Vacuum Stability in U(1)-Prime Extensions of the Standard Model with TeV Scale Right Handed Neutrinos

TL;DR

This paper explores the vacuum stability of a minimal U(1)' extension of the Standard Model with TeV-scale right-handed neutrinos, analyzing constraints on charges, masses, and mixing angles relevant for LHC detection.

Contribution

It introduces a modified beta function for scalar quartic couplings and demonstrates how right-handed neutrino Yukawa couplings can destabilize the vacuum, extending previous analyses.

Findings

Vacuum stability constrains U(1)' charge assignments and neutrino parameters.

Right-handed neutrino Yukawa couplings can destabilize the scalar potential.

Parameter space compatible with TeV-scale new physics at the LHC.

Abstract

We investigate a minimal $U(1)'$ extension of the Standard Model with one extra complex scalar and generic gauge charge assignments. We use a type-I seesaw mechanism with three heavy right handed neutrinos to illustrate the constraints on the charges, on their mass and on the mixing angle of the two scalars, derived by requiring the vacuum stability of the scalar potential. We focus our study on a scenario which could be accessible at the LHC, by selecting a vacuum expectation value of the extra Higgs in the TeV range and determining the constraints that emerge in the parameter space. To illustrate the generality of the approach, specific gauge choices corresponding to $U(1)_{B-L}, U(1)_R$ and $U(1)_\chi$ are separately analyzed. Our results are based on a modified expression of one of the $\beta$ functions of the quartic couplings of the scalar potential compared to the previous literature. This is due to a change in the coefficient of the Yukawa term of the right handed neutrinos. Differently from previous analysis, we show that this coupling may destabilize the vacuum.