# Flavourful $Z'$ models for $R_{K^{(*)}}$

## TL;DR

This paper demonstrates how to extend flavour conserving $Z'$ models to explain anomalies in $B$ decay ratios by introducing mixing with a fourth family of vector-like fermions, providing a general formalism and concrete examples.

## Contribution

It develops a general formalism for flavour violation in $Z'$ models and applies it to specific models to explain $R_K$ and $R_{K^*}$ anomalies.

## Key findings

- Successfully accounts for $R_K$ and $R_{K^*}$ anomalies
- Provides a framework applicable to various $Z'$ models
- Shows how mixing with vector-like fermions induces flavour violation

## Abstract

We show how any flavour conserving $Z'$ model can be made flavour violating and non-universal by introducing mass mixing of quarks and leptons with a fourth family of vector-like fermions with non-universal $Z'$ couplings. After developing a general formalism, we focus on two concrete examples, namely a fermiophobic model, and an $SO(10)$ GUT model, and show how they can account for the anomalous $B$ decay ratios $R_K$ and $R_{K^*}$. A similar analysis could be performed for $B-L$ models, $E_6$ models, composite models, and so on.