Flavourful Z′ models for RK∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {R}_{K^{\left(\ast \right)}} $$\end{document}

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 RK and RK∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {R_K}_{{}^{\ast }} $$\end{document}. A similar analysis could be performed for B − L models, E6 models, composite models, and so on.