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Article
Report number	arXiv:1808.00069 ; CERN-TH-2018-165 ; CP3-18-46 ; FR-PHENO-2018-007
Title	Coaction for Feynman integrals and diagrams
Author(s)	Abreu, Samuel (Freiburg U.) ; Britto, Ruth (Hamilton Math. Inst., Dublin ; Trinity Coll., Dublin ; IPhT, Saclay) ; Duhr, Claude (CERN ; Louvain U., CP3) ; Gardi, Einan (U. Edinburgh, Higgs Ctr. Theor. Phys.) ; Matthew, James (U. Edinburgh, Higgs Ctr. Theor. Phys.)
Publication	SISSA, 2018-07-31
Imprint	2018-07-31
Number of pages	10
Note	10 pages, talk given at Loops and Legs in Quantum Field Theory 2018
In:	PoS LL2018 (2018) 047
In:	14th DESY Workshop on Elementary Particle Physics : Loops and Legs in Quantum Field Theory 2018, St Goar, Germany, 29 Apr - 04 May 2018, pp.047
DOI	10.22323/1.303.0047
Subject category	hep-ph ; Particle Physics - Phenomenology ; hep-th ; Particle Physics - Theory
Abstract	We propose a general coaction for families of integrals appearing in the evaluation of Feynman diagrams, such as multiple polylogarithms and generalized hypergeometric functions. We further conjecture a link between this coaction and graphical operations on Feynman diagrams. At one-loop order, there is a basis of integrals for which this correspondence is fully explicit. We discuss features and present examples of the diagrammatic coaction on two-loop integrals. We also present the coaction for the functions ${}_{p+1}F_p$ and Appell $F_1$.
Copyright/License	preprint: (License: arXiv nonexclusive-distrib 1.0) publication: (License: CC-BY-NC-ND-4.0)

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