Hadron Collider Sensitivity to Fat Flavourful $Z^\prime$s for $R_{K^{(\ast)}}$

We further investigate the case where new physics in the form of a massive $Z^\prime$ particle explains apparent measurements of lepton flavour non-universality in $B \rightarrow K^{(\ast)} l^+ l^-$ decays. Hadron collider sensitivities for direct production of such $Z^\prime$s have been previously studied in the narrow width limit for a $\mu^+ \mu^-$ final state. Here, we extend the analysis to sizeable decay widths and improve the sensitivity estimate for the narrow width case. We estimate the sensitivities of the high luminosity 14 TeV Large Hadron Collider (HL-LHC), a high energy 27 TeV LHC (HE-LHC), as well as a potential 100 TeV future circular collider (FCC). The HL-LHC has sensitivity to narrow $Z^\prime$ resonances consistent with the anomalies. In one of our simplified models the FCC could probe 23 TeV $Z^\prime$ particles with widths of up to 0.35 of their mass at 95\% confidence level (CL). In another model, the HL-LHC and HE-LHC cover sizeable portions of parameter space, but the whole of perturbative parameter space can be covered by the FCC.