On distinguishing the direct and spontaneous CP violation in 2HDM
  The most general Two Higgs Doublet Model (2HDM) allows both for the explicit and the spontaneous CP violation in the scalar sector. Here we discuss CP violation in terms of basis-independent quantities and show how using two different sets of known CP-odd weak-basis invariants one can distinguish between CP conservation, explicit CP violation and spontaneous CP violation. The special case of CP violation without CP mixing, in which the neutral Higgs gauge boson interaction respects CP while Higgs self-interaction violates CP symmetry, is also presented. 
Dorota Sokolowska, Maria Krawczyk, K.A. Kanishev