CP-Violation in Bosonic Sector of SM with two Higgs Doublets

We investigate CP-violation effects in the bosonic sector of the Standard Model (SM) with two Higgs doublets. First we calculate the mass eigenstates of the physical neutral Higgses for small but nonzero CP-violation parameter $\xi_{\ast}$, and then a ``forward-backward'' asymmetry ${\cal A}_{fb}$ for the decay $H \to W^+W^-Z$ that would be a signal of CP-violation. Although the effects are in general small (${\cal A}_{fb} = \Gamma_{fb}/\Gamma \sim {\cal O}(10^{-3})$), ${\cal A}_{fb}$ turns out to be a rather clean signal of CP-violation, since neither the CP-conserving final state interactions nor the direct production background events contribute to $\Gamma_{fb}$. The process is a counterexample to the widespread belief that CP-violation processes must involve fermions. The CKM-type CP-violation effects that could in principle also contribute to ${\cal A}_{fb}$ are negligible. The nonzero ${\cal A}_{fb}$ could possibly be detected at some later stage in future colliders such as LHC or SSC.