Short- vs. long-distance physics in B K^ (*) ^+ ^-: a data-driven analysis

Abstract We analyze data on B K ^+ ^- B → K μ + μ - and B K^* ^+ ^- B → 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 c c c ¯ narrow resonances are taken into account by employing a dispersive approach. For each available q²=m² q 2 = m μ μ 2 bin and each helicity amplitude an independent determination of the Wilson coefficient C₉ C 9, describing b s ^+ ^- b → s ℓ + ℓ - transitions at short distances, is obtained. The consistency of the C₉ 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 s ^+ ^- b → s μ + μ - amplitude of short-distance origin.