Muon anomalies and the $SU(5)$ Yukawa relations

Abstract

We show that, within the framework of $SU(5)$ Grand Unified Theories (GUTs), multiple vector-like families at the GUT scale which transform under a gauged $U(1{)}^{\prime }$ (under which the three chiral families are neutral) can result in a single vector-like family at low energies which can induce non-universal and flavourful $Z^{\prime }$ couplings, which can account for the B physics anomalies in $R_{K^{(\ast )}}$. In such theories, we show that the same muon couplings which explain $R_{K^{(\ast )}}$ also correct the Yukawa relation $Y_e=Y_d^T$ in the muon sector without the need for higher Higgs representations. To illustrate the mechanism, we construct a concrete a model based on $SU(5)\times A_4\times Z_3\times Z_7$ with two vector-like families at the GUT scale, and two right-handed neutrinos, leading to a successful fit to quark and lepton (including neutrino) masses, mixing angles and CP phases, where the constraints from lepton flavour violation require $Y_e$ to be diagonal.

Comments: 38 pages, 3 figures. Published version