Neutral minima in two-Higgs doublet models

We study the neutral minima of two-Higgs doublet models, showing that these potentials can have at least two such minima with different depths. We analyse the phenomenology of these minima for the several types of two-Higgs doublet potentials, where CP is explicitly broken, spontaneously broken or preserved. We discover that it is possible to have a neutral minimum in these potentials where the masses of the known particles have their standard values, with another deeper minimum where those same particles acquire different masses.