Algebraic Structure of Cut Feynman Integrals and the Diagrammatic Coaction

作者：Abreu Samuel^*; Britto Ruth; Duhr Claude; Gardi Einan

来源：Physical Review Letters, 2017, 119(5): 051601.

DOI：10.1103/PhysRevLett.119.051601

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.

• 出版日期2017-7-31
• 单位中国地震局