Constraints on Abelian Extensions of the Standard Model from Two-Loop Vacuum Stability and $U(1)_{B-L}$

TL;DR

This paper investigates the stability of a minimal $U(1)_{B-L}$ extension of the Standard Model up to the Planck scale, emphasizing the importance of two-loop effects and kinetic mixing in constraining model parameters.

Contribution

It provides a comprehensive two-loop renormalization group analysis of the scalar potential, including kinetic mixing effects, to derive constraints on heavy neutrino masses and gauge couplings.

Findings

Two-loop effects are crucial for vacuum stability analysis.

Kinetic mixing significantly influences the model's parameter space.

Constraints on heavy neutrino masses and gauge couplings are established.

Abstract

We present a renormalization group study of the scalar potential in a minimal $U(1)_{B-L}$ extension of the Standard Model involving one extra heavier Higgs and three heavy right-handed neutrinos with family universal B-L charge assignments. We implement a type-I seesaw for the masses of the light neutrinos of the Standard Model. In particular, compared to a previous study, we perform a two-loop extension of the evolution, showing that two-loop effects are essential for the study of the stability of the scalar potential up to the Planck scale. The analysis includes the contribution of the kinetic mixing between the two abelian gauge groups, which is radiatively generated by the evolution, and the one-loop matching conditions at the electroweak scale. By requiring the stability of the potential up to the Planck mass, significant constraints on the masses of the heavy neutrinos, on the gauge couplings and the mixing in the Higgs sector are identified.