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Title: Elliptic polylogarithms and Feynman parameter integrals

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2];  [3];  [4];  [4]
  1. Humboldt Univ. of Berlin (Germany)
  2. European Organization for Nuclear Research (CERN), Geneva (Switzerland); Université Catholique de Louvain, Louvain-la-Neuve (Belgium)
  3. SLAC National Accelerator Lab., Menlo Park, CA (United States)
  4. European Organization for Nuclear Research (CERN), Geneva (Switzerland)
+ Show Author Affiliations

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.

Research Organization:
SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC02-76SF00515
OSTI ID:
1532395
Journal Information:
Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 5 Vol. 2019; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English

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Two-loop planar master integrals for Higgs → 3 partons with full heavy-quark mass dependence text January 2016
Maximal cuts in arbitrary dimension text January 2017
All orders structure and efficient computation of linearly reducible elliptic Feynman integrals text January 2019
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Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes text January 2012
Uniqueness of two-loop master contours text January 2012
Multiloop integrals in dimensional regularization made simple text January 2013
The elliptic dilogarithm for the sunset graph text January 2013
The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory text January 2014
The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms text January 2014
A Feynman integral via higher normal functions text January 2014
Bootstrapping an NMHV amplitude through three loops text January 2014
Elliptic multiple zeta values and one-loop superstring amplitudes text January 2014
The two-loop sunrise integral around four space-time dimensions and generalisations of the Clausen and Glaisher functions towards the elliptic case preprint January 2015
The iterated structure of the all-order result for the two-loop sunrise integral text January 2015
Local mirror symmetry and the sunset Feynman integral preprint January 2016
Bootstrapping a Five-Loop Amplitude Using Steinmann Relations text January 2016
Elliptic Polylogarithms and Basic Hypergeometric Functions text January 2016
Heptagons from the Steinmann Cluster Bootstrap text January 2016
Baikov-Lee Representations Of Cut Feynman Integrals text January 2017
Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams text January 2017
An Elliptic Generalization of Multiple Polylogarithms text January 2017
The planar double box integral for top pair production with a closed top loop to all orders in the dimensional regularisation parameter text January 2018
Analytic results for the planar double box integral relevant to top-pair production with a closed top loop text January 2018
Harmonic Polylogarithms text January 1999
The two loop crossed ladder vertex diagram with two massive exchanges text January 2008
On the maximal cut of Feynman integrals and the solution of their differential equations text January 2017
A non-planar two-loop three-point function beyond multiple polylogarithms text January 2017
A non-planar two-loop three-point function beyond multiple polylogarithms text January 2017

Cited By (21)

Algorithms and tools for iterated Eisenstein integrals journal February 2020
An analytic solution for the equal-mass banana graph journal September 2019
Prescriptive unitarity with elliptic leading singularities journal December 2021
Elliptic, Yangian-Invariant “Leading Singularity” journal May 2021
Calculation of master integrals in terms of elliptic multiple polylogarithms journal May 2020
The complete set of two-loop master integrals for Higgs + jet production in QCD text January 2020
Local Unitarity: a representation of differential cross-sections that is locally free of infrared singularities at any order text January 2021
Evaluating two-loop non-planar master integrals for Higgs + jet production with full heavy-quark mass dependence text January 2019
Embedding Feynman Integral (Calabi-Yau) Geometries in Weighted Projective Space text January 2019
Photon pair production in gluon fusion: Top quark effects at NLO with threshold matching text January 2019
Sunrise integral with two internal masses and pseudo-threshold kinematics in terms of elliptic polylogarithms preprint January 2020
Modular Graph Forms and Scattering Amplitudes in String Theory text January 2020
Cuts and Isogenies text January 2021
Massive kite diagrams with elliptics text January 2020
Three-loop contributions to the ρ parameter and iterated integrals of modular forms journal February 2020
PolyLogTools — polylogs for the masses journal August 2019
An analytic solution for the equal-mass banana graph journal September 2019
Prescriptive unitarity for non-planar six-particle amplitudes at two loops journal December 2019
Landau-Khalatnikov-Fradkin transformation and the mystery of even ζ -values in Euclidean massless correlators journal November 2019
PolyLogTools - Polylogs for the masses text January 2019
Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops text January 2019

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Related Subjects

97 MATHEMATICS AND COMPUTING
NLO Computations
QCD Phenomenology