Vacuum stability in the U(1)x extended model with vanishing scalar potential at the Planck scale

Abstract

We investigate the vacuum stability in a scale invariant local U (1)χ model with vanishing scalar potential at the Planck scale. We find that it is impossible to realize the Higgs mass of 125 GeV while keeping the Higgs quartic coupling χH positive in all energy scales, that is, the same as the standard model. Once one allows χH < 0, the lower bounds of the Z boson mass ares obtained through the positive definiteness of the scalar mass squared eigenvalues, while the bounds are smaller than the LHC bounds. On the other hand, the upper bounds strongly depend on the number of relevant Majorana Yukawa couplings of the right-handed neutrinos Nχ. Considering decoupling effects of the Z boson and the right-handed neutrinos, the condition of the singlet scalar quartic coupling χf > 0 gives the upper bound in the Nχ = 1 case, while it does not constrain the Nχ = 2 and 3 cases. In particular, we find that the Z boson mass is tightly restricted for the Nχ = 1 case as MZ 3.7 TeV.