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The rare decay B -> K* nu anti-nu allows a transparent study of Z penguin andother electroweak penguin effects in New Physics (NP) scenarios in the absenceof dipole operator contributions and Higgs (scalar) penguin contributions thatare often more important than Z contributions in B -> K* l+l- and B(s) -> l+l-decays. We present a new analysis of B -> K* nu anti-nu with improved formfactors and of the decays B -> K nu anti-nu and B -> X(s) nu anti-nu in the SMand in a number of NP scenarios like the general MSSM, general scenarios withmodified Z/Z' penguins and in a singlet scalar extension of the SM. We alsosummarize the results in the Littlest Higgs model with T-parity and aRandall-Sundrum (RS) model with custodial protection of left-handed Z-di-djcouplings. Our SM prediction BR(B -> K* nu anti-nu)=(6.8^+1.0_-1.1) x 10^-6turns out to be significantly lower than the ones present in the literature.Our improved calculation BR(B -> X(s) nu anti-nu)=(2.7+-0.2) x 10^-5 in the SMavoids the normalization to the BR(B -> X(c) e anti-nu(e)) and, with less than10% total uncertainty, is the most accurate to date. The results for the SM andNP scenarios can be transparently summarized in a (epsilon,eta) plane with anon-vanishing eta signalling the presence of new right-handed down-quarkflavour violating couplings which can be ideally probed by the decays inquestion. Measuring the three branching ratios and one additional polarizationobservable in B -> K* nu anti-nu allows to overconstrain the resulting point inthe (epsilon,eta) plane with (epsilon,eta)=(1,0) corresponding to the SM. Thecorrelations of these three channels with the rare decays K+ -> pi+ nu anti-nu,KL -> pi0 nu anti-nu, B -> X(s) l+ l- and B(s) -> mu+ mu- offer powerful testsof New Physics with new right-handed couplings and non-MFV interactions.

New strategies for New Physics search in B -> K* nu anti-nu, B -> K nu anti-nu and B -> X(s) nu anti-nu decays