We present an analysis of the rare exclusive B decays B→Kνν¯\documentclass[12pt]{minimal}
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\begin{document}$$ B\to K\nu \overline{\nu} $$\end{document} and B→K∗νν¯\documentclass[12pt]{minimal}
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\begin{document}$$ B\to {K}^{\ast}\nu \overline{\nu} $$\end{document} within the Standard Model (SM), in a model-independent manner, and in a number of new physics (NP) models. 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, we obtain the SM predictions BRB+→K+νν¯=4.0±0.5×10−6\documentclass[12pt]{minimal}
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\begin{document}$$ \mathrm{B}\mathrm{R}\left({B}^{+}\to {K}^{+}\nu \overline{\nu}\right)=\left(4.0\pm 0.5\right)\times 1{0}^{-6} $$\end{document} and BRB0→K∗0νν¯=9.2±1.0×10−6\documentclass[12pt]{minimal}
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\begin{document}$$ \mathrm{B}\mathrm{R}\left({B}^0\to {K}^{\ast 0}\nu \overline{\nu}\right)=\left(9.2\pm 1.0\right)\times 1{0}^{-6} $$\end{document}, more precise and more robust than previous estimates. 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→sνν¯\documentclass[12pt]{minimal}
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\begin{document}$$ b\to s\nu \overline{\nu} $$\end{document} transitions to b → sℓ+ℓ− transitions and use the wealth of experimental data on B → K(∗)ℓ+ℓ− and related modes to constrain NP effects in B→K∗νν¯\documentclass[12pt]{minimal}
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\begin{document}$$ B\to {K}^{\left(\ast \right)}\nu \overline{\nu} $$\end{document}. We then consider several specific NP models, including Z′ models, the MSSM, models with partial compositeness, and leptoquark models, demonstrating that the correlations between b→sνν¯\documentclass[12pt]{minimal}
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\begin{document}$$ b\to s\nu \overline{\nu} $$\end{document} observables among themselves and with Bs → μ+μ− and b → sℓ+ℓ− transitions offer powerful tests of NP with new right-handed couplings and non-MFV interactions.
