Planar Double Box Integral for Top Pair Production with a Closed Top Loop to all orders in the Dimensional Regularization Parameter

We compute systematically for the planar double box Feynman integral relevant to top pair production with a closed top loop the Laurent expansion in the dimensional regularization parameter epsilon. This is done by transforming the system of differential equations for this integral and all its sub-topologies to a form linear in epsilon, where the epsilon(0) part is strictly lower triangular. This system is easily solved order by order in the dimensional regularization parameter epsilon. This is an example of an elliptic multiscale integral involving several elliptic subtopologies. Our methods are applicable to similar problems.