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.

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New neutral heavy gauge bosons (Z′) are predicted within many extensions of the Standard Model. While in case they couple to quarks the LHC bounds are very stringent, leptophilic Z′ bosons (even with sizable couplings) can be much lighter and therefore lead to interesting quantum effects in precision observables (like (g − 2)μ) and generate flavour violating decays of charged leptons. In particular, $$ \mathrm{\ell}\to \mathrm{\ell}^{\prime }v\overline{v} $$ ℓ → ℓ ′ v v ¯ decays, anomalous magnetic moments of charged leptons, ℓ → ℓ′γ and ℓ → 3ℓ′ decays place stringent limits on leptophilic Z′ bosons. Furthermore, in case of mixing Z′ with the SM Z, Z pole observables are affected. In light of these many observables we perform a global fit to leptophilic Z′ models with the main goal of finding the bounds for the Z′ couplings to leptons. To this end we consider a number of scenarios for these couplings. While in generic scenarios correlations are weak, this changes once additional constraints on the couplings are imposed. In particular, if one considers an Lμ− Lτ symmetry broken only by left-handed rotations, or considers the case of τ − μ couplings only. In the latter setup, on can explain the (g − 2)μ anomaly and the hint for lepton flavour universality violation in $$ \tau \to \mu v\overline{v}/\tau \to ev\overline{v} $$ τ → μv v ¯ / τ → ev v ¯ without violating bounds from electroweak precision observables.