Hide and Seek with the Third Family Hypercharge Model's $Z^\prime$ at the Large Hadron Collider

The Third Family Hypercharge Model predicts a $Z^\prime$ gauge boson with flavour dependent couplings which has been used to explain anomalies in meson decay processes which involve the $b\rightarrow s\mu^+\mu^-$ transition. The model predicts that a TeV-scale $Z^\prime$ should decay to particle-antiparticle pairs of muons, taus, top quarks and bottom quarks with appreciable branching ratios. We reinterpret various ATLAS and CMS search limits for $Z^\prime$ production followed by such decays at the LHC over a parameter space of the model that results from a successful combined fit to the $b\rightarrow s l^+ l^-$ data and precision electroweak observables. Current exclusions in parameter space and expected sensitivities of the various different channels in the high-luminosity run are compared. We find that the high-luminosity run of the LHC will significantly increase the sensitivity to the model beyond the existing observational limits, which we find to be surprisingly weak.Comment: 15 pages, 22 figure