Collider signatures of dark CP-violation

We study an extension of the Standard Model (SM) in which two copies of the SM-Higgs doublet which do not acquire a vacuum expectation value, and hence are {\it inert}, are added to the scalar sector. The lightest particle from the inert sector, which is protected from decaying to SM particles through the conservation of a $Z_2$ symmetry, is a viable dark matter candidate. We allow for CP-violation in this extended dark sector and evaluate the $ZZZ$ vertex and its CP-violating form factor in several benchmark scenarios. We provide collider signatures of this dark CP-violation in the form of potentially observable asymmetries and cross sections for the $f\bar f\to Z^*\to ZZ$ process at both leptonic and hadronic machines.