Evaluating Two-Loop massive Operator Matrix Elements with Mellin-Barnes Integrals

The use of Mellin-Barnes integrals became a widespread technique for calculating Feynman diagrams throughout the last years [ 1], in particular to calculate double and triple box-diagrams. In Ref. [ 2], it was possible to expand the scalar two-loop two-point function in all orders in the dimensional regularization parameter ε, using additionally the gluing operation of Feynman diagrams, defined by Kreimer [ 3]. In this paper, we will apply this technique to a more complex problem, namely the calculation of massive five– propagator 2–loop Feynman Diagrams with operator insertions, stemming from light-cone expansion, which are needed for the calculation of the heavy flavor coefficient functions in deep–inelastic scattering. These Wilson coefficients have been calculated before up to next-to-leading order [ 4]. Fully analytic results could only be obtained in the limit Q ≫ m using mass factorization [ 5]. The heavy flavor Wilson coefficients are obtained as a convolution of the massless Wilson coefficients C 2(L),i (