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

Several current measurements of $b\to s{l}^{+}{l}^{-}$ 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 $Z^{\mathrm{\prime }}$ 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 $M_{Z^{\mathrm{\prime }}}$. We estimate that the HL-LHC can roughly double the current sensitivity in $M_{Z^{\mathrm{\prime }}}$, but covering the whole parameter space would take a more powerful machine, such as a 100 TeV $pp$ collider.