Master integrals for the 2-loop QCD virtual corrections to the forward–backward asymmetry

Abstract

We present the master integrals needed for the calculation of the two-loop QCD corrections to the forward–backward asymmetry of a quark–antiquark pair produced in electron–positron annihilation events. The Abelian diagrams entering in the evaluation of the vector form factors were calculated in a previous paper. We consider here the non-Abelian diagrams and the diagrams entering in the computation of the axial form factors, for arbitrary space-like momentum transfer Q 2 and finite heavy quark mass m. Both the UV and IR divergences are regularized in the continuous D-dimensional scheme. The master integrals are Laurent-expanded around D=4 and evaluated by the differential equation method; the coefficients of the expansions are expressed as 1-dimensional harmonic polylogarithms of maximum weight 4.