Loopedia Record

Edge list:	(e,0\|z) (0,1\|1) (0,1\|1) (0,1\|1) (0,1\|1) (e,1\|z)
Nickel index:	e1111\|e\|:z1111\|z\|
Database path:	3/2/4/e1111\|e\|/12/z1111\|z\|

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Orders in ε: 0 Reference: arXiv:1406.2664 Authors: Spencer Bloch, Matt Kerr, Pierre Vanhove Description: The three-loop banana graph with four equal masses is computed in D = 2 dimensions. The result is obtained in terms of elliptic trilogarithms at sixth roots of unity. A family of K3 surfaces is associated to the graph polynomial. Submitter: bogner@math.hu-berlin.de	Record 1501614231.C4m3 added 01 Aug 2017 19:03 UTC last modified 06 Sep 2017 07:53 UTC
Type: other whole topology Orders in ε: 0 Number of master integrals: 3 Reference: arXiv:1704.05465 Authors: Amedeo Primo, Lorenzo Tancredi Description: The master integrals for the family of the three-loop banana integral with four equal masses are computed in 2 dimensions. The result involves integrals over elliptic integrals. Submitter: bogner@math.hu-berlin.de	Record 1501614913.a5Lf added 01 Aug 2017 19:15 UTC last modified 31 Aug 2017 22:40 UTC
Non-standard propagator powers: P4=1,2,3 Orders in ε: -3,-2,-1,0 Reducible by: IBP Number of master integrals: 3 Reference: arXiv:2510.12885 Equations: B.4,B.6-7,D.11-16 Authors: Laurent Lellouch, Alessandro Lupo, Mattias Sjö, Kálmán Szabo, Pierre Vanhove Description: Expansion in d=4-2ε dimensions. Finite parts given in terms of 2-dimensional integral. Submitter: mattias.sjo@cpt.univ-mrs.fr	Record 1763118637.pt2H added 14 Nov 2025 11:10 UTC last modified 14 Nov 2025 11:10 UTC

If you use these results in your calculation, please also cite arXiv:1709.01266.

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