Triple and quartic interactions of Higgs bosons in the two-Higgs-doublet model with CP-violation

We consider the two-Higgs-doublet model with explicit CP-violation, where the effective Higgs potential is not CP-invariant at the tree level. The three neutral Higgs bosons of the model are the mixtures of CP-even and CP-odd bosons which exist in the CP-conserving limit of the theory. The mass spectrum and tree-level couplings of the neutral Higgs bosons to gauge bosons and fermions are significantly dependent on the parameters of the Higgs boson mixing matrix. We calculate the Higgs-gauge boson, Higgs-fermion, triple and quartic Higgs self-interactions in the MSSM with explicit CP-violation in the Higgs sector and CP-violating Yukawa interactions of the third generation scalar quarks. In some regions of the MSSM parameter space substantial changes of the self-interaction vertices take place, leading to significant suppression or enhancement of the multiple Higgs boson production cross sections. (orig.)