Elliptic polylogarithms and Feynman parameter integrals

Johannes Broedel (Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin, IRIS Adlershof, Zum Grossen Windkanal 6, Berlin, 12489, Germany) ; Claude Duhr (TH Department, CERN, 1 Esplanade des Particules, Geneva 23, CH-1211, Switzerland; Centre for Cosmology, Particle Physics and Phenomenology (CP3), Université Catholique de Louvain, Louvain-la-Neuve, B-1348, Belgium) ; Falko Dulat (SLAC National Accelerator Laboratory, Stanford University, 2575 Sand Hill Road, Stanford, CA, 94309, U.S.A.) ; Brenda Penante (TH Department, CERN, 1 Esplanade des Particules, Geneva 23, CH-1211, Switzerland) ; Lorenzo Tancredi (TH Department, CERN, 1 Esplanade des Particules, Geneva 23, CH-1211, Switzerland)

In this paper we study the calculation of multiloop Feynman integrals that cannot be expressed in terms of multiple polylogarithms. We show in detail how certain types of two- and three-point functions at two loops, which appear in the calculation of higher order corrections in QED, QCD and in the electroweak theory (EW), can naturally be expressed in terms of a recently introduced elliptic generalisation of multiple polylogarithms by direct integration over their Feynman parameter representation. Moreover, we show that in all examples that we considered a basis of pure Feynman integrals can be found.

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      "value": "In this paper we study the calculation of multiloop Feynman integrals that cannot be expressed in terms of multiple polylogarithms. We show in detail how certain types of two- and three-point functions at two loops, which appear in the calculation of higher order corrections in QED, QCD and in the electroweak theory (EW), can naturally be expressed in terms of a recently introduced elliptic generalisation of multiple polylogarithms by direct integration over their Feynman parameter representation. Moreover, we show that in all examples that we considered a basis of pure Feynman integrals can be found."
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Published on:
21 May 2019
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2019 (2019)
Issue 5
Pages 1-38
DOI:
https://doi.org/10.1007/JHEP05(2019)120
arXiv:
1902.09971
Copyrights:
The Author(s)
Licence:
CC-BY-3.0

Fulltext files: