W boson mass anomaly and grand unification

Abstract

It is known that the recently reported shift of the W boson mass can be easily explained by an SU(2)L triplet Higgs boson with a zero hypercharge if it obtains a vacuum expectation value (VEV) of O(1) GeV. Surprisingly, the addition of a TeV scale complex triplet Higgs boson to the standard model (SM) leads to a precise unification of the gauge couplings at around 1014 GeV. We consider that it is a consequence of SU(5) grand unification and show a possible potential for the Higgs fields yielding a weak scale complex SU(2) triplet scalar boson. Although it seems the proton decay constraint would doom such a low-scale unification, we show that the constraint can be avoided by introducing vector-like fermions which mix with the SM fermions through mass terms involving the VEV of GUT breaking Higgs field. Importantly, the simplest viable model only requires the addition of one pair of vector-like fermions transforming 10 and 10‾.