Utility of a hybrid approach to the hadronic vacuum polarization contribution to the muon anomalous magnetic moment

Journal Article · 29 January 2025 · Physical Review. D.

DOI: https://doi.org/10.1103/PhysRevD.111.014513 · OSTI ID:2507393

Davies, C. T. H. ; Kronfeld, A. S. ; Lepage, G. P. ; McNeile, C. ; Van de Water, R. S.

An accurate calculation of the leading-order hadronic vacuum polarization (LOHVP) contribution to the anomalous magnetic moment of the muon ( $a_{\mu }$ ) is key to determining whether a discrepancy, suggesting new physics, exists between the Standard Model and experimental results. This calculation can be expressed as an integral over Euclidean time of a current-current correlator $G\left(t\right)$ , where $G\left(t\right)$ can be calculated using lattice QCD or, with dispersion relations, from experimental data for $e^{+}{e}^{-}\to \text{hadrons}$ . The BMW/DMZ collaboration recently presented a hybrid approach in which $G\left(t\right)$ is calculated using lattice QCD for most of the contributing $t$ range, but using experimental data for the largest $t$ (lowest energy) region. Here we study the advantages of varying the position $t=t_1$ separating lattice QCD from data-driven contributions. The total LOHVP contribution should be independent of $t_1$ , providing both a test of the experimental input and the robustness of the hybrid approach. We use this criterion and a correlated fit to show that Fermilab/HPQCD/MILC lattice QCD results from 2019 strongly favor the CMD-3 cross section data for $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ over a combination of earlier experimental results for this channel. Further, the resulting total LOHVP contribution obtained is consistent with the result obtained by BMW/DMZ, and supports the scenario in which there is no significant discrepancy between the experimental value for $a_{\mu }$ and that expected in the Standard Model. We then discuss how improved lattice results in this hybrid approach could provide a more accurate total LOHVP across a wider range of $t_1$ values with an uncertainty that is smaller than that from either lattice QCD or data-driven approaches on their own. Published by the American Physical Society 2025

• Research Organization: Cornell U., LEPP; Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Glasgow U.; Plymouth U.
• Sponsoring Organization: US Department of Energy; USDOE
• Grant/Contract Number: 89243024CSC000002
• OSTI ID: 2507393
• Report Number(s): FERMILAB-PUB-24-0783-T; 014513
• Journal Information: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 1 Vol. 111; ISSN PRVDAQ; ISSN 2470-0010
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English