NNLO QCD corrections to the B¯→Xsγ matrix elements using interpolation in mcmc

One of the most troublesome contributions to the NNLO QCD corrections to B¯→Xsγ originates from three-loop matrix elements of four-quark operators. A part of this contribution that is proportional to the QCD beta-function coefficient β0β0 was found in 2003 as an expansion in mc/mbmc/mb. In the present paper, we evaluate the asymptotic behaviour of the complete contribution for mc≫mb/2mc≫mb/2. The asymptotic form of the β0β0-part matches the small-mcmc expansion very well at the threshold mc=mb/2mc=mb/2. For the remaining part, we perform an interpolation down to the measured value of mcmc, assuming that the β0β0-part is a good approximation at mc=0mc=0. Combining our results with other contributions to the NNLO QCD corrections, we find B(B¯→Xsγ)=(3.15±0.23)×10−4 for Eγ>1.6 GeVEγ>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%).