Hadronic vacuum polarization (HVP) is not only a critical part of the standard model (SM) prediction for the anomalous magnetic moment of the muon $(g-2{)}_{\mu }$, 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 $\mathrm{\Delta }{\alpha }_{\text{had}}^{(5)}$. We find that with modern EW precision data, including the measurement of the Higgs mass, the global fit alone provides a competitive, independent determination of $\mathrm{\Delta }{\alpha }_{\text{had}}^{(5)}{|}_{\mathrm{EW}}=270.2(3.0)\times {10}^{-4}$. This value actually lies below the range derived from $e^{+}{e}^{-}\to \text{hadrons}$ 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 $(g-2{)}_{\mu }$ 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 $(g-2{)}_{\mu }$ by adjusting HVP would thus not necessarily weaken the case for physics beyond the SM (BSM), but to some extent shift it from $(g-2{)}_{\mu }$ to the EW fit. We briefly explore some options of BSM scenarios that could conceivably explain the ensuing tension.

• Received 16 July 2020
• Accepted 3 August 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.091801

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Published by the American Physical Society