Two-loop amplitudes with nested sums: Fermionic contributions to e+ e- --> q qbar g

Sven Moch^[1], Peter Uwer ^[1] and S. Weinzierl ^[2],

^[1] Institut Theoretische Teilchenphysik, Univerisitat Karlsruhe, 76128 Karlsruhe, Germany
^[2]Universita` degli Studi di Parma and I.N.F.N., Gruppo collegato di Parma, Parco Area delle Scienze, 43100 Parma, Italy

Abstract

We present the calculation of the nf-contributions to the two-loop amplitude for e+ e- --> q qbar g and give results for the full one-loop amplitude to order eps^2 in the dimensional regularization parameter. Our results agree with those recently obtained by Garland et al.. The calculation makes extensive use of an efficient method based on nested sums to calculate two-loop integrals with arbitrary powers of the propagators. The use of nested sums leads in a natural way to multiple polylogarithms with simple arguments, which allow a straightforward analytic continuation.