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We construct an expression for a general lepton flavour universality (LFU)ratio, $R_{X}$, in $b\to s l^+ l^-$ decays in terms of a series of hadronicquantities which can be treated as nuisance parameters. This expression allowsto include any LFU ratio in global fits of $b\to s l^+ l^-$ short-distanceparameters, even in the absence of a precise knowledge of the correspondinghadronic structure. The absence of sizeable LFU violation and the approximateleft-handed structure of the Standard Model amplitude imply that only a verylimited set of hadronic parameters hamper the sensitivity of $R_X$ to apossible LFU violation of short-distance origin. A global $b\to s l^+ l^-$combination is performed including the measurement of $R_{pK}$ for the firsttime, resulting in a significance of new physics of $4.2\,\sigma$. In light ofthis, we evaluate the impact on the global significance of new physics using aset of experimentally promising non-exclusive $R_X$ measurements that LHCb canperform, and find that they can significantly increase the discovery potentialof the experiment.

A general effective field theory description of $b \to s l^+ l^-$ lepton universality ratios