Massive $Z^{\prime }$-gauge bosons act as excellent harbingers for string compactifications with a low string scale. In D-brane models they are associated to $U(1)$ gauge symmetries that are either anomalous in four dimensions or exhibit a hidden higher-dimensional anomaly. We discuss the possible signals of massive $Z^{\prime }$-gauge bosons at hadron collider machines (Tevatron, LHC) in a minimal D-brane model consisting out of four stacks of D-branes. In this construction, there are two massive gauge bosons, which can be naturally associated with baryon number $B$ and $B-L$ ($L$ being lepton number). Here baryon number is always anomalous in four dimensions, whereas the presence of a four-dimensional $B-L$ anomaly depends on the $U(1)$-charges of the right-handed neutrinos. In case $B-L$ is anomaly-free, a mass hierarchy between the two associated $Z^{\prime }$-gauge bosons can be explained. In our phenomenological discussion about the possible discovery of massive $Z^{\prime }$-gauge bosons, we take as a benchmark scenario the dijet plus $W$ signal, recently observed by the CDF Collaboration at Tevatron. It reveals an excess in the dijet-mass range $150\mathrm{GeV}/{\mathrm{c}}^2$, $4.1\sigma$ beyond standard modelexpectations. We show that in the context of low-mass string theory this excess can be associated with the production and decay of a leptophobic $Z^{\prime }$, a singlet partner of $SU(3)$ gluons coupled primarily to baryon number. Even if the CDF signal disappears, as indicated by the more recent D0 results, our analysis can still serve as the basis for future experimental search for massive $Z^{\prime }$-gauge bosons in low string scale models. We provide the relevant cross sections for the production of $Z^{\prime }$-gauge bosons in the TeV region, leading to predictions that are within reach of the present or the next LHC run.

• Received 22 July 2011

DOI:https://doi.org/10.1103/PhysRevD.85.086003