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.

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 present the calculation of the virtual-and bremsstrahlung corrections of O(α s ) to the matrix elements d ℓ + ℓ − |O i |b . This is the missing piece in the full next-to-next-to-leading logarithmic (NNLL) results for various observables associated with the process B → X d ℓ + ℓ − , like the branching ratio, the CP-rate asymmetry and the forward-backward asymmetry. This paper is an extension of analogous calculations done by some of us for the process B → X s ℓ + ℓ − . As the contributions of the diagrams induced by the four-quark operators O u 1 and O u 2 with a u-quark running in the quark loop are strongly CKM suppressed, they were omitted in the analysis of B → X s ℓ + ℓ − . This is no longer possible for B → X d ℓ + ℓ − , as the corresponding contributions are not suppressed. The main new work therefore consists of calculating the O(α s ) corrections to d ℓ + ℓ − |O u 1,2 |b . In this paper we restrict ourselves to the range 0.05 ≤ s/m 2 b ≤ 0.25 (s is the invariant mass of the lepton pair), which lies above the ρ-and ω-resonances and below the J/ψ-resonance. We present the analytic results for the mentioned observables related to the process B → X d ℓ + ℓ − as expansions in the small parametersŝ = s/m 2 b , z = m 2 c /m 2 b and s/(4 m 2 c). In the phenomenological analysis at the end of the paper we discuss the impact of the NNLL corrections on the observables mentioned above. * Electronic address: hrachia@jerewan1.yerphi.am † Electronic address: bierik@itp.unibe.ch ‡ Electronic address: greub@itp.unibe.ch § Electronic address: walker@itp.unibe.ch,mwalker@bioc.unizh.ch However, restricting √ s to a region below thecc resonances, the long distance effects in B → X s ℓ + ℓ − are under control. The same is true for B → X d ℓ + ℓ − when choosing a region of √ s which is below the J/ψ-and above the ρ, ω-resonance regions. It turns out that in those ranges of √ s the corrections to the pure perturbative picture can be analyzed within the heavy quark effective theory (HQET). In particular, all available studies indicate that for the region 0.05 <ŝ = s/m 2 b < 0.25 the non-perturbative effects are below 10% [ [12][13][14][15][16][17]. Consequently, observables like differential decay rates, forward-backward asymmetries and CP-rate asymmetries for B → X s,d ℓ + ℓ − can be precisely predicted in this region of √ s using renormalization group improved perturbation theory. It was pointed out in the literature

No abstract

We compute the decay rate for the Cabibbo-Kobayashi-Maskawa (CKM)-suppressed electromagnetic penguin decay B → X d + γ (and its charge conjugate) in the next-to-leading order in QCD, including leading power corrections in 1/m 2 b and 1/m 2 c in the standard model. The average branching ratio B(B → X d + γ) of the decay B → X d + γ and its charge conjugate B → X d + γ is estimated to be in the range 6.0 × 10 −6 ≤ B(B → X d + γ) ≤ 2.6 × 10 −5 , obtained by varying the CKM-Wolfenstein parameters ρ and η in the range −0.1 ≤ ρ ≤ 0.4 and 0.2 ≤ η ≤ 0.46 and taking into account other parametric dependence. In the NLL approximation and in the stated range of the CKM parameters, we find the ratio R(dγ/sγ) ≡ B(B → X d γ) / B(B → X s γ) to lie in the range 0.017 ≤ R(dγ/sγ) ≤ 0.074. Theoretical uncertainties in this ratio are estimated and found to be small. Hence, this ratio is well suited to provide independent constraints on the CKM parameters. The CP-asymmetry in the decay rates, defined as, is found to be in the range (7 − 35)%. Both the decay rates and CP asymmetry are measurable in forthcoming experiments at B factories and possibly at HERA-B.