Reducing differential equations for multiloop master integrals

By Roman N. Lee. 2014

274 citations recorded by the source corpus.

A bstractWe present an algorithm of the reduction of the differential equations for master integrals the Fuchsian form with the right-hand side matrix linearly depending on dimensional regularization parameter ϵ. We consider linear transformations of the functions column which are rational in the variable and in ϵ. Apart from some degenerate cases described below, the algorithm allows one to obtain the required transformation or to ascertain irreducibility to the form required. Degenerate cases are quite anticipated and likely to correspond to irreducible systems.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/e0e86167a81ac96348772d7bab4ed941c4434ac3

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Citations in the corpus

Maximal cuts and differential equations for Feynman integrals. An application to the three-loop massive banana graph (2017, unknown): “05 46”
Decomposition of Feynman integrals on the maximal cut by intersection numbers (2019, methodology): “Together with novel algorithms for simplifying the solution of systems of differential equations [9], which triggered further studies [33–38], the calculations of several multi-scale, multi-loop, multi-particle amplitudes became feasible [39–57].”
A Systematic and Efficient Method to Compute Multi-loop Master Integrals (2017, unknown): “[38] and references therein for different algorithms).”
Cuts of Feynman Integrals in Baikov representation (2017, background): “First of all, despite recent efforts [57, 58, 59], and the existence of sufficient conditions that a given MI can be expressed in terms of GPs, no criterion, with practical applicability, that is at the same time necessary and sufficient has been introduced so far.”
Lectures on differential equations for Feynman integrals (2014, methodology): “As we have seen above, the latter can appear when integrating out ε terms, or, equivalently, when normalizing eigenvalues [41].”
Feynman integrals and intersection theory (2018, methodology): “This is a Fuchsian system, which can be solved using standard techniques [8, 9, 54, 86, 87].”