An algorithmic approach to finding canonical differential equations for elliptic Feynman integrals

A bstract In recent years, differential equations have become the method of choice to compute multi-loop Feynman integrals. Whenever they can be cast into canonical form, their solution in terms of special functions is straightforward. Recently, progress has been made in understanding the precise ca...

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Bibliographic Details
Published inThe journal of high energy physics Vol. 2023; no. 8; pp. 120 - 25
Main Authors Dlapa, Christoph, Henn, Johannes M., Wagner, Fabian J.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 18.08.2023
Springer Nature B.V
SpringerOpen
Subjects
Algorithms
Automation
Canonical forms
Classical and Quantum Gravitation
Differential equations
Elementary Particles
Elliptic functions
High energy physics
Higher-Order Perturbative Calculations
Integrals
Kinematics
Mathematical analysis
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Scattering Amplitudes
String Theory
Scattering Amplitudes
Automation
Higher-Order Perturbative Calculations
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Summary:A bstract In recent years, differential equations have become the method of choice to compute multi-loop Feynman integrals. Whenever they can be cast into canonical form, their solution in terms of special functions is straightforward. Recently, progress has been made in understanding the precise canonical form for Feynman integrals involving elliptic polylogarithms. In this article, we make use of an algorithmic approach that proves powerful to find canonical forms for these cases. To illustrate the method, we reproduce several known canonical forms from the literature and present examples where a canonical form is deduced for the first time. Together with this article, we also release an update for INITIAL, a publicly available Mathematica implementation of the algorithm.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP08(2023)120