LHC di-lepton searches for $Z^\prime$ bosons which explain measurements of $b \rightarrow s l^+l^-$ transitions

Several current measurements of $b \rightarrow s l^+ l^-$ processes are in tension with Standard Model predictions, whereas others (e.g.\ $R_K$ and $R_{K^\ast}$) are in reasonable agreement with them. We examine some recent $Z^\prime$ models that fit the data as a whole appreciably better than does the Standard Model, confronting the models with ATLAS resonance searches in the $e^+e^-$ and $\mu^+\mu^-$ channels. Both channels constrain the models; we find that the searches rule out less than one fifth of the allowed range of $M_{Z^\prime}$. We estimate that the HL-LHC can roughly double the current sensitivity in $M_{Z^\prime}$, but covering the whole parameter space would take a more powerful machine, such as a 100 TeV $pp$ collider.