Global Analysis of Leptophilic $Z^\prime$ Bosons

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} $ 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 L$_{μ}$− L$_{τ}$ 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} $ without violating bounds from electroweak precision observables.