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

TL;DR

This paper proposes a Grand Unified Theory framework where vector-like families induce flavor-specific Z' couplings, explaining B physics anomalies and correcting Yukawa relations without extra Higgs representations.

Contribution

It introduces a model with vector-like families and flavor-specific Z' couplings within SU(5) GUTs, addressing B anomalies and Yukawa relation corrections simultaneously.

Findings

Successfully explains B physics anomalies in R_K(*)

Corrects muon sector Yukawa relations without extra Higgs

Fits quark and lepton masses and mixings including neutrinos

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.