Exploring a Gauge Horizontal Model for Charged Fermion Masses

We investigate an extension of the Standard Model (SM) incorporating a gauge $U(1)$ horizontal symmetry that is free of anomalies. This extension introduces four additional un-Higgsed scalar doublets that do not develop vacuum expectation values, two scalar singlets, and a pair of vector-like fermionic singlets. Within this framework, the masses of third-generation charged fermions are generated through the conventional SM Yukawa interactions, while the masses of second-generation charged fermions are suppressed via a mechanism reminiscent of Froggatt-Nielsen. In contrast, the masses of first-generation charged fermions are predominantly determined by radiative corrections. Unlike traditional implementations of the Froggatt-Nielsen mechanism, our model does not require additional colored vector or chiral fermions beyond the SM. This model provides an economical ultraviolet-complete mechanism to explain the observed patterns in charged fermion masses and Cabibbo-Kobayashi-Maskawa matrix elements. Notably, the electron electric dipole moment vanishes automatically at the two-loop level, and there is no charged lepton flavor violation to all orders. We also discuss potential experimental signatures that could distinguish this model from other $Z'$ models, such as specific patterns in gauge boson decays and associated collider signatures.