ORCID

Abstract

We present complete results for the hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment aμ in the short- and intermediate-distance window regions, which account for roughly 10% and 35% of the total HVP contribution to aμ, respectively. In particular, we perform lattice-QCD calculations for the isospin-symmetric connected and disconnected contributions, as well as corrections due to strong-isospin breaking. For the short-distance window observables, we investigate the so-called log-enhancement effects as well as the significant oscillations associated with staggered quarks in this region. For the dominant, isospin-symmetric light-quark-connected contribution, we obtain aμll,SD(conn)=48.139(11)stat(91)syst[92]total×10-10 and aμll,W(conn)=206.90(14)stat(61)syst[63]total×10-10. We use Bayesian model averaging to fully estimate the covariance matrix between the individual contributions. Our determinations of the complete window contributions are aμSD=69.05(1)stat(21)syst[21]total×10-10 and aμW=236.45(17)stat(83)syst[85]total×10-10. This work is part of our ongoing effort to compute all contributions to HVP with an overall uncertainty at the few-permille level.

Publication Date

2025-05-12

Publication Title

Phys.Rev.D

Volume

111

Issue

9

Acceptance Date

2025-01-01

Deposit Date

2025-05-20

Funding

We thank Claude Bernard, Urs Heller, Paul Mackenzie, Bob Sugar, and Doug Toussaint for their scientific leadership and collaboration. In particular, we are grateful to Bob and Paul for their tireless efforts to obtain computational resources, to Claude for guidance on chiral perturbation theory, to Doug for his invaluable expertise in creating so many of our gauge-field ensembles, and to Urs for essential contributions to previous projects that formed the basis for this work. Computations for this work were carried out in part with computing and long-term storage resources provided by the USQCD Collaboration, the National Energy Research Scientific Computing Center (Cori), the Argonne Leadership Computing Facility (Mira) under the INCITE program, and the Oak Ridge Leadership Computing Facility (Summit) under the Innovative and Novel Computational Impact on Theory and Experiment (INCITE) and the ASCR Leadership Computing Challenge (ALCC) programs, which are funded by the Office of Science of the U.S. Department of Energy. This work used the Extreme Science and Engineering Discovery Environment (XSEDE) supercomputer Stampede 2 at the Texas Advanced Computing Center (TACC) through allocation TG-MCA93S002. The XSEDE program is supported by the National Science Foundation under Grant No. ACI-1548562. Computations on the Big Red II+, Big Red 3, and Big Red 200 supercomputers were supported in part by Lilly Endowment, Inc., through its support for the Indiana University Pervasive Technology Institute. The parallel file system employed by Big Red II+ was supported by the National Science Foundation under Grant No. CNS-0521433. This work utilized the RMACC Summit supercomputer, which is supported by the National Science Foundation (Awards No. ACI-1532235 and No. ACI-1532236), the University of Colorado Boulder, and Colorado State University. The Summit supercomputer is a joint effort of the University of Colorado Boulder and Colorado State University. Some of the computations were done using the Blue Waters sustained-petascale computer, which was supported by the National Science Foundation (Awards No. OCI-0725070 and No. ACI-1238993) and the State of Illinois. Blue Waters was a joint effort of the University of Illinois at Urbana-Champaign and its National Center for Supercomputing Applications. We also used the Cambridge Service for Data Driven Discovery (CSD3), part of which is operated by the University of Cambridge Research Computing Service on behalf of the Science and Technology Facilities Council (STFC) DiRAC HPC Facility. The DiRAC component of CSD3 was funded by BEIS capital funding via STFC capital Grants No. ST/P002307/1 and No. ST/R002452/1 and STFC operations Grant No. ST/R00689X/1. This work was supported in part by the U.S. Department of Energy, Office of Science, under Awards No. DE-SC0010005 (E.\u2009T.\u2009N. and J.\u2009W.\u2009S.), No. DE-SC0010120 (S.\u2009G.), No. DE-SC0015655 (A.\u2009X.\u2009E.-K., S.\u2009L., M.\u2009L., A.\u2009T.\u2009L.), No. DE-SC0009998 (J.\u2009L.), the \u201CHigh Energy Physics Computing Traineeship for Lattice Gauge Theory\u201D No. DE-SC0024053 (J.\u2009W.\u2009S.), and the Funding Opportunity Announcement Scientific Discovery through Advanced Computing: High Energy Physics, LAB 22-2580 (D.\u2009A.\u2009C., C.\u2009T.\u2009P., L.\u2009H., M.\u2009L., S.\u2009L.); by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration (H.\u2009J.); by the National Science Foundation under Grants No. PHY20-13064 and No. PHY23-10571 (C.\u2009D., D.\u2009A.\u2009C., S.\u2009L., A.\u2009V.), No. PHY23-09946 (A.\u2009B.), and Grant No. 2139536 for Characteristic Science Applications for the Leadership Class Computing Facility (L.\u2009H., H.\u2009J.); by the Simons Foundation under their Simons Fellows in Theoretical Physics program (A.\u2009X.\u2009E.-K.); by the Universities Research Association Visiting Scholarship Awards No. 20-S-12 and No. 21-S-05 (S.\u2009L.); by MICIU/AEI/10.13039/501100011033 and FEDER (EU) under Grant No. PID2022-140440NB-C21 (E.\u2009G.); by Consejeria de Universidad, Investigaci\u00F3n e Innovaci\u00F3n and Gobierno de Espa\u00F1a and EU\u2013NextGenerationEU, under Grant No. AST22 8.4 (E.\u2009G.); by AEI (Spain) under Grant No. RYC2020-030244-I / AEI / 10.13039/501100011033 (A.\u2009V.); and by U.K. Science and Technology Facilities Council under Grant No. ST/T000945/1 (C.\u2009T.\u2009H.\u2009D.). A.\u2009X.\u2009E.-K. and E.\u2009T.\u2009N. are grateful to the Pauli Center for Theoretical Studies and the ETH Z\u00FCrich for support and hospitality. A.\u2009X.\u2009K., A.\u2009S.\u2009K., and E.\u2009T.\u2009N. are grateful to the Kavli Institute for Theoretical Physics (KITP) for hospitality and support during the \u201DWhat is Particle Theory?\u201D program. The KITP is supported in part by the National Science Foundation under Grant PHY-2309135. This document was prepared by the Fermilab Lattice, HPQCD, and MILC Collaborations using the resources of the Fermi National Accelerator Laboratory (Fermilab), a U.S. Department of Energy, Office of Science, HEP User Facility. Fermilab is managed by Fermi Research Alliance, LLC (FRA), acting under Contract No. DE-AC02-07CH11359.

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