Composite two-Higgs model with dynamical CP-violation

Quark models with four-fermion interaction including derivatives of fields are exploited as prototypes for composite-Higgs extensions of the Standard Model. In the non-trivial case of two- and four-derivative insertions the dynamical breaking of chiral symmetry occurs in two channels, giving rise to two composite Higgs doublets. For special configuration of four-fermion coupling constants the dynamical CP-violation in the Higgs sector appears as a result of complexity of two v.e.v. for Higgs doublets. In this scenario the second Higgs doublet is regarded as a radial excitation of the first one.