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Hadronic Vacuum Polarization for the Muon $g - 2$ from Lattice QCD: Long-Distance and Full Light-Quark Connected Contribution

Alexei Bazavov ¹, Claude W. Bernard ², David A. Clarke ³, Christine Davies ⁴, Carleton DeTar ³, Aida X. El-Khadra ^5,6, Elvira Gámiz ⁷, Steven Gottlieb ⁸, Anthony V. Grebe⁹ et al. (Fermilab Lattice, HPQCD, and MILC Collaborations)

Anthony V. Grebe⁹, Leon Hostetler ⁸, William I. Jay ¹⁰, Hwancheol Jeong ⁸, Andreas S. Kronfeld ⁹, Shaun Lahert ^3,*, Jack Laiho ¹¹, G. Peter Lepage ¹², Michael Lynch ^5,6,†, Andrew T. Lytle ^5,6, Craig McNeile ¹³, Ethan T. Neil ¹⁴, Curtis T. Peterson ¹, James N. Simone ⁹, Jacob W. Sitison ^14,‡, Ruth S. Van de Water⁹, and Alejandro Vaquero ^3,15,16 (Fermilab Lattice, HPQCD, and MILC Collaborations)

¹Department of Computational Mathematics, Science and Engineering, and Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
²Department of Physics, Washington University, St. Louis, Missouri 63130, USA
³Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah 84112, USA
⁴SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom
⁵Department of Physics, University of Illinois Urbana-Champaign, Urbana, Illinois 61801, USA
⁶Illinois Center for Advanced Studies of the Universe, University of Illinois Urbana-Champaign, Urbana, Illinois 61801, USA
⁷CAFPE and Departamento de Física Teórica y del Cosmos, Universidad de Granada, E-18071 Granada, Spain
⁸Department of Physics, Indiana University, Bloomington, Indiana 47405, USA
⁹Theory Division, Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
¹⁰Department of Physics, Colorado State University, Fort Collins, Colorado 80523, USA
¹¹Department of Physics, Syracuse University, Syracuse, New York 13244, USA
¹²Laboratory for Elementary-Particle Physics, Cornell University, Ithaca, New York 14853, USA
¹³Centre for Mathematical Sciences, University of Plymouth, Plymouth PL4 8AA, United Kingdom
¹⁴Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
¹⁵Departmento de Física Teórica, Universidad de Zaragoza, 50009 Zaragoza, Spain
¹⁶Center for Astroparticles and High Energy Physics (CAPA), Calle Pedro Cerbuna 12, 50009 Zaragoza, Spain

^*Contact author: shaun.lahert@gmail.com
^†Contact author: ml11@illinois.edu
^‡Contact author: jacob.sitison@colorado.edu

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Phys. Rev. Lett. 135, 011901 – Published 1 July, 2025

DOI: https://doi.org/10.1103/d583-yhfs

Abstract

We present results for the dominant light-quark connected contribution to the long-distance window of the hadronic vacuum polarization (HVP) contribution to the muon $g - 2$ from lattice quantum chromodynamics. Specifically, with a new determination of the lattice scale on MILC’s physical-mass HISQ ensembles, using the $Ω^{-}$ baryon mass, we obtain a result of $a_{μ}^{l l, LD} (conn) = 400.2 (2.3)_{stat} (3.7)_{syst} [4.3]_{total} \times 10^{- 10}$ . Summing this result with our recent determinations of the light-quark connected contributions to the short- and intermediate-distance windows, we obtain a subpercent precision determination of the light-quark-connected contribution to HVP of $a_{μ}^{l l} (conn) = 655.2 (2.3)_{stat} (3.9)_{syst} [4.5]_{total} \times 10^{- 10}$ . Finally, as a consistency check, we verify that an independent analysis of the full contribution is in agreement with the sum of individual windows. We discuss our future plans for improvements of our HVP calculations to meet the target precision of the Fermilab $g - 2$ experiment.

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Phys. Rev. Lett. 135, 011901– Published 1 July, 2025

Vol. 135, Iss. 1 — 2 July 2025

Received 22 January 2025
Revised 25 April 2025
Accepted 20 May 2025

DOI: https://doi.org/10.1103/d583-yhfs

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Hadronic Vacuum Polarization for the Muon $g - 2$ from Lattice QCD: Long-Distance and Full Light-Quark Connected Contribution

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Hadronic Vacuum Polarization for the Muon g−2 from Lattice QCD: Long-Distance and Full Light-Quark Connected Contribution

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Hadronic Vacuum Polarization for the Muon $g - 2$ from Lattice QCD: Long-Distance and Full Light-Quark Connected Contribution