Simple criterium for $CP$ conservation in the most general 2HDM

We find a set of necessary and sufficient conditions for the $CP$ conservation in the most general 2HDM in terms of observable quantities. This set contains two simple and relatively easily testable conditions instead of the more complex conditions usually discussed.

Figure 1

Mixing provided by the $H^{+}{H}^{-}$ loop (up) and by one of $CP$ violated vertices (13) (down).