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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 ϵ 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 twoloop 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.
Original language  English 

Article number  131 
Pages (fromto)  164 
Number of pages  64 
Journal  Journal of High Energy Physics 
Issue number  10 
DOIs  
Publication status  Published  15 Oct 2021 
Keywords
 hepth
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 1 Finished

Particle Theory at the Higgs Centre
Ball, R., Boyle, P., Del Debbio, L., Gardi, E., Horsley, R., Kennedy, A., O'Connell, D., Smillie, J. & Zwicky, R.
1/10/17 → 30/09/21
Project: Research