We carry out a detailed analysis of the general two Higgs doublet model with CP violation. We describe two different parametrizations of this model, and then study the Higgs boson masses and the trilinear Higgs couplings for these two parametrizations. Within a rather general model, we find that the trilinear Higgs couplings have a significant dependence on the details of the model, even when the lightest Higgs boson mass is taken to be a fixed parameter. We include radiative corrections in the one-loop effective potential approximation in our analysis of the Higgs boson masses and the Higgs trilinear couplings. The one-loop corrections to the trilinear couplings of the two Higgs doublet model also depend significantly on the details of the model, and can be rather large. We study quantitatively the trilinear Higgs couplings, and show that these couplings are typically several times larger than the corresponding Standard Model trilinear Higgs coupling in some regions of the parameter space. We also briefly discuss the decoupling limit of the two Higgs doublet model.
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