English

An analytic solution for the equal-mass banana graph

High Energy Physics - Theory 2019-10-23 v1 High Energy Physics - Phenomenology

Abstract

We present fully analytic results for all master integrals for the three-loop banana graph with four equal and non-zero masses. The results are remarkably simple and all integrals are expressed as linear combinations of iterated integrals of modular forms of uniform weight for the same congruence subgroup as for the two-loop equal-mass sunrise graph. We also show how to write the results in terms of elliptic polylogarithms evaluated at rational points.

Keywords

Cite

@article{arxiv.1907.03787,
  title  = {An analytic solution for the equal-mass banana graph},
  author = {Johannes Broedel and Claude Duhr and Falko Dulat and Robin Marzucca and Brenda Penante and Lorenzo Tancredi},
  journal= {arXiv preprint arXiv:1907.03787},
  year   = {2019}
}

Comments

35 pages, a healthy amount of bananas

R2 v1 2026-06-23T10:15:14.804Z