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 discuss the observables for the B → K * (→ Kπ)ℓ + ℓ − decay, focusing on both CP-averaged and CP-violating observables at large and low hadronic recoil with special emphasis on their low sensitivity to form-factor uncertainties. We identify an optimal basis of observables that balances theoretical and experimental advantages, which will guide the New Physics searches in the short term. We discuss some advantages of the observables in the basis, and in particular their improved sensitivity to New Physics compared to other observables. We present predictions within the Standard Model for the observables of interest, integrated over the appropriate bins including lepton mass corrections. Finally, we present bounds on the S-wave contribution to the distribution coming from the B → K * 0 ℓ + ℓ − decay, which will help to establish the systematic error associated to this pollution.
We present in detail the calculation of the O(α s ) virtual corrections to the matrix element for b → sγ. Besides the one-loop virtual corrections of the electromagnetic and color dipole operators O 7 and O 8 , we include the important two-loop contribution of the four-Fermi operator O 2 . By applying the Mellin-Barnes representation to certain internal propagators, the result of the two-loop diagrams is obtained analytically as an expansion in m c /m b . These results are then combined with existing O(α s ) Bremsstrahlung corrections in order to obtain the inclusive rate for B → X s γ. The new contributions drastically reduce the large renormalization scale dependence of the leading logarithmic result. Thus a very precise Standard Model prediction for this inclusive process will become possible once also the corrections to the Wilson coefficients are available.
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