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Tests of lepton-universality as rate ratios in $b\to s \ell\ell$ transitionscan be predicted very accurately in the Standard Model. The deficits withrespect to expectations reported by the LHCb experiment in muon-to-electronratios of the $B\to K^{(*)}\ell\ell$ decay rates thus point to genuinemanifestations of lepton non-universal new physics. In this paper, we analysethese measurements in the context of effective field theory. First, we discussthe interplay of the different operators in $R_K$ and $R_{K^*}$ and providepredictions for $R_{K^*}$ in the Standard Model and in new-physics scenariosthat can explain $R_K$. We also provide approximate numerical formulas forthese observables in bins of interest as functions of the relevant Wilsoncoefficients. Secondly, we perform frequentist fits to $R_{K}$ and $R_{K^*}$.The SM disagrees with these measurements at $3.7\sigma$ significance. We findexcellent fits in scenarios with combinations of $\mathcal O_{9(10)}^\ell=\bars\gamma^\mu b_L~\ell\gamma_\mu(\gamma_5) \ell$ operators, with pulls relativeto the Standard Model in the region of $4\sigma$. An important conclusion ofour analysis is that a lepton-specific contribution to $\mathcal O_{10}$ isessential to understand the data. Under the hypothesis that new-physics couplesselectively to the muons, we also present fits to other $b\to s\mu\mu$ datawith a conservative error assessment, and comment on more general scenarios.Finally, we discuss new lepton universality ratios that, if new physics is theorigin of the observed discrepancy, should contribute to the statisticallysignificant discovery of new physics in the near future.

Towards the discovery of new physics with lepton-universality ratios of $b\to s\ell\ell$ decays