NNLO QCD corrections to the B -> Xs gamma matrix elements using interpolation in mc
Abstract
One of the most troublesome contributions to the NNLO QCD corrections to B -> Xs 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 beta0 was found in 2003 as an expansion in mc/mb. In the present paper, we evaluate the asymptotic behaviour of the complete contribution for mc >> mb/2. The asymptotic form of the beta0-part matches the small-mc expansion very well at the threshold mc = mb/2. For the remaining part, we perform an interpolation down to the measured value of mc, assuming that the beta0-part is a good approximation at mc=0. Combining our results with other contributions to the NNLO QCD corrections, we find BR(B -> Xs gamma) = (3.15 + 0.23) x 10-4 for Egamma > 1.6 GeV in the B-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%).
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