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Magnus and Dyson Series for Master Integrals

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arxiv 1401.2979 v2 pith:NAY3DKO7 submitted 2014-01-13 hep-ph

Magnus and Dyson Series for Master Integrals

Mario Argeri , Stefano Di Vita , Pierpaolo Mastrolia , Edoardo Mirabella , Johannes Schlenk , Ulrich Schubert , Lorenzo Tancredi This is my paper
classification hep-ph
keywords integralsdimensionalparametersystemsdependencedysonequationsmagnus
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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.

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