Inclusive decay rate for B→Xd+γ in next-to-leading logarithmic order and CP asymmetry in the standard model

We compute the decay rate for the Cabibbo-Kobayashi-Maskawa (CKM)-suppressed electromagnetic penguin decay B→Xd+γ (and its charge conjugate) in the next-to-leading order in QCD, including leading power corrections in 1/mb2 and 1/mc2 in the standard model. The average branching ratio 〈B(B→Xd+γ)〉 of the decay B→Xd+γ and its charge conjugate B→Xd+γ is estimated to be in the range 6.0×10−6≤〈B(B→Xd+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→Xdγ)〉/〈B(B→Xsγ) 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 aCP(B→Xdγ)≡(Γ(B→Xdγ)−Γ(B→Xdγ))/(Γ(B→Xdγ)+Γ(B→Xdγ)), 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.