Abstract

We study generalized P and CP transformations in the three-Higgs-doublet model (3HDM) with Higgs and gauge fields only. We impose the requirement that applying such a transformation twice gives back the original fields, apart from possibly an SU(2)(L) x U(1)(Y) gauge transformation. We find that there are two equivalence classes, with respect to basis transformations, of generalized P transformations, and there is only one class of CP transformations. We discuss the conditions that the potential has to satisfy in order to be invariant under these transformations. We apply the method of bilinears, which we briefly review. We discuss the relation to the conventional basis, where the potential is written in terms of scalar products of the doublet fields. In particular, we give an explicit derivation of the result for the 3HDM (known for the analogous case of the THDM), that a potential is invariant under CP transformations, satisfying the above requirement, if and only if there is a conventional basis where all parameters are real. This result no longer holds if the above requirement is dropped. Eventually, we study standard P and CP transformations in the n-Higgs-doublet model (nHDM). We show that for the bilinears of the nHDM, the standard CP transformation corresponds to a diagonal linear transformation with only +/- 1 as diagonal elements. We give this matrix explicitly for arbitrary n.