Searching for a dark matter coupling to the Standard Model with a Stueckelberg extension

We investigate a double extension to the Standard Model (SM). A first extension introduces, via minimal coupling, a massive $Z'$ boson. This enlarged SM is coupled to a dark matter sector through the Stueckelberg mechanism by a $A'$ boson. However, the $A'$ boson does not interact directly with the SM fermions. In our study, we found that the $A'$ is a massless photon-like particle in dark sector. Constraints on the mass for $Z'$ and corrections to $Z$ mass are obtained.