{R}_{K^{left(*right)}} and the origin of Yukawa couplings

Abstract

We explore the possibility that the semi-leptonic B decay ratios {R}_{K^{left(*right)}} which violate μ − 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′) was used to generate fermion mass hierarchies and mixing patterns without introducing any family symmetry. Recently the idea of inducing flavourful Z′ couplings via mixing with a vector-like fourth family which carries gauged U(1)′ 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^{left(*right)}} 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′ to muons.