NNLO QCD corrections to the (B)over-bar → Xsγ matrix elements using interpolation in mc

One of the most troublesome contributions to the NNLO QCD corrections to (B) over bar -> X-S gamma originates from three-loop matrix elements of four-quark operators. A part of this contribution that is proportional to the QCD beta-function coefficient beta(0) was found in 2003 as an expansion in m(c)/m(b) In the present paper, we evaluate the asymptotic behaviour of the complete contribution for me >> M-b/2. The asymptotic form of the beta(0)-part matches the small-m(c) expansion very well at the threshold m(c) = m(b)/2. For the remaining part, we perform an interpolation down to the measured value of m(c) assuming that the beta(0)-part is a good approximation at m(c) = 0. Combining our results with other contributions to the NNLO QCD corrections, we find B((B) over bar -> X-S gamma) = (3.15 +/- 0.23) x 10(-4) for E-gamma > 1.6 GeV in the (B) over bar -meson rest frame. The indicated error has been obtained by adding in quadrature the following uncertainties: Non-perturbative (5%), parametric (3%), higher-order perturbative (3%), and the interpolation ambiguity (3%). (c) 2006 Elsevier B.V. All rights reserved.