Banana integrals in configuration space

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 epsilon expansion of the two loop banana integrals, for d = j -2 epsilon, j = 2, 3, 4.(c) 2023 The Author(s). Published by Elsevier B.V.This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/). Funded by SCOAP3.

Automated summary

This research reconsiders the computation of banana integrals at different loops in the configuration space. We demonstrate how the 2-loop banana integral can be computed directly using the configuration space representation and include the analytic extension of the diagram in the space of complex masses. We also explicitly determine the epsilon expansion of the two loop banana integrals.