Probing a Very Narrow $Z^{\mathrm{\prime }}$ Boson with CDF and D0 Data

The 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 of the Standard Model (StSM), which predict a $Z^{\mathrm{\prime }}$ boson whose mass is of topological origin with a very narrow decay width. A Drell-Yan analysis for dilepton production via this $Z^{\mathrm{\prime }}$ shows that the current data put constraints on the parameter space of the StSM. With a total integrated luminosity of $8$ ${\text{fb}}^{-1}$, the very narrow $Z^{\mathrm{\prime }}$ can be discovered up to a mass of about 600 GeV. The StSM $Z^{\mathrm{\prime }}$ will be very distinct since it can occur in the region where a Randall-Sundrum graviton is excluded.