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Report number arXiv:1703.05064 ; CERN-TH-2017-056
Title The algebraic structure of cut Feynman integrals and the diagrammatic coaction
Related titleThe algebraic structure of cut Feynman integrals and the diagrammatic coaction
Author(s) Abreu, Samuel (Freiburg U.) ; Britto, Ruth (IPhT, Saclay ; Trinity Coll., Dublin) ; Duhr, Claude (CERN ; Louvain U., CP3) ; Gardi, Einan (U. Edinburgh, Higgs Ctr. Theor. Phys.)
Publication 2017-07-31
Imprint 2017-03-15
Number of pages 6
In: Phys. Rev. Lett. 119 (2017) 051601
DOI 10.1103/PhysRevLett.119.051601
Subject category math.NT ; Mathematical Physics and Mathematics ; math.MP ; Mathematical Physics and Mathematics ; math-ph ; Mathematical Physics and Mathematics ; hep-ph ; Particle Physics - Phenomenology ; hep-th ; Particle Physics - Theory
Abstract We study the algebraic and analytic structure of Feynman integrals by proposing an operation that maps an integral into pairs of integrals obtained from a master integrand and a corresponding master contour. This operation is a coaction. It reduces to the known coaction on multiple polylogarithms, but applies more generally, e.g. to hypergeometric functions. The coaction also applies to generic one-loop Feynman integrals with any configuration of internal and external masses, and in dimensional regularization. In this case, we demonstrate that it can be given a diagrammatic representation purely in terms of operations on graphs, namely contractions and cuts of edges. The coaction gives direct access to (iterated) discontinuities of Feynman integrals and facilitates a straightforward derivation of the differential equations they admit. In particular, the differential equations for any one-loop integral are determined by the diagrammatic coaction using limited information about their maximal, next-to-maximal, and next-to-next-to-maximal cuts.
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publication: © 2017-2025 authors (License: CC-BY-4.0)

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 Record created 2017-04-11, last modified 2023-11-30


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