Probing a Very Narrow $Z'$ Boson with CDF and D0 Data

The cumulative CDF and D0 data of nearly $475 $ $ \text{pb}^{-1}$ in the dilepton channel is used to probe a recent class of models (Stueckelberg extensions) with an extra $U(1)_X$ gauge group where the mass generation of the $Z'$ is of topological origin and its decay width is exceptionally narrow. We carry out a Drell-Yan analysis for dilepton production via this $Z'$ and show that the current data already puts constraints on the parameter space of the Stueckelberg extensions. Further, with a total integrated luminosity of $8 $ $ \text{fb}^{-1}$, the very narrow $Z'$ can be discovered up to a mass of about 600 GeV. The signal from the Stueckelberg $Z'$ will be very distinct since it manifests precisely in the region where a Randall-Sundrum graviton is already excluded by precision electroweak data.