Bounds from Stability and Symmetry Breaking on Parameters in the Two-Higgs-Doublet Potential

The most general SU(2) × U(1)Y -symmetric quartic potential with two Higgs doublets, subject to an only softly broken discrete symmetry (φ1, φ2) → (−φ1, φ2), is considered. At tree-level, analytic bounds on the parameters are derived that ensure a stable vacuum, breaking SU(2)× U(1)Y down to U(1)em. email: [email protected] In the minimal standard model, spontaneous symmetry breaking of the SU(2)× U(1)Y gauge symmetry down to U(1)em is caused by the potential of a single Higgs-SU(2) doublet. However, since the exact symmetry breaking mechanism is not known, it is natural to consider extensions of the Higgs sector. The simplest such extension is to have another SU(2)-doublet scalar field. In fact, there are many reasons to discuss the two-doublet model. For associated particle phenomenology, see e.g. [1, 2] and references therein. More recently, the model has also received attention in cosmological contexts, mainly in connection with baryogenesis in the early universe [3]. Assume we want to prescribe the minimum of the two-doublet potential as < Φ1 >= 1 √ 2 (