CP violation in the two-Higgs-doublet model: an example

In a general two-scalar-doublet model without fermions, there is a unique source of CP violation, $J_1$, in the gauge interactions of the scalars. It arises in the mixing of the three neutral physical scalars $X_1$, $X_2$ and $X_3$. CP violation may be observed via different decay rates for $X_1 \rightarrow H^+ W^-$ and $X_1 \rightarrow H^- W^+$ (or, alternatively, for $H^+ \rightarrow X_1 W^+$ and $H^- \rightarrow X_1 W^-$ --- depending on which decays are kinematically allowed). I compute the part of those CP-violating decay-rate differences which is proportional to $J_1$. The CP-invariant final-state-interaction phase is provided by the absorptive parts of the one-loop diagrams. I check the gauge invariance of the whole calculation.