4 v 1 3 0 D ec 2 00 3 Tree - level unitarity constraints in the 2 HDM with CP - violation

We obtain tree-level unitarity constraints for the Two Higgs Doublet Model (2HDM) with explicit CP -violation. We limit ourselves to the case with soft violation of the discrete Z2 symmetry of theory. The key role is played by the rephasing invariance of the 2HDM lagrangian. Our simple approach for derivation of these constraints can be easily transferred to other forms of Higgs sector. We briefly discuss correspondence between possible violation of tree level unitarity limitation and physical content of theory. The Electroweak Symmetry Breaking in the Standard Model is described usually with the Higgs mechanism. In its simplest variant, an initial Higgs field is an isodoublet of scalar fields with weak isospin ~σ. The simplest extension of the Higgs sector known as two-Higgs-doublet model (2HDM) consists in introducing two Higgs weak isodoublets of scalar fields φ1 and φ2 with hypercharge Y = +1 (for a review, see [1]). We consider the Higgs potential of 2HDM in the form V = λ1 2 (φ†1φ1) 2 + λ2 2 (φ†2φ2) 2 + λ3(φ † 1φ1)(φ † 2φ2) + λ4(φ † 1φ2)(φ † 2φ1) + 1 2 [ λ5(φ † 1φ2) 2 + λ5(φ † 2φ1) 2 ]