CP-odd invariants in models with several Higgs doublets
  We present CP-odd Higgs-basis invariants, which can be used to signal CP violation in a multi-Higgs system, written in an arbitrary Higgs basis. It is shown through specific examples how these CP-odd invariants can also be useful to determine the character of CP breaking (i.e. whether it is hard or soft CP breaking) in a given Higgs Lagrangian. We analyse in detail the cases of two and three Higgs doublets. 
Gustavo C. Branco, M. N. Rebelo and J. I. Silva-Marcos