Short- vs. long-distance physics in $B\to K^{(*)} \ell^+\ell^-$: a data-driven analysis
We analyze data on $B\to Kμ^+μ^-$ and $B\to K^*μ^+μ^-$ decays in the whole dilepton invariant mass spectrum with the aim of disentangling short- vs. long-distance contributions. The sizable long-distance amplitudes from $c \bar{c}$ narrow resonances are taken into account by employing a dispersive approach. For each available $q^2=m_{μμ}^2$ bin and each helicity amplitude an independent determination of the Wilson coefficient $C_9$, describing $b\to s\ell^+\ell^-$ transitions at short distances, is obtained. The consistency of the $C_9$ values thus obtained provides an a posteriori check of the absence of additional, sizable, long-distance contributions. The systematic difference of these values from the Standard Model expectation supports the hypothesis of a non-standard $b\to s μ^+μ^-$ amplitude of short-distance origin.