We present the complete set of renormalization group equations at one loop for the nonexotic minimal $U(1)$ extension of the standard model (SM). It includes all models that are anomaly-free with the SM fermion content augmented by one right-handed neutrino per generation. We then pursue the numerical study of the pure $B-L$ model, deriving the triviality and vacuum stability bounds on an enlarged scalar sector comprising one additional Higgs singlet field with respect to the SM.

• Received 14 May 2010

DOI:https://doi.org/10.1103/PhysRevD.82.055018