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 $U(1)'$ (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 $R_{K^{(*)}}$. In such theories, we show that the same muon couplings which explain $R_{K^{(*)}}$ 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.
Highlights
Most Z0 models [1] have universal couplings to the three families of quarks and leptons
Z0 couplings, which can account for the B physics anomalies in RKðÃÞ
In this paper we focus on an SUð5Þ × Uð1Þ0 model with a vectorlike fourth family where the three chiral families do not couple to the Uð1Þ0, but the fourth vectorlike family has arbitrary Uð1Þ0 charges for the different multiplets, which mix with the three families, thereby inducing effective nonuniversal couplings for the light physical mixed quarks and leptons
Summary
Most Z0 models [1] have universal couplings to the three families of quarks and leptons. The reason for this is both theoretical and phenomenological. Many theoretical models naturally predict universal Z0 couplings. The phenomenological motivation for considering nonuniversal Z0 models has increased due to mounting evidence for semileptonic B decays which violate μ − e universality at rates which exceed those predicted by the Standard Model (SM) [2,3,4]. Following the recent measurement of RKÃ [6], a number of phenomenological analyses of these data (see, e.g., [7,8,9,10,11,12]) favor a new physics operator of the CN9μP 1⁄4 −CN10Pμ form [13,14],
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