https://doi.org/10.1140/epjc/s2005-02151-y
theoretical physics
Heavy quark vacuum polarization: first two moments of the 
contribution
1
Institut für Theoretische Teilchenphysik, Universität Karlsruhe, 76128, Karlsruhe, Germany
2
Department of Physics and Astronomy, UCLA, CA 90095-1547, Los Angeles, USA
* e-mail: chet@particle.uni-karlsruhe.de
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 
. 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 
contribution.
© Springer-Verlag, 2005
