====== TTP04-25 Heavy-quark vacuum polarization: first two moments of the O(alphas^3 nf^2) contribution ====== The vacuum polarization due to a virtual heavy quark pair and specifically the coefficients of its Taylor expansion in the external momentum are closely related to moments of the cross section for quark-antiquark pair production in electron-positron annihilation. Relating measurement and theoretically calculated Taylor coefficients, an accurate value for charm- and bottom-quark mass can be derived, once corrections from perturbative QCD are sufficiently well under control. Up to three-loop order these have been evaluated previously. We now present a subset of four-loop contributions to the lowest two moments, namely those from diagrams which involve two internal loops from massive and massless fermions coupled to virtual gluons, hence of order alphas^3 nf^2. The calculation demonstrates the applicability of Laporta's algorithm to four-loop vacuum diagrams with both massive and massless propagators and should be considered a first step towards the full evaluation of the order alphas^3 contribution. |**K.G. Chetyrkin, J.H. Kühn, P. Mastrolia and C. Sturm** | |** Eur. Phys. J. C40 361-366 2005 ** | | {{preprints:2004:ttp04-25.pdf|PDF}} {{preprints:2004:ttp04-25.ps|PostScript}} [[http://arxiv.org/abs/hep-ph/0412055|arXiv]] | | |