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 (Centre for Cosmology, Particle Physics and Phenomenology (CP3), Université Catholique de Louvain, Louvain-la-Neuve, B-1348, Belgium, TH Department, CERN, 1 Esplanade des Particules, Geneva 23, CH-1211, Switzerland); 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.
