W boson mass anomaly and grand unification

TL;DR

This paper explains the W boson mass anomaly with a triplet Higgs, proposes a grand unification model at a low scale, and addresses proton decay constraints with vector-like fermions.

Contribution

It introduces a minimal grand unification model that accounts for the W boson mass shift and achieves gauge coupling unification at a low scale using a triplet Higgs and vector-like fermions.

Findings

Triplet Higgs explains W boson mass shift.

Gauge couplings unify at ~10^{14} GeV.

Proton decay constraints are mitigated by vector-like fermions.

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 $10^{14}$ 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 ${\bf 10}$ and $\overline{\bf 10}$.