Analytic results for the planar double box integral relevant to top-pair production with a closed top loop

Abstract

In this article we give the details on the analytic calculation of the master integrals for the planar double box integral relevant to top-pair production with a closed top loop. We show that these integrals can be computed systematically to all order in the dimensional regularisation parameter $\epsilon$. This is done by transforming the system of differential equations into a form linear in $\epsilon$, where the ${\epsilon }^0$-part is a strictly lower triangular matrix. Explicit results in terms of iterated integrals are presented for the terms relevant to NNLO calculations.

78 pages, additional file "supplementary_material.mpl" attached, v2: version to be published