The Stueckelberg $Z'$ Extension with Kinetic Mixing and Milli-Charged Dark Matter From the Hidden Sector

Abstract

An analysis is given of the Stueckelberg extension of the Standard Model with a hidden sector gauge group $U(1)_X$ where the mass growth for the extra gauge boson occurs via the Stueckelberg mechanism, and where the kinetic mixing in the $U(1)_X\times U(1)_Y$ sector is included. Such a kinetic mixing is generic in a broad class of supergravity and string models. We carry out a detailed global fit of the model with the precision LEP data on and off the $Z$ pole, with $χ^2$ within 1% of the $χ^2$ of the Standard Model fit. Further, it is shown that in the absence of matter in the hidden sector, there is a single effective parameter that controls the deviations from the Standard Model predictions, and the dependence on the kinetic mixing emerges only when matter in the hidden sector is included. An analysis is also given of milli-charged dark matter arising from the hidden sector, where it is shown that such dark matter from the Stueckelberg extension can satisfy WMAP-3 data while allowing for a sharp $Z'$ resonance which can be detected at the Tevatron and at the LHC via a dilepton signal generated by the Drell-Yan process.