$$ {R}_{K^{\left(*\right)}} $$ and the origin of Yukawa couplings
A bstract We explore the possibility that the semi-leptonic B decay ratios $$ {R}_{K^{\left(*\right)}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>R</mml:mi> <mml:msup> <mml:mi>K</mml:mi> <mml:mfenced> <mml:mo>*</mml:mo> </mml:mfenced> </mml:msup> </mml:msub> </mml:math> 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 $$ {R}_{K^{\left(*\right)}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>R</mml:mi> <mml:msup> <mml:mi>K</mml:mi> <mml:mfenced> <mml:mo>*</mml:mo> </mml:mfenced> </mml:msup> </mml:msub> </mml:math> 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.