Revisiting $B\to K^{(\ast)} \nu \bar{\nu}$ decays in the Standard Model and beyond

In this letter we revisit the Standard Model predictions for $\mathcal{B}(B\to K^{(\ast)}\nu\bar{\nu})$ and discuss the opportunities that open up when combining its partial decay rate with that of $B\to K^{(\ast)}\ell\ell$. In the Standard Model a suitable ratio of these two modes can be used to extract $C_9^\mathrm{eff}$, which is essential for a reliable phenomenological analysis of the $B\to K^{(\ast)}\ell\ell$ angular observables. The same ratio also proves to be more sensitive to the presence of New Physics in many plausible extensions of the Standard Model. We also suggest that the separate measurement of $\mathcal{B}(B\to K\nu\bar{\nu})$ for high and for low $q^2$'s can be helpful for testing the assumed shape of the vector form factor, because the lattice QCD data are obtained at high $q^2$'s, whereas the low $q^2$ region is obtained through an extrapolation.