Magnus and Dyson Series for Master Integrals

Abstract

We elaborate on the method of differential equations for evaluating Feynman integrals. We focus on systems of equations for master integrals having a linear dependence on the dimensional parameter. For these systems we identify the criteria to bring them in a canonical form, recently identified by Henn, where the dependence of the dimensional parameter is disentangled from the kinematics. The determination of the transformation and the computation of the solution are obtained by using Magnus and Dyson series expansion. We apply the method to planar and non-planar two-loop QED vertex diagrams for massive fermions, and to non-planar two-loop integrals contributing to 2 -> 2 scattering of massless particles. The extension to systems which are polynomial in the dimensional parameter is discussed as well.

32 pages, 6 figures, 2 ancillary files. v2: references added, typos corrected in the text and in the ancillary files

References in corpus (4)

• The Magnus expansion and some of its applications
• Feynman Diagrams and Differential Equations
• Schouten identities for Feynman graph amplitudes; the Master Integrals for the two-loop massive sunrise graph
• Evaluating single-scale and/or non-planar diagrams by differential equations

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