NNLO QCD corrections to the image matrix elements using interpolation in image Original Research Article

One of the most troublesome contributions to the NNLO QCD corrections to image originates from three-loop matrix elements of four-quark operators. A part of this contribution that is proportional to the QCD beta-function coefficient image was found in 2003 as an expansion in image. In the present paper, we evaluate the asymptotic behaviour of the complete contribution for image. The asymptotic form of the image-part matches the small-image expansion very well at the threshold image. For the remaining part, we perform an interpolation down to the measured value of image, assuming that the image-part is a good approximation at image. Combining our results with other contributions to the NNLO QCD corrections, we find image for image in the image-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%).