Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2004-12-03
Eur.Phys.J.C40:361-366,2005
Physics
High Energy Physics
High Energy Physics - Phenomenology
10 pages, 17 figures; references added for section 1, accepted for publication in Eur. Phys. J. C
Scientific paper
10.1140/epjc/s2005-02151-y
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.
Chetyrkin K. G.
Kuhn Johann H.
Mastrolia Pierpaolo
Sturm Chris
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