Leptophilic Gauge Interactions in the SMEFT Era

TL;DR

The paper develops a universal, UV-agnostic EFT framework that maps general leptophilic $U(1)'_\ell$ gauge interactions to low-energy observables in SMEFT and LEFT. A minimal anomaly-free UV completion with a heavy $Z_\ell$ mediator and vectorlike leptons yields a compact tree-level matching: four-lepton operators and Higgs–current structures, with kinetic mixing controlled by $\mathrm{Tr}(YQ')$; the Wilson coefficients run under SMEFT RGEs down to the electroweak scale and match onto LEFT, producing a coherent set of leptonic vector–vector and four-lepton operators. A central result is the emergence of a single effective scale $\Lambda_{\rm eff} = \frac{M_{Z_\ell}}{g_\ell\sqrt{|q_\alpha q_\beta|}}$ that governs all leading EFT signatures, enabling direct reinterpretation of LEP-II dilepton data, neutrino trident production, $\nu e$ scattering, parity-violating Møller observables, and muon-decay parameters. The framework provides a plug-and-play interface for global fits, collider recasts, and future collider projections, and identifies concrete benchmark scenarios (e.g., universal charges and $L_\mu-L_\tau$) within a consistent EFT description that remains valid away from the $Z_\ell$ pole and below the heavy-vectorlike thresholds.

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.