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Maximal cuts and differential equations for Feynman integrals : An application to the three-loop massive banana graph

Primo, Amedeo; Tancredi, Lorenzo

We consider the calculation of the master integrals of the three-loop massive banana graph. In the case of equal internal masses, the graph is reduced to three master integrals which satisfy an irreducible system of three coupled linear differential equations. The solution of the system requires finding a 3 ×3 matrix of homogeneous solutions. We show how the maximal cut can be used to determine all entries of this matrix in terms of products of elliptic integrals of first and second kind of suitable arguments. All independent solutions are found by performing the integration which defines the maximal cut on different contours. Once the homogeneous solution is known, the inhomogeneous solution can be obtained by use of Euler’s variation of constants.

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DOI: 10.5445/IR/1000071139
DOI: 10.1016/j.nuclphysb.2017.05.018
Zitationen: 23
Web of Science
Zitationen: 21
Zugehörige Institution(en) am KIT Institut für Theoretische Teilchenphysik (TTP)
Publikationstyp Zeitschriftenaufsatz
Jahr 2017
Sprache Englisch
Identifikator ISSN: 0550-3213, 1873-1562
KITopen-ID: 1000071139
Erschienen in Nuclear physics <Amsterdam> / B
Band 921
Seiten 316-356
Nachgewiesen in Web of Science
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