Long-distance effects in $B\to K^*\ell\ell$ from Analyticity

We discuss a novel approach to systematically determine the long-distance contribution to $B\to K^*\ell\ell$ decays in the kinematic region where the dilepton invariant mass is below the open charm threshold. This approach provides the most consistent and reliable determination to date and can be used to compute Standard Model predictions for all observables of interest, including the kinematic region where the dilepton invariant mass lies between the $J/\psi$ and the $\psi(2S)$ resonances. We illustrate the power of our results by performing a New Physics fit to the Wilson coefficient $C_9$. This approach is systematically improvable from theoretical and experimental sides, and applies to other decay modes of the type $B\to V\ell\ell$, $B\to P\ell\ell$ and $B\to V\gamma$.