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We investigate the stability of the scalar potential in a minimal $U(1)'$extension of the Standard Model augmented by an extra complex scalar and threeright handed neutrinos. We consider a type-I seesaw scenario for the generationof the small neutrino masses. Moreover, we focus our analysis on a class ofmodels potentially accessible at the LHC experiment, in which the vacuumexpectation value of the extra scalar is chosen in the TeV range. We show thatthe requirements of stability of the potential within the perturbativeevolution under the renormalization group impose significant constraints on theYukawa couplings of the right handed neutrinos.

Stability constraints of the scalar potential in extensions of the Standard Model with TeV scale right handed neutrinos