Symmetries of Two Higgs Doublet Model and CP violation
  We use the invariance of physical picture under a change of Lagrangian, the reparametrization invariance in the space of Lagrangians and its particular case -- the rephrasing invariance, for analysis of the two-Higgs-doublet extension of the SM. We found that some parameters of theory like tan beta are reparametrization dependent and therefore cannot be fundamental. We use the Z2-symmetry of the Lagrangian, which prevents a phi_1 <-> phi_2 transitions, and the different levels of its violation, soft and hard, to describe a physical content of the model. In general, the broken Z2-symmetry allows for a CP violation in the physical Higgs sector. We argue that the 2HDM with a soft breaking of Z2-symmetry is a natural model in the description of EWSB. To simplify an analysis we choose among different forms of Lagrangian describing the same physical reality a specific one, in which the vacuum expectation values of both Higgs fields are real. A possible CP violation in the Higgs sector is described by using a two-step procedure with the first step identical to a diagonalization of mass matrix for CP-even fields in the CP conserved case. We find very simple necessary and sufficient condition for a CP violation in the Higgs sector. We determine the range of parameters for which CP violation and Flavor Changing Neutral Current effects are naturally small,what corresponds to a small dimensionless mass parameter nu= Re m_{12}^2/(2v1v2). We discuss how for small nu some Higgs bosons can be heavy, with mass up to about 0.6 TeV, without violating of the unitarity constraints. We discuss main features of the large nu case, which corresponds for nu -> infty to a decoupling of heavy Higgs bosons. 
Ilya F. Ginzburg and Maria Krawczyk