Muon anomalies and the SU (5) Yukawa relations

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)′ (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′ couplings, which can account for the B physics anomalies in RK(∗). In such theories, we show that the same muon couplings which explain RK(∗) also correct the Yukawa relation Ye=YTd 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)×A4×Z3×Z7 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 Ye to be diagonal.