CERN Accelerating science

Article
Report number	arXiv:1907.03787 ; CP3-19-34 ; CERN-TH-2019-105 ; HU-Mathematik-2019-04 ; HU-EP-19/20, SLAC-PUB-17453 ; HU-EP-19/20, SLAC-PUB-17453
Title	An analytic solution for the equal-mass banana graph
Author(s)	Broedel, Johannes (Humboldt U., Berlin) ; Duhr, Claude (CERN ; Louvain U., CP3) ; Dulat, Falko (SLAC) ; Marzucca, Robin (Louvain U., CP3) ; Penante, Brenda (CERN) ; Tancredi, Lorenzo (CERN)
Publication	2019-09-16
Imprint	2019-07-08
Number of pages	36
Note	35 pages, a healthy amount of bananas
In:	JHEP 1909 (2019) 112
DOI	10.1007/JHEP09(2019)112
Subject category	hep-ph ; Particle Physics - Phenomenology ; hep-th ; Particle Physics - Theory
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.
Copyright/License	publication: © 2019-2024 The authors (License: CC-BY-4.0) preprint: (License: CC-BY-4.0)

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