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

The rare decay B -> K* nu anti-nu allows a transparent study of Z penguin and other electroweak penguin effects in New Physics (NP) scenarios in the absence of dipole operator contributions and Higgs (scalar) penguin contributions that are 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 form factors and of the decays B -> K nu anti-nu and B -> X(s) nu anti-nu in the SM and in a number of NP scenarios like the general MSSM, general scenarios with modified Z/Z' penguins and in a singlet scalar extension of the SM. We also summarize the results in the Littlest Higgs model with T-parity and a Randall-Sundrum (RS) model with custodial protection of left-handed Z-di-dj couplings. Our SM prediction BR(B -> K* nu anti-nu)=(6.8^+1.0_-1.1) x 10^-6 turns 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 SM avoids the normalization to the BR(B -> X(c) e anti-nu(e)) and, with less than 10% total uncertainty, is the most accurate to date. The results for the SM and NP scenarios can be transparently summarized in a (epsilon,eta) plane with a non-vanishing eta signalling the presence of new right-handed down-quark flavour violating couplings which can be ideally probed by the decays in question. Measuring the three branching ratios and one additional polarization observable in B -> K* nu anti-nu allows to overconstrain the resulting point in the (epsilon,eta) plane with (epsilon,eta)=(1,0) corresponding to the SM. The correlations 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 tests of New Physics with new right-handed couplings and non-MFV interactions.