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Abstract. We show that in two Higgs doublet models at tree-level the potential minimum preserving electric charge and CP symmetries, when it exists, is the global one. Furthermore, we derived a very simple condition, involving only the coefficients of the quartic terms of the potential, that guarantees spontaneous CP breaking.In the Standard Model (SM) of the electroweak interactions the existence of the scalar Higgs doublet is a fundamental piece of the theory. Through it SU (2) W × U (1) Y gauge invariance is broken, the W ± and Z 0 bosons and the fermions acquire their masses and the renormalisability of the theory is preserved. Despite its importance, the scalar sector of the SM has not yet been directly tested and there is considerable interest in studying its extensions. The simplest of those extensions is the two Higgs doublet model (2HDM). One of the main reasons of interest in this class of models is the possibility of having spontaneous CP violation [1], thus helping to solve the baryogenesis problem [2] (for a review, see [3]). One problem of these models, though, is their immense parameter space -the most general potential that preserves the SM gauge group and does not explicitly break CP has ten independent parameters, and little is known of their allowed values. A similar difficulty afflicts Supersymmetric models, where the parameter space is generally larger. One idea that has been applied to Supersymmetric theories to restrict their allowed parameter space is to use charge and colour breaking (CCB) bounds. If a given combination of parameters causes the appearance in the potential of a minimum where charged/coloured fields have vacuum expectation values (vevs), then that combination should be rejected. This appealing idea was introduced by Frére et al [4] and applied, in numerous papers, to several supersymmetric theories [5]. Phenomenological analysis of supersymmetric Higgs masses use this tool to increase the models' predictive power [6]. It is therefore of interest to apply similar techniques to the 2HDM and try to limit its parameter space. The scalars of this theory have no colour quantum numbers but there are charged fields so charge breaking (CB) extrema are in principle possible. Recent work in 2HDM [7], for instance, assumed that the choice of parameters made was such that the scalar potential respected the U (1) em gauge

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.Comment: 22 pages, 10 figure

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.Comment: 20 pages, 3 figure

We show that, for the most generic model with two Higgs doublets possessing a minimum that preserves the $U(1)_{em}$ symmetry, charge breaking (CB) cannot occur. If CB does not occur, the potential could have two different minima, and there is in principle no general argument to show which one is the deepest. The depth of the potential at a stationary point that breaks CB or CP, relative to the $U(1)_{em}$ preserving minimum, is proportional to the squared mass of the charged or pseudoscalar Higgs, respectively