Journal of High Energy Physics

, 2016:144

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

  • Johannes M. Henn
  • Alexander V. Smirnov
  • 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 q2 are expressed in terms of multiple polylogarithms, and results for fiftyone master integrals at the threshold q2 = 4m2 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 

Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Johannes M. Henn
    • 1
    • 2
  • Alexander V. Smirnov
    • 3
  • 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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