A B−anomaly motivated Z′ boson at the energy and precision frontiers

TeV-scale $Z^{\prime }$ bosons with family-dependent couplings can explain some anomalies inferred from $B-$meson measurements of processes involving the $b\to s{\ell }^{+}{\ell }^{-}$ transition. A $Z^{\prime }$ originating from kinetically-mixed spontaneously broken $U{\left(1\right)}_{B_3-L_2}$ gauge symmetry has been shown to greatly ameliorate global fits [1] in a ‘flavour-preferred’ region of parameter space. We provide an exploration of this region at the high luminosity (HL-)LHC with particular attention to which signals could be verified across different discovery modes. Even if the HL-LHC does not discover the $Z^{\prime }$ boson in a resonant di-lepton channel, a FCC-ee $Z$-pole run would detect oblique corrections to the electroweak precision observables (EWPOs). Changes due to $Z^{\prime }$-induced non-oblique corrections are unlikely to be detected, to within experimental precision. In any case, the extended discovery potential offered by a 100 TeV $pp-$collider would afford sensitivity to the entire flavour-preferred region and enable a fine-grained and forensic analysis of the model.