Hadronic vacuum polarization (HVP) is not only a critical part of the standard model (SM) prediction for the anomalous magnetic moment of the muon ðg − 2Þ μ , but also a crucial ingredient for global fits to electroweak (EW) precision observables due to its contribution to the running of the fine-structure constant encoded in Δα ð5Þ had . We find that with modern EW precision data, including the measurement of the Higgs mass, the global fit alone provides a competitive, independent

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... of Δα ð5Þ had j EW ¼ 270.2ð3.0Þ × 10 −4 . This value actually lies below the range derived from e þ e − → hadrons cross section data, and thus goes into the opposite direction as would be required if a change in HVP were to bring the SM prediction for ðg − 2Þ μ into agreement with the Brookhaven measurement. Depending on the energy where the bulk of the changes in the cross section occurs, reconciling experiment and SM predictions for ðg − 2Þ μ by adjusting HVP would thus not necessarily weaken the case for physics beyond the SM (BSM), but to some extent shift it from ðg − 2Þ μ to the EW fit. We briefly explore some options of BSM scenarios that could conceivably explain the ensuing tension.