Tree-level metastability bounds in two-Higgs doublet models

The two Higgs doublet model has a rich vacuum structure, including the possibility of existence of two Standard Model-like minima at tree-level. It is therefore possible that the universe's vacuum is metastable, and a deeper minimum exists. We present the analytical conditions one must demand of the potential's parameters to prevent that possibility, and analyse what the current LHC data tells us about the eventual existence of that second minimum.