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

In this talk an analysis of the rare exclusive $B$ decays $B\to K\nu\bar\nu$ and $B\to K^{*}\nu\bar\nu$ within and beyond the Standard Model is presented. Combining new form factor determinations from lattice QCD with light-cone sum rule results and including complete two-loop electroweak corrections to the SM Wilson coefficient, precise Standard Model predictions will be given. Beyond the SM, we make use of an effective theory with dimension-six operators invariant under the SM gauge symmetries to relate NP effects in $b\to s\bar\nu\nu$ transitions to $b\to s\ell^+\ell^-$ transitions and use the wealth of experimental data on $B\to K^{(*)}\ell^+\ell^-$ and related modes to constrain NP effects in $B\to K^{(*)}\nu\bar\nu$. We then consider leptoquark models as a showcase for models where in principle large effects are possible.