A Stueckelberg Extension of the Standard Model

An extension of the standard model of electro-weak interactions by an extra abelian gauge boson is given, in which the extra gauge boson and the hypercharge gauge boson both couple to an axionic scalar in a form that leads to a Stueckelberg mass term. The theory leads to a massive Z$'$ whose couplings to fermions are uniquely determined and suppressed by small mixing angles. Such a Z$'$ could have low mass and appear in $e^+e^-$ collisions as a sharp resonance. The branching ratios into $f\bar f$ species, and the forward-backward asymmetry are found to have distinctive features. The model also predicts a new unit of electric charge $e'=Q'e$, where $Q'$ is in general irrational, in the coupling of the photon with hidden matter that is neutral under $SU(2)_L\times U(1)_Y$.