$R_{K^{(\ast )}}$ and the origin of Yukawa couplings

Abstract

We explore the possibility that the semi-leptonic $B$ decay ratios $R_{K^{(\ast )}}$ which violate $\mu -e$ universality are related to the origin of the fermion Yukawa couplings in the Standard Model. Some time ago, a vector-like fourth family (without a $Z^{\prime }$) was used to generate fermion mass hierarchies and mixing patterns without introducing any family symmetry. Recently the idea of inducing flavourful $Z^{\prime }$ couplings via mixing with a vector-like fourth family which carries gauged $U(1{)}^{\prime }$ charges has been proposed as a simple way of producing controlled flavour universality violation while elegantly cancelling anomalies. We show that the fusion of these two ideas provides a nice connection between $R_{K^{(\ast )}}$ and the origin of Yukawa couplings in the quark sector. However the lepton sector requires some tuning of Yukawa couplings to obtain the desired coupling of $Z^{\prime }$ to muons.

Minor corrections to phenomenology section to match published version. 19 pages, 4 figures

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