Within two Higgs doublet models, it is possible that the current vacuum is not the global minimum, in which case it could possibly decay at a later stage. We discuss the tree-level conditions which must be obeyed by the most general scalar potential in order to preclude that possibility. We propose a new procedure which is not only more general but also easier to implement than the previously published one, including $CP$ conserving as well as $CP$ violating scalar sectors. We illustrate these conditions within the context of the $Z_2$ model, softly broken by a complex, $CP$ violating parameter.

• Received 24 July 2015

DOI:https://doi.org/10.1103/PhysRevD.92.055017