Hadronic vacuum polarization: $(g-2)_\mu$ versus global electroweak fits

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 $\Delta\alpha^{(5)}_\text{had}$. 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 $\Delta \alpha^{(5)}_\text{had}\big|_\text{EW}=270.2(3.0)\times 10^{-4}$. 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 prediction 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.