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Article
Report number	arXiv:1803.05894 ; CERN-TH-2018-002 ; CP3-18-01 ; Edinburgh 2018/1 ; FR-PHENO-2018-001 ; EDINBURGH-2018-1
Title	The diagrammatic coaction and the algebraic structure of cut Feynman integrals
Author(s)	Abreu, Samuel (Freiburg U.) ; Britto, Ruth (Trinity Coll., Dublin ; IPhT, Saclay) ; Duhr, Claude (CERN ; Louvain U., CP3) ; Gardi, Einan (Edinburgh U.)
Publication	SISSA, 2018-03-15
Imprint	2018-03-15
Number of pages	10
Note	10 pages. Talk at RADCOR 2017, the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology), 25-29 September, 2017, St. Gilgen, Austria
In:	PoS RADCOR (2018) 002
In:	13th International Symposium on Radiative Corrections : Application of Quantum Field Theory to Phenomenology, St. Gilgen, Austria, 24 - 29 Sep 2017, pp.002
DOI	10.22323/1.290.0002
Subject category	hep-ph ; Particle Physics - Phenomenology ; hep-th ; Particle Physics - Theory
Abstract	We present a new formula for the coaction of a large class of integrals. When applied to one-loop (cut) Feynman integrals, it can be given a diagrammatic representation purely in terms of pinches and cuts of the edges of the graph. The coaction encodes the algebraic structure of these integrals, and offers ways to extract important properties of complicated integrals from simpler functions. In particular, it gives direct access to discontinuities of Feynman integrals and facilitates a straightforward derivation of the differential equations they satisfy, which we illustrate in the case of the pentagon.
Copyright/License	preprint: (License: arXiv nonexclusive-distrib 1.0)

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