VDM: A model for Vector Dark Matter

We construct a model based on a new $U(1)_X$ gauge symmetry and a discrete $Z_2$ symmetry under which the new gauge boson is odd. The model contains new complex scalars which carry $U(1)_X$ charge but are singlets of the Standard Model. The $U(1)_X$ symmetry is spontaneously broken but the $Z_2$ symmetry is maintained, making the new gauge boson a dark matter candidate. In the minimal version there is only one complex scalar field but by extending the number of scalars to two, the model will enjoy rich phenomenology which comes in various phases. In one phase, CP is spontaneously broken. In the other phase, an accidental $Z_2$ symmetry appears which makes one of the scalars stable and therefore a dark matter candidate along with the vector boson. We discuss the discovery potential of the model by colliders as well as the direct dark matter searches.