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Solving differential equations for Feynman integrals by expansions near singular points

  • Roman N. Lee
  • Alexander V. Smirnov
  • Vladimir A. Smirnov
Open Access
Regular Article - Theoretical Physics

Abstract

We describe a strategy to solve differential equations for Feynman integrals by powers series expansions near singular points and to obtain high precision results for the corresponding master integrals. We consider Feynman integrals with two scales, i.e. non-trivially depending on one variable. The corresponding algorithm is oriented at situations where canonical form of the differential equations is impossible. We provide a computer code constructed with the help of our algorithm for a simple example of four-loop generalized sunset integrals with three equal non-zero masses and two zero masses. Our code gives values of the master integrals at any given point on the real axis with a required accuracy and a given order of expansion in the regularization parameter ϵ.

Keywords

Scattering Amplitudes Perturbative QCD 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Roman N. Lee
    • 1
  • Alexander V. Smirnov
    • 2
  • Vladimir A. Smirnov
    • 3
  1. 1.Budker Institute of Nuclear PhysicsNovosibirskRussia
  2. 2.Research Computing CenterMoscow State UniversityMoscowRussia
  3. 3.Skobeltsyn Institute of Nuclear Physics of Moscow State UniversityMoscowRussia

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