Stability of the vacuum as constraint on $U$(1) extensions of the standard model

Abstract: In the standard model the running quartic coupling becomes negative during its renormalization group flow, which destabilizes the vacuum. We consider U(1) extensions of the standard model, with an extra complex scalar field and a Majorana-type neutrino Yukawa coupling. These additional couplings affect the renormalization group flow of the quartic couplings. We compute the beta-functions of the extended model at one-loop order in perturbation theory and study how the parameter space of the new scalar couplings can be constrained by the requirement of stable vacuum and perturbativity up to the Planck scale.