CERN Accelerating science

Article
Report number	arXiv:2106.01280
Title	The diagrammatic coaction beyond one loop
Author(s)	Abreu, Samuel (CERN ; UCLA ; U. Edinburgh, Higgs Ctr. Theor. Phys.) ; Britto, Ruth (Trinity Coll., Dublin ; Hamilton Math. Inst., Dublin ; IPhT, Saclay) ; Duhr, Claude (CERN) ; Gardi, Einan (U. Edinburgh, Higgs Ctr. Theor. Phys.) ; Matthew, James (U. Edinburgh, Higgs Ctr. Theor. Phys.)
Publication	2021-10-15
Imprint	2021-06-02
Number of pages	65
In:	JHEP 2110 (2021) 131
DOI	10.1007/JHEP10(2021)131
Subject category	hep-th ; Particle Physics - Theory
Abstract	The diagrammatic coaction maps any given Feynman graph into pairs of graphs and cut graphs such that, conjecturally, when these graphs are replaced by the corresponding Feynman integrals one obtains a coaction on the respective functions. The coaction on the functions is constructed by pairing a basis of differential forms, corresponding to master integrals, with a basis of integration contours, corresponding to independent cut integrals. At one loop, a general diagrammatic coaction was established using dimensional regularisation, which may be realised in terms of a global coaction on hypergeometric functions, or equivalently, order by order in the $\epsilon$ expansion, via a local coaction on multiple polylogarithms. The present paper takes the first steps in generalising the diagrammatic coaction beyond one loop. We first establish general properties that govern the diagrammatic coaction at any loop order. We then focus on examples of two-loop topologies for which all integrals expand into polylogarithms. In each case we determine bases of master integrals and cuts in terms of hypergeometric functions, and then use the global coaction to establish the diagrammatic coaction of all master integrals in the topology. The diagrammatic coaction encodes the complete set of discontinuities of Feynman integrals, as well as the differential equations they satisfy, providing a general tool to understand their physical and mathematical properties.
Copyright/License	publication: © 2021-2024 The Authors (License: CC-BY-4.0), sponsored by SCOAP³ preprint: (License: CC BY 4.0)

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