Gauge coupling unification in a minimal non-supersymmetric $E_6$ GUT

Abstract

We consider a minimal renormalizable non-supersymmetric $E_6$ Grand Unified Theory using fundamental representation $27$ for fermions and scalars. The scalar with adjoint representation ${78}$ is also taken for direct breaking of $E_{6}$ to SM. The proposed model, guided by TeV-scale vector-like fermions and scalar leptoquark offer successful gauge unification even in the absence of any intermediate symmetry. Embedded with threshold corrections, it is shown to be compatible with the present experimental limit on proton decay lifetime. The unique feature of the model shows that, the GUT threshold corrections to the unification mass, is controlled by superheavy gauge bosons only, thereby minimising the uncertainty of the GUT predictions. The scalar leptoquark and vector-like fermions residing in $27$ representation can explain flavor physics anomalies like $R_{D^{(\ast)}}$ as reported by the LHCb collaboration and the muon anomalous magnetic moment reported by the recent muon $g-2$ experiment at Fermilab. The model can also predict a sub-eV scale neutrino at one-loop level via exchange of $W$ and $Z$ gauge bosons through MRIS mechanism.