Vacuum stability in the $U(1)_\chi$ extended model with vanishing scalar potential at the Planck scale

Understand

We investigate the vacuum stability in a scale invariant local $U(1)_\chi$ 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 $\lambda_H$ to be positive in all energy scale, that is the same as the standard model.
• Once one allows $\lambda_H<0$, the lower bounds of the $Z'$ boson mass are 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 $N_\nu$.