Journal of High Energy Physics

, 2016:144 | Cite as

Analytic results for planar three-loop integrals for massive form factors

  • Johannes M. Henn
  • Alexander V. SmirnovEmail author
  • Vladimir A. Smirnov
Open Access
Regular Article - Theoretical Physics


We use the method of differential equations to analytically evaluate all planar three-loop Feynman integrals relevant for form factor calculations involving massive particles. Our results for ninety master integrals at general q 2 are expressed in terms of multiple polylogarithms, and results for fiftyone master integrals at the threshold q 2 = 4m 2 are expressed in terms of multiple polylogarithms of argument one, with indices equal to zero or to a sixth root of unity.


Perturbative QCD Scattering Amplitudes 


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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© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Johannes M. Henn
    • 1
    • 2
  • Alexander V. Smirnov
    • 3
    Email author
  • Vladimir A. Smirnov
    • 4
    • 5
  1. 1.PRISMA Cluster of ExcellenceJohannes Gutenberg Universität MainzMainzGermany
  2. 2.Kavli Institute for Theoretical PhysicsUC Santa BarbaraSanta BarbaraU.S.A.
  3. 3.Research Computing CenterMoscow State UniversityMoscowRussia
  4. 4.Skobeltsyn Institute of Nuclear Physics of Moscow State UniversityMoscowRussia
  5. 5.Institut für Theoretische Teilchenphysik, Karlsruhe Institute of Technology (KIT)KarlsruheGermany

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