Kinetic mixing, dark photons and an extra dimension. Part I

Extra dimensions (ED) can provide a useful tool for model-building. In this paper we introduce a single, flat ED extension of the kinetic-mixing/dark photon (DP) portal for dark matter (DM) interactions with the Standard Model (SM) assuming a compactification 'radius' of order R-1 similar to 10-1000 MeV and examine the resulting modifications to and augmentation of the usual DP phenomenology. In the present scenario, both the DP and DM experience the full 5-D while the SM fields are constrained to lie on a 4-D brane at the boundary of the ED. Such a setup can naturally yield the observed value of the DM relic density and explain the required rough degeneracy of the DM and DP masses needed to obtain it. Gauge symmetry breaking can occur via boundary conditions without the introduction of an additional singlet Higgs scalar thus avoiding all constraints associated with the coupling of such a field to the usual SM Higgs field in 5-D. The self-consistency in the removal of the kinetic mixing terms is found to lead to a brane localized kinetic term for the 5-D gauge field on the SM brane. Multiple variations of this scenario are found to be possible which are consistent with current experimental constraints but which predict very different phenomenologies. In this paper, we discuss the case of a complex scalar 5-D DM field, consistent with constraints arising from the CMB, which may or may not obtain a vacuum expectation value (vev). This approach can lead to interesting and distinctive signatures while being constrained by a wide array of existing measurements but with the details being dependent upon the model specifics.