An anomaly-free leptophilic $U(1)'_{\ell}$ completion of the Standard Model

Abstract

We develop a minimal and fully anomaly-free realization of a universal leptophilic $U(1)'_{\ell}$ gauge symmetry, under which all Standard-Model leptons carry a common charge while quarks remain neutral. Gauge consistency is restored by introducing one vectorlike lepton family and singlet scalars whose vacuum expectation values both break $U(1)'_{\ell}$ and generate masses for the new gauge boson $Z_{\ell}$ and the heavy leptons. We derive compact anomaly-cancellation conditions, closed-form $Z_{\ell}$ couplings and decay widths, and the structure of gauge--kinetic mixing, including the trace condition $\mathrm{Tr}(YQ')=0$ that suppresses radiative mixing. The setup naturally embeds a type-I seesaw for neutrino masses and provides a stable singlet field as a minimal dark-matter candidate. Collider and precision constraints are expressed analytically over the full parameter space, covering pure leptophilic production, small-mixing hadron colliders, and the contact-interaction limit $M_{Z_{\ell}}\!\gg\!\sqrt{s}$. The model therefore provides a single, internally consistent benchmark that unifies gauge, scalar, Yukawa, neutrino, and dark-matter sectors, and is directly suited for global data recasts and targeted searches at future lepton and hadron colliders.