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

TL;DR

The work constructs a fully anomaly-free UV-complete leptophilic gauge extension based on $U(1)'_\ell$, where all leptons carry common charges and quarks are neutral. By introducing a single vectorlike lepton family and SM-singlet scalars, the model cancels gauge and gravitational anomalies, spontaneously breaks $U(1)'_\ell$, and yields a massive $Z_\ell$ whose couplings and decays are computed with kinetic-mixing effects controlled by $\,\mathrm{Tr}(YQ')=0$. It unifies the gauge, scalar, Yukawa, neutrino, and dark-matter sectors into a compact framework with closed-form relations, enabling analytic mappings of collider, precision, and cosmological observables onto the $(M_{Z_\ell},g_{\rm eff})$ plane and a minimal dark-matter sector that can be fermionic or scalar. The model naturally accommodates a type-I seesaw mechanism for neutrino masses and provides a stable dark-matter candidate, while the vectorlike leptons yield characteristic collider signatures. Overall, the work offers a well-defined benchmark for global data recasts and targeted searches at current and future lepton and hadron colliders, linking collider phenomenology to neutrino physics and cosmology within one coherent framework.

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.

Figures (1)

• Figure 1: Global sensitivity map in the $(M_{Z_\ell},\,|g_{\rm eff}|)$ plane. Diagonal lines illustrate representative contact scales $\Lambda = M_{Z_\ell}/|g_{\rm eff}|$; moving along a line preserves the LEP contact reach. The shaded band schematically marks the regime where invisible decays dominate, in which visible dilepton searches weaken while missing-energy and precision handles become comparatively stronger.