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) over bar-->(X) over bar(d)+gamma (and its charge conjugate) in the next-to-leading order in QCD, including leading power corrections in 1/m(b)(2), and 1/m(c)(2) in the standard model. The average branching ratio [B(B -->X-d+ gamma)] of the decay B --> X-d + gamma and its charge conjugate (B) over bar-->(X) over bar(d) + gamma is estimated to be in the range 6.0 X 10(-6) less than or equal to [B(B-->X-d + gamma)] less than or equal to 2.6 X 10(-5), obtained by varying the CKM-Wolfenstein parameters rho and eta in the range -0.1 less than or equal to rho less than or equal to 0.4 and 0.2 less than or equal to eta less than or equal to 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(d gamma/s gamma)= [B(B -->X(d)gamma)]/[B(B -->X(s)gamma) to lie in the range 0.017 less than or equal to R(d gamma/s gamma) less than or equal to 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 a(CP)(B -->X(d)gamma) = (Gamma(B --> X(d)gamma) - Gamma((B) over bar-->(X) over bar(d)gamma))/(Gamma(B --> X(d)gamma)+ Gamma((B) over bar-->(X) over bar(d)gamma)), 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. (C) 1998 Elsevier Science B.V. All rights reserved.