Leptophilic Gauge Interactions in the SMEFT Era

Abstract: We develop a "precision-ready", model-independent EFT framework that connects general leptophilic gauge interactions to their low-energy manifestations in SMEFT and LEFT. Starting from a broad U(1)'_ell extension in which leptons carry family-dependent charges (q_e, q_mu, q_tau) while quarks remain neutral, quantum consistency is ensured through a minimal set of vectorlike leptons, chiral under U(1)'_ell but vectorlike under the SM, together with singlet scalars responsible for symmetry breaking and the masses of both Z_ell and the heavy leptons. In the heavy-mediator limit, we integrate out Z_ell at tree level and derive compact, analytic SMEFT Wilson coefficients for four-lepton operators and Higgs-current structures, including hypercharge-U(1)'_ell kinetic mixing proportional to Tr(Y Q'). Renormalization-group evolution down to the electroweak scale and matching onto LEFT produce closed-form expressions directly applicable to e+e- -> l+l-, neutrino trident production, nu e scattering, parity-violating Moeller observables, and muon-decay parameters. A single parameter combination, Lambda_eff = M_Zell / (g_ell * sqrt(|q q'|)), governs all leading EFT signatures, offering a unified way to map UV charge assignments onto precision observables. We delineate the validity domain of this EFT and outline its use as a "plug-and-play" interface for global fits, collider recasts, and future-collider projections.