We build a model containing two scalar doublets and a scalar singlet with a specific discrete symmetry. After spontaneous symmetry breaking, the model has Standard Model-like phenomenology, as well as a hidden scalar sector which provides a viable dark matter candidate. We show that CP violation in the scalar sector occurs exclusively in the hidden sector, and consider possible experimental signatures of this CP violation. In particular, we study contribution to anomalous gauge couplings from the hidden scalars.PACS numbers:
I. INTRODUCTIONThe LHC discovery of a scalar with mass of 125 GeV [1, 2] completed the Standard Model particle content. The fact that precision measurements of the properties of this particle [3,4] indicate that it behaves very much in a Standard Model (SM)-like manner is a further confirmation of the validity and effectiveness of that model. Nonetheless, the SM leaves a lot to be explained, and many extensions of the theory have been proposed to attempt to explain such diverse phenomena as the existence of dark matter, the observed universal matter-antimatter asymmetry and others. In particular, numerous SM extensions consist of enlarged scalar sectors, with singlets, both real and complex, being added to the SM Higgs doublet [5][6][7][8][9][10][11][12][13]; or doublets, the simplest example of which is the two-Higgs doublet model (2HDM) [14,15]. Certain versions of singlet-doublet models provide dark matter candidates, as does the Inert version of the 2HDM (IDM) [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Famously, the 2HDM was introduced in 1973 by Lee to allow for the possibility of spontaneous CP violation. But models with dark matter candidates and extra sources of CP violation (other than the SM mechanism of CKM-matrix generated CP violation) are rare. Even rarer are models for which a "dark" sector exists, providing viable dark matter candidates, and where the extra CP violation originates exclusively in the "dark" sector. To the best of our knowledge, the only model with scalar CP violation in the dark sector is the recent work of Refs. [31,32], for which a three-doublet model was considered. The main purpose of Refs. [31,32] was to describe the dark matter properties of the model. In Ref. [33] an argument was presented to prove that the model is actually CP violating, adapting the methods of Refs. [34,35] for the complex 2HDM (C2HDM).In the current paper we will propose a model, simpler than the one in [31], but which boasts the same interesting properties, to wit: (a) a SM-like Higgs boson, h, "naturally" aligned due to the vacuum of the model preserving a discrete symmetry; (b) a viable dark matter candidate, the stability of which is guaranteed by the aforementioned vacuum and whose mass and couplings satisfy all existing dark matter search constraints; and (c) extra sources of CP *