The planar double box integral for top pair production with a closed top loop to all orders in the dimensional regularisation parameter

Abstract

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 regularisation 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 regularisation parameter $\epsilon$. This is an example of an elliptic multi-scale integral involving several elliptic sub-topologies. Our methods are applicable to similar problems.

6 pages, version to be published