English

Magnus and Dyson Series for Master Integrals

High Energy Physics - Phenomenology 2015-06-18 v2

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.

Keywords

Cite

@article{arxiv.1401.2979,
  title  = {Magnus and Dyson Series for Master Integrals},
  author = {Mario Argeri and Stefano Di Vita and Pierpaolo Mastrolia and Edoardo Mirabella and Johannes Schlenk and Ulrich Schubert and Lorenzo Tancredi},
  journal= {arXiv preprint arXiv:1401.2979},
  year   = {2015}
}

Comments

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

R2 v1 2026-06-22T02:44:24.253Z