%0 Journal Article
%T Analytic results for planar three-loop four-point integrals from a Knizhnik-Zamolodchikov equation
%A Johannes M. Henn
%A Alexander V. Smirnov
%A Vladimir A. Smirnov
%J Physics
%D 2013
%I arXiv
%R 10.1007/JHEP07(2013)128
%X 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.
%U http://arxiv.org/abs/1306.2799v2