New strategies for new physics search in B → K ^*vv̄ B → Kvv̄ and B → X ₈vv̄ decays

The rare decay B K*ν is regarded as one of the important channels in B physics as it 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*ν with improved form factors and of the decays B Kν and B X _sν 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 Zd _ij couplings. Our SM prediction BR(B K*ν) = (6.8 ^+1.0 _-1.1) × 10 ^-6 turns out to be significantly lower than the ones present in the literature. Our improved calculation BR(B X _sν) = (2.70.2) × 10 ^-5 in the SM avoids the normalization to the BR(B X _ce _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 (,η) plane analogous to the known (,) plane with a non-vanishing η signalling this time not CP violation but 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*ν allows to overconstrain the resulting point in the (,η) plane with (,η) = (1,0) corresponding to the SM. We point out that the correlations of these three channels with the rare decays K ⁺ π ⁺ν, K _L π ⁰ν, B X _sℓ ⁺ℓ ^- and B _s μ ⁺μ ^- offer powerful tests of New Physics with new right-handed couplings and non-MFV interactions.