Towards a NNLO calculation in hadronic heavy hadron production

Abstract

We calculate the Laurent series expansion up to ${\cal O}(\epsilon^2)$ for all scalar one-loop one-, two-, three- and four-point integrals that are needed in the calculation of hadronic heavy flavour production. The Laurent series up to ${\cal O}(\epsilon^2)$ is needed as input to that part of the NNLO corrections to heavy hadron production at hadron colliders where the one-loop integrals appear in the loop-by-loop contributions. The four-point integrals are the most complicated. The ${\cal O}(\epsilon^2)$ expansion of the four-point integrals contains polylogarithms up to $ Li_4$ and the multiple polylogarithms.