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

Abstract

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 hadronic quantities which can be treated as nuisance parameters. This expression allows to include any LFU ratio in global fits of $b\to s l^+ l^-$ short-distance parameters, even in the absence of a precise knowledge of the corresponding hadronic structure. The absence of sizeable LFU violation and the approximate left-handed structure of the Standard Model amplitude imply that only a very limited set of hadronic parameters hamper the sensitivity of $R_X$ to a possible LFU violation of short-distance origin. A global $b\to s l^+ l^-$ combination is performed including the measurement of $R_{pK}$ for the first time, resulting in a significance of new physics of $4.2\,σ$. In light of this, we evaluate the impact on the global significance of new physics using a set of experimentally promising non-exclusive $R_X$ measurements that LHCb can perform, and find that they can significantly increase the discovery potential of the experiment.