Analytic results for planar three-loop four-point integrals from a Knizhnik-Zamolodchikov equation
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Publication:303453
DOI10.1007/JHEP07(2013)128zbMATH Open1342.81352arXiv1306.2799OpenAlexW3106210717MaRDI QIDQ303453
Author name not available (Why is that?)
Publication date: 12 August 2016
Published in: (Search for Journal in Brave)
Abstract: We apply a recently suggested new strategy to solve differential equations for master integrals for families of Feynman integrals. After a set of master integrals has been found using the integration-by-parts method, the crucial point of this strategy is to introduce a new basis where all master integrals are pure functions of uniform transcendentality. In this paper, we apply this method to all planar three-loop four-point massless on-shell master integrals. We explicitly find such a basis, and show that the differential equations are of the Knizhnik-Zamolodchikov type. We explain how to solve the latter to all orders in the dimensional regularization parameter epsilon, including all boundary constants, in a purely algebraic way. The solution is expressed in terms of harmonic polylogarithms. We explicitly write out the Laurent expansion in epsilon for all master integrals up to weight six.
Full work available at URL: https://arxiv.org/abs/1306.2799
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