Disentangling short- vs. long-distance dynamics in $B\to K^{*}μ^+μ^-$

Abstract

We present an updated data-driven analysis of short- vs. long-distance dynamics in $B\to K^{*}μ^+μ^-$. The analysis is based on the recent LHCb measurement of the full angular distribution of this process, taking advantage of the previously published global amplitude fit. Thanks to the precise di-lepton invariant-mass binning and angular observables directly sensitive to absorptive phases, current data provide novel insights into non-local contributions. We analyze the latter using a dispersive description, whose free parameters are determined via the amplitude fit. The dispersive model provides a satisfactory overall description of current data, without the need to introduce additional ad hoc hadronic parameters. The extracted value of the short-distance coefficient $C_9$ is lower than its Standard Model prediction, but significantly closer to it than in analyses where long-distance contributions are not constrained by data. The overall tension with the SM does not exceed the $2σ$ level. We also obtain precise postdictions for the angular observables $S_{7,8,9}$, and envisage novel consistency tests among them. In view of future, more precise data, these could provide valuable tests of the description of non-local effects in this process that, if further validated, would enable an even more robust extraction of short-distance information.