Mellin moments of the image heavy flavor contributions to unpolarized deep-inelastic scattering at image and anomalous dimensions Original Research Article

We calculate the image heavy flavor contributions to the Wilson coefficients of the structure function image and the massive operator matrix elements (OMEs) for the twist-2 operators of unpolarized deeply inelastic scattering in the region image. The massive Wilson coefficients are obtained as convolutions of massive OMEs and the known light flavor Wilson coefficients. We also compute the massive OMEs which are needed to evaluate heavy flavor parton distributions in the variable flavor number scheme (VFNS) to 3-loop order. All contributions to the Wilson coefficients and operator matrix elements but the genuine constant terms at image of the OMEs are derived in terms of quantities, which are known for general values in the Mellin variable N. For the operator matrix elements image, image and image the moments image, for image to image, and for image, image, image to image are computed. These terms contribute to the light flavor +-combinations. For the flavor non-singlet terms, we calculate as well the odd moments image, corresponding to the light flavor −-combinations. We also obtain the moments of the 3-loop anomalous dimensions, their color projections for the present processes respectively, in an independent calculation, which agree with the results given in the literature.