 80309, USA

  • *christine.davies@glasgow.ac.uk
  • †g.p.lepage@cornell.edu
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Phys. Rev. D 106, 074509 – Published 24 October, 2022

DOI: https://doi.org/10.1103/PhysRevD.106.074509

Abstract

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 σ(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 2.7σ 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.

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Phys. Rev. D 106, 074509– Published 24 October, 2022
  • Received 18 July 2022
  • Accepted 27 September 2022
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