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A tree-loop duality relation at two loops and beyond. (English) Zbl 1291.81381
Summary: The duality relation between one-loop integrals and phase-space integrals, developed in a previous work, is extended to higher-order loops. The duality relation is realized by a modification of the customary \(+i0\) prescription of the Feynman propagators, which compensates for the absence of the multiple-cut contributions that appear in the Feynman tree theorem. We rederive the duality theorem at one-loop order in a form that is more suitable for its iterative extension to higher-loop orders. We explicitly show its application to two-and three-loop scalar master integrals, and we discuss the structure of the occurring cuts and the ensuing results in detail.

MSC:
81V05 Strong interaction, including quantum chromodynamics
81T18 Feynman diagrams
81T80 Simulation and numerical modelling (quantum field theory) (MSC2010)
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