Combining our results for various O(alpha[s]) corrections to the weak radiative B-meson decay, we are able to present the first estimate of the branching ratio at the next-to-next-to-leading order in QCD. We find B(B[over ]-->X[s]gamma)=(3.15+/-0.23) x 10(-4) for Egamma>1.6 GeV in the B[over ]-meson rest frame. The four types of uncertainties:nonperturbative (5%), parametric (3%), higher-order (3%), and m(c)-interpolation ambiguity (3%) have been added in quadrature to obtain the total error.

We report on a calculation of Higgs-boson contributions to the decays B s → l + l − andB → Kl + l − (l = e, µ) which are governed by the effective Hamiltonian describing b → sl + l − . Compact formulae for the Wilson coefficients are provided in the context of the type-II two-Higgs-doublet model (2HDM) and supersymmetry (SUSY) with minimal flavour violation, focusing on the case of large tan β. We derive, in a model-independent way, constraints on Higgs-boson-mediated interactions, using present experimental results on rare B decays including b → sγ,B s → µ + µ − , andB → K ( * ) µ + µ − . In particular, we assess the impact of possible scalar and pseudoscalar interactions transcending the standard model (SM) on the branching ratio ofB s → µ + µ − and the forward-backward (FB) asymmetry of µ − inB → Kµ + µ − decay. The average FB asymmetry, which is unobservably small within the SM, and therefore a potentially valuable tool to search for new physics, is predicted to be no greater than 4% for a nominal branching ratio of about 6 × 10 −7 . Moreover, striking effects on the decay spectrum ofB → Kµ + µ − are already ruled out by experimental data on theB s → µ + µ − branching fraction. In addition, we study the constraints on the parameter space of the 2HDM and SUSY with minimal flavour violation. While the type-II 2HDM does not give any sizable contributions to the above decay modes, we find that SUSY contributions obeying the constraint on b → sγ can significantly affect the branching ratio ofB s → µ + µ − . We also comment on previous calculations *

Weak radiative decays of the B mesons belong to the most important flavor changing processes that provide constraints on physics at the TeV scale. In the derivation of such constraints, accurate standard model predictions for the inclusive branching ratios play a crucial role. In the current Letter we present an update of these predictions, incorporating all our results for the O(α_{s}^{2}) and lower-order perturbative corrections that have been calculated after 2006. New estimates of nonperturbative effects are taken into account, too. For the CP- and isospin-averaged branching ratios, we find B_{sγ}=(3.36±0.23)×10^{-4} and B_{dγ}=(1.73_{-0.22}^{+0.12})×10^{-5}, for E_{γ}>1.6 GeV. Both results remain in agreement with the current experimental averages. Normalizing their sum to the inclusive semileptonic branching ratio, we obtain R_{γ}≡(B_{sγ}+B_{dγ})/B_{cℓν}=(3.31±0.22)×10^{-3}. A new bound from B_{sγ} on the charged Higgs boson mass in the two-Higgs-doublet-model II reads M_{H^{±}}>480 GeV at 95% C.L.

We study the branching ratios of rare K and B decays in models with minimal flavour violation, using the presently available information from the universal unitarity triangle analysis and from the measurements of Br(B → X s γ), Br(B → X s l + l − ) and Br(K + → π + νν). We find the following upper bounds: Br(K + → π + νν) < 11.9 × 10 −11 ,at 95% probability. We analyze in detail various possible scenarios with positive or negative interference of Standard Model and New Physics contributions, and show how an improvement of experimental data corresponding to the projected 2010 B factory integrated luminosities will allow to disentangle and test these different possibilities. Finally, anticipating that subsequently the leading role in constraining this kind of new physics will be taken over by the rare decays K + → π + νν, K L → π 0 νν and B s,d → µ + µ − , that are dominated by the Z 0 -penguin function C, we also present plots for several branching ratios as functions of C. We point out an interesting triple correlation between K + → π + νν, B → X s γ and B → X s l + l − present in MFV models.Recently, great experimental progress has been made in the study of Flavour Changing Neutral Current (FCNC) decays, leading not only to an impressive accuracy in the extraction of CKM parameters from the Unitarity Triangle (UT) analysis [1,2], but also to stringent constraints on models with extra sources of flavour and CP violation, although an accidental agreement of the UT analysis with the Standard Model (SM) cannot yet be excluded [3,4].One is then naturally led to consider models with Minimal Flavour Violation (MFV) [5], in which flavour and CP violation is governed entirely by the CKM matrix [6,7] and the relevant operators in effective Hamiltonians for weak decays are the same as in the SM.As pointed out in [5], there exists a universal unitarity triangle (UUT) valid in all these models, that can be constructed independently of the parameters specific to a given model. Moreover, there exist several relations between various branching ratios that allow straightforward tests of these models. A review has been given in [8].This formulation of MFV agrees with the one of [9, 10] except for the case of models with two Higgs doublets at large tan β, where also additional operators, strongly suppressed in the SM, can contribute significantly and the relations in question are not necessarily satisfied. In the present paper, MFV will be defined as in [5,8].As reviewed in [8], this class of models can be formulated to a very good approximation in terms of eleven parameters: four parameters of the CKM matrix and seven values of the universal master functions F i (v) that parametrize the short distance contributions to rare decays with v denoting symbolically the parameters of a given MFV model. However, as argued in [8], the new physics contributions to the functions S(v), C(v), D ′ (v), (1.1)

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