Heavy quark vacuum polarization function at image and image Original Research Article

We determine the full mass and image dependence of the heavy quark vacuum polarization function image and its contribution to the total image cross section at image and image in perturbative QCD. We use known results for the expansions of image at high energies, in the threshold region and around image, conformal mapping and the Padé approximation method. From our results for image we determine numerically at image the previously unknown non-logarithmic contributions in the high-energy expansion at order image for image and the coefficients in the expansion around image at order image with image. We also determine at image the previously unknown image constant term in the expansion of image in the threshold region, where v is the quark velocity. Our method allows for a quantitative estimate of uncertainties and can be systematically improved once more information in the three kinematic regions becomes available by future multi-loop computations. For the contributions to the total image cross section at image we confirm results obtained earlier by Chetyrkin, Kühn and Steinhauser.