Muon anomalies and the SU(5) Yukawa relations

We show that, within the framework of SU(5) grand unified theories (GUTs), multiple vectorlike 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 vectorlike family at low energies which can induce nonuniversal and flavorful 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 = YdT in the muon sector without the need for higher Higgs representations. To illustrate the mechanism, we construct a concrete model based on SU(5) × A4 × Z3 × Z7 with two vectorlike 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-flavor violation require Ye to be diagonal.