Short- vs. long-distance physics in $$B\rightarrow K^{(
Marzia Bordone (Theoretical Physics Department, CERN, Geneva 23, 1211 , Switzerland); Gino Isidori (Physik-Institut, Universität Zürich, Zurich, 8057, Switzerland); Sandro Mächler (Physik-Institut, Universität Zürich, Zurich, 8057, Switzerland); Arianna Tinari (Physik-Institut, Universität Zürich, Zurich, 8057, Switzerland)
We analyze data on $$B\rightarrow K\mu ^+\mu ^-$$ and $$B\rightarrow K^*\mu ^+\mu ^-$$ decays in the whole dilepton invariant mass spectrum with the aim of disentangling short- vs. long-distance contributions. The sizable long-distance amplitudes from $$c \overline{c}$$ narrow resonances are taken into account by employing a dispersive approach. For each available $$q^2=m^2_{\mu \mu }$$ bin and each helicity amplitude an independent determination of the Wilson coefficient $$C_9$$ , describing $$b\rightarrow 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\rightarrow s \mu ^+\mu ^-$$ amplitude of short-distance origin.