Journal of High Energy Physics

, 2018:24 | Cite as

Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections

  • Janko Böhm
  • Alessandro Georgoudis
  • Kasper J. Larsen
  • Hans Schönemann
  • Yang ZhangEmail author
Open Access
Regular Article - Theoretical Physics


We present the powerful module-intersection integration-by-parts (IBP) method, suitable for multi-loop and multi-scale Feynman integral reduction. Utilizing modern computational algebraic geometry techniques, this new method successfully trims traditional IBP systems dramatically to much simpler integral-relation systems on unitarity cuts. We demonstrate the power of this method by explicitly carrying out the complete analytic reduction of two-loop five-point non-planar hexagon-box integrals, with degree-four numerators, to a basis of 73 master integrals.


Differential and Algebraic Geometry Scattering Amplitudes Perturbative QCD 


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

  • Janko Böhm
    • 1
  • Alessandro Georgoudis
    • 2
  • Kasper J. Larsen
    • 3
  • Hans Schönemann
    • 1
  • Yang Zhang
    • 4
    • 5
    • 6
    Email author
  1. 1.Department of MathematicsUniversity of KaiserslauternKaiserslauternGermany
  2. 2.Department of Physics and AstronomyUppsala UniversityUppsalaSweden
  3. 3.School of Physics and AstronomyUniversity of SouthamptonSouthamptonUnited Kingdom
  4. 4.PRISMA Cluster of ExcellenceJohannes Gutenberg UniversityMainzGermany
  5. 5.Institute for Theoretical PhysicsETH ZürichZürichSwitzerland
  6. 6.Kavli Institute for Theoretical PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.

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