Top-philic $Z^{\prime }$ forces at the LHC

Despite extensive searches for an additional neutral massive gauge boson at the LHC, a $Z^{\prime }$ at the weak scale could still be present if its couplings to the first two generations of quarks are suppressed, in which case the production in hadron colliders relies on tree-level processes in association with heavy flavors or one-loop processes in association with a jet. We consider the low-energy effective theory of a top-philic $Z^{\prime }$ and present possible UV completions. We clarify theoretical subtleties in evaluating the production of a top-philic $Z^{\prime }$ at the LHC and examine carefully the treatment of an anomalous $Z^{\prime }$ current in the low-energy effective theory. Recipes for properly computing the production rate in the $Z^{\prime }+j$ channel are given. We discuss constraints from colliders and low-energy probes of new physics. As an application, we apply these considerations to models that use a weak-scale $Z^{\prime }$ to explain possible violations of lepton universality in $B$ meson decays, and show that the future running of a high luminosity LHC can potentially cover much of the remaining parameter space favored by this particular interpretation of the $B$ physics anomaly.