Stabilizing electroweak vacuum in a vectorlike fermion model

Abstract

To avoid possible electroweak vacuum instability in the vectorlike fermion model, we introduce a new singlet scalar to the model, which couples to the vectorlike fermion and also mixes with the Higgs boson after spontaneous symmetry breaking. We investigate the vectorlike fermion predominantly coupled to the third-generation quarks, and its mass is generated from the vacuum expectation value of the new scalar field in the model. In this setup, as running towards high energies, the new scalar provides a positive contribution to the running of the Higgs quartic coupling, and the matching on the scale of the scalar mass gives rise to a threshold effect that lifts up the Higgs quartic coupling strength. The two effects help stabilize the electroweak vacuum of the Higgs potential. Therefore, this setup could evade possible vacuum instability in the vectorlike fermion model. We show that a large range of parameter space is allowed to have both stable Higgs vacuum and perturbativity of all the running couplings, up to the Planck scale. We also examine the experimental constraints from the electroweak precision observables such as oblique corrections $S,T$ and nonoblique corrections to the $Z{b}_{L}{\overline{b}}_{L}$ coupling, the Higgs coupling precision measurements, and the current LHC direct searches.