Boundedness from below in the $U(1)\times U(1)$ three-Higgs-Doublet model

Understand

Establishing if multi-Higgs potentials are bounded from below (BFB) can be rather challenging, and it may impede efficient investigation of all phenomenological consequences of such models.

• In this paper, we find the necessary and sufficient BFB conditions for the Three-Higgs-Doublet model (3HDM) with the global symmetry group $U(1)\times U(1)$.
• We observed an important role played by charge-breaking directions in the Higgs space, even for situations when a good-looking neutral minimum exists.
• This remark is not limited to the particular model we consider but represents a rather general feature of elaborate multi-Higgs potentials which must be carefully dealt with.