Towards a NNLO calculation in hadronic heavy hadron production

Abstract

We calculate the Laurent series expansion up to $\mathcal{O}({ϵ}^2)$ 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 $\mathcal{O}({ϵ}^2)$ 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 $\mathcal{O}({ϵ}^2)$ expansion of the four-point integrals contains polylogarithms up to $L{i}_4$ and the multiple polylogarithms.

Comments: 5 pages, 2 Postscript figures