# Complete Vector-like Fourth Family and new $\mathrm{U(1)^\prime}$ for Muon Anomalies

## TL;DR

This paper proposes a model extending the Standard Model with a new U(1)' gauge symmetry and a complete vector-like fourth family, explaining muon g-2 and B decay anomalies while fitting existing data.

## Contribution

It introduces a unified model with a new Z' boson and vector-like fermions that explains multiple anomalies and remains consistent with current experimental constraints.

## Key findings

- Good fit to muon g-2 and B decay anomalies
- Model consistent with existing high-energy data
- Potential for future experimental tests

## Abstract

We consider the Standard Model (SM) with the addition of a $\mathrm{U(1)^\prime}$ gauge symmetry and a complete fourth family of quarks and leptons which are vector-like with respect to the full $\mathrm{SU(3)_C}\times \mathrm{SU(2)_L} \times \mathrm{U(1)_Y}\times \mathrm{U(1)^\prime}$ gauge symmetry. The model provides a unified explanation of experimental anomalies in $(g - 2)_\mu$ as well as $b \rightarrow s \ell^+ \ell^-$ decays. We find good fits to the deviations from the SM, while at the same time fitting all other SM observables. The model includes a new $Z^\prime$ gauge boson, a $\mathrm{U(1)^\prime}$-breaking scalar, and vector-like leptons all with mass of order a few $100$ GeV. It is consistent with all currently released high energy experimental data, however, it appears imminently testable with well designed future searches. Also precision flavor experiments, especially more accurate direct determinations of CKM matrix elements, would allow to probe the best fit points.