On the significance of the flavour anomalies

A coherent pattern of deviations from Standard Model predictions has been observed in $b$-hadron decays of the type $b\to s\ell^+\ell^-$. These deviations seem to indicate the existence of a new fundamental interaction that breaks lepton flavour universality (LFU). We discuss the Look Elsewhere Effect in estimating the significance of this hypothesis and, more generally, any new physics of short-distance origin in this system, by combining different observables. We show that even using a very conservative approach towards theory uncertainties, and very general new-physics hypotheses, a significance of about 4 sigma is obtained. In view of future experimental tests of LFU in these channels, we present a general expression that allows one to include in the fit of modified Wilson coefficients also observables such as $R_{pK}$, $R_{K\pi}$ and $R_{K\pi\pi}$, for which the form factors are unknown. We show that the inclusion of such observables can have a dramatic effect on the new physics significance.