Metastability bounds on the two Higgs doublet model

TL;DR

This paper derives bounds on the parameters of the two Higgs doublet model's scalar potential to prevent vacuum metastability, analyzing their implications for phenomenology and collider constraints.

Contribution

It provides analytical and practical methods to determine vacuum stability bounds in the two Higgs doublet model, including the most general CP-conserving potential.

Findings

Derived tree-level bounds for the softly broken $Z_2$ potential.

Discussed the impact of bounds on model phenomenology.

Presented a simple method for generic CP-conserving potentials.

Abstract

In the two Higgs doublet model, there is the possibility that the vacuum where the universe resides in is metastable. We present the tree-level bounds on the scalar potential parameters which have to be obeyed to prevent that situation. Analytical expressions for those bounds are shown for the most used potential, that with a softly broken $Z_2$ symmetry. The impact of those bounds on the model's phenomenology is discussed in detail, as well as the importance of the current Large Hadron Collider results in determining whether the vacuum we live in is or is not stable. We demonstrate how the vacuum stability bounds can be obtained for the most generic CP-conserving potential, and provide a simple method to implement them.