Predicted Signatures at the LHC from U(1) Extensions of the Standard Model.

We discuss the U(1)(X) extensions of the standard model with focus on the Stueckelberg mechanism for mass growth for the extra U(1)(X) gauge boson. The assumption of an axionic connector field which carries dual U(1) quantum numbers, i.e., quantum numbers for the hypercharge U(1)(Y) and for the hidden sector gauge group U(1)(X), allows a non -trivial mixing between the mass growth for the neutral gauge vector bosons in the SU(2)L x U(1)(Y) sector and the mass growth for the vector boson by the Stueckelberg mechanism in the U(1)(X) sector. This results in an extra Z' which can be very narrow, but still detectable at the Large Hadron Collider (LHC). The U(1)(X) extension of the minimal supersymmetric standard model is also considered and the role of the Fayet-Illiopoulos term in such an extension discussed. The U(1)(X) extensions of the SM and of the MSSM lead to new candidates for dark matter.