The ε-form of the differential equations for Feynman integrals in the elliptic case

2018/02/28 by Luise Adams, Stefan Weinzierl · 126 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic and Geometric Analysis #Algebraic number #Basis (linear algebra) #Black Holes and Theoretical Physics #Differential (mechanical device) #Differential equation #Feynman diagram #Feynman integral #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Order of integration (calculus) #Physics #Pure mathematics #Quantum mechanics #hep-ph #hep-th

paper · pdf · open access · doi:10.1016/j.physletb.2018.04.002

published in Physics Letters B 781, 270-278 (Elsevier BV) · 15 pages, version to be published

openalex created_date 2018/02/23 · arxiv created 2018/04/02 · openalex publication_date 2018/04/05 · arxiv updated 2018/04/11 · openalex updated_date 2026/08/05

Abstract

Feynman integrals are easily solved if their system of differential equations is in ε-form. In this letter we show by the explicit example of the kite integral family that an ε-form can even be achieved, if the Feynman integrals do not evaluate to multiple polylogarithms. The ε-form is obtained by a (non-algebraic) change of basis for the master integrals.

Citations

• Towards multiple elliptic polylogarithms
• Multiple Elliptic Polylogarithms
• Explicit solutions of the multi-loop integral recurrence relations and its application
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