Magnus and Dyson series for Master Integrals

By M. Argeri, S. Vita, Pierpaolo Mastrolia, E. Mirabella, Johannes Schlenk, U. Schubert, L. Tancredi. 2014

171 citations recorded by the source corpus.

A bstractWe 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.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/a0249d149cfcb4ed7bc0c99f40d614da44231a75

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In Nuclear and High Energy Physics

Citations in the corpus

Decomposition of Feynman integrals on the maximal cut by intersection numbers (2019, methodology): “The matrix P plays an important role in the construction of canonical systems of differential equation [9], as it was observed in [70–72], generalizing the role of Magnus exponential matrix [33] to the case of elliptic equations.”
Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral (2016, background): “came out to be a subset of the much larger class of multiple polylogarithms, MPLs, see [6–9] and references therein), the definition of a so-called canonical basis [10] for dealing with increasingly larger systems of differential equations and the use of the Magnus exponentiation [11].”
Feynman integrals and hyperlogarithms (2015, methodology): “Recently significant progress in the evaluation of Feynman integrals was achieved in particular using modern summation techniques [3, 5, 131] and with considerable improvements of the method of differential equations [9, 91, 97, 99].”
Maximal cuts and differential equations for Feynman integrals. An application to the three-loop massive banana graph (2017, unknown): “05 46”
Lectures on differential equations for Feynman integrals (2014, unknown): “in [9, 24–27].”
On the maximal cut of Feynman integrals and the solution of their differential equations (2016, background): “Currently, they are all limited to special situations, such as a linear dependence on [13] or the dependence on a single kinematic variable [14–16].”