Two-loop helicity amplitudes in QCD

Abstract

We compute the σ(α3/8) virtual QCD corrections for the process e+e- →qqg arising from the interference of the two-loop and tree amplitudes and from the self-interference of the one-loop amplitude. The results are presented in the form of both matrix elements and helicity amplitudes. The calculation of the matrix elements is performed by the direct evaluation of the Feynman diagrams and corresponding loop integrals. The helicity amplitudes are derived in a scheme-independent way from the coefficients appearing in the general expression for the tensorial structure of this process. The tensor coefficients are then extracted from the Feynman diagrams by means of projectors. The one- and two-loop integrals appearing in the amplitudes are reduced to a small set of known master integrals by means of integration-by-parts identities. This reduction has been automated by construction of an algorithm based on that proposed by Laporta. The infrared pole structure of both the matrix elements and helicity amplitudes is shown to agree with the predictions made by the infrared factorisation formula of Catani. The analytic results for the finite terms, regularised in conventional dimensional regularisation and renormalised in the MS scheme, are presented, expressed in terms of one- and two-dimensional harmonic polylogarithms.