Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Preprint 2019-04


Johannes Broedel, Claude Duhr, Falko Dulat, Robin Marzucca, Brenda Penante, Lorenzo Tancredi


An analytic solution for the equal-mass banana graph. 


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: Feynman integrals, elliptic polylogarithms, modular forms.


Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2019-04


36 pp.