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

Understand

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 $\varepsilon$.
• This is done by transforming the system of differential equations into a form linear in $\varepsilon$, where the $\varepsilon^0$-part is a strictly lower triangular matrix.
• Explicit results in terms of iterated integrals are presented for the terms relevant to NNLO calculations.