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 determination 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.

Recently, discrepancies of up to 4σ between the different determinations of the Cabibbo angle were observed. In this context, we point out that this "Cabibbo-angle anomaly" can be explained by lepton flavor universality violating new physics in the neutrino sector. However, modified neutrino couplings to standard model gauge bosons also affect many other observables sensitive to lepton flavor universality violation, which have to be taken into account in order to assess the viability of this explanation. Therefore, we perform a model-independent global analysis in a Bayesian approach and find that the tension in the Cabibbo angle is significantly reduced, while the agreement with other data is also mostly improved. In fact, nonzero modifications of electron and muon neutrino couplings are preferred at more than 99.99% C.L. (corresponding to more than 4σ). Still, since constructive effects in the muon sector are necessary, simple models with right-handed neutrinos (whose global fit we update as a by-product) cannot fully explain data, pointing towards more sophisticated new physics models.

The “Cabibbo Angle Anomaly” (CAA) originates from the disagreement between the CKM elements Vud and Vus extracted from superallowed beta and kaon decays, respectively, once compared via CKM unitarity. It points towards new physics with a significance of up to 4 σ, depending on the theoretical input used, and can be explained through modified W couplings to leptons. In this context, vector-like leptons (VLLs) are prime candidates for a corresponding UV completion since they can affect Wℓν couplings at tree-level, such that this modification can have the dominant phenomenological impact. In order to consistently assess agreement data, a global fit is necessary which we perform for gauge-invariant dimension-6 operators and all patterns obtained for the six possible representations (under the SM gauge group) of VLLs. We find that even in the lepton flavour universal case, including the measurements of the CKM elements Vus and Vud into the electroweak fit has a relevant impact, shifting the best fit point significantly. Concerning the VLLs we discuss the bounds from charged lepton flavour violating processes and observe that a single representation cannot describe experimental data significantly better than the SM hypothesis. However, allowing for several representations of VLLs at the same time, we find that the simple scenario in which N couples to electrons via the Higgs and Σ1 couples to muons not only explains the CAA but also improves the rest of the electroweak fit in such a way that its best fit point is preferred by more than 4 σ with respect to the begin.