Algebraic Structure of Cut Feynman Integrals and the Diagrammatic Coaction
(2017) Physical Review Letters — Vol. 119, p. 51601 (2017)
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- 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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Abreu, S., Britto, R., Duhr, C., & Gardi, E. (2017). Algebraic Structure of Cut Feynman Integrals and the Diagrammatic Coaction. Physical Review Letters, 119, 51601. https://doi.org/10.1103/physrevlett.119.051601 (Original work published 2017)