# Light Mediators in Anomaly Free $U(1)_X$ Models I - Theoretical Framework

## TL;DR

This paper explores theoretical aspects of anomaly-free $U(1)_X$ extensions of the Standard Model, focusing on the properties of light mediators like dark photons and $Z'$ bosons, and their potential UV completions.

## Contribution

It introduces a class of $U(1)_X$ models with anomaly cancellation per generation, detailing their structure, fermion charge assignments, and possible UV completions with dark matter candidates.

## Key findings

- $U(1)_X$ models can be anomaly-free with minimal modifications to $Z$ interactions.
- Light $A'$ (dark photon) and $Z'$ bosons can be distinguished by their axial-vector currents.
- Models can be UV completed with stable fermions or right-handed neutrinos.

## Abstract

We examine theoretical features of $U(1)_X$ extensions of the Standard Model whose quantum anomalies are canceled per generation. Similarly to other versions, the theory consists of a Two-Higgs-Doublet Model plus a scalar singlet embedded into the $SM \otimes U(1)_X$ gauge group, and introduces small modifications to the $Z$-boson interactions. These changes can be minimized by exclusively charging right-handed fermions under the new Abelian symmetry, and are compensated by the neutral $X$-boson exchange. Non-universality of fermion couplings can also be achieved by requiring one single $X$-charged family. In general, $X$ gauge bosons can be separated into $A'$ (dark photons) and $Z'$ subsets, distinguished by the presence of axial-vector currents. $A'$ physics is commonly simpler to constrain and therefore favored by experimental tests. Finally, the model can be UV completed both by stable $\chi$ fermions or by right-handed neutrinos. The prior case may provide cold WIMPs in the theory.