Banana integrals in configuration space

Abstract

We reconsider the computation of banana integrals at different loops, by working in the configuration space, in any dimension. We show how the 2-loop banana integral can be computed directly from the configuration space representation, without the need to resort to differential equations, and we include the analytic extension of the diagram in the space of complex masses. We also determine explicitly the $\varepsilon$ expansion of the two loop banana integrals, for $d=j-2\varepsilon$, $j=2,3,4$.