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The duality relation between one-loop integrals and phase-space integrals,developed in a previous work, is extended to higher-order loops. The dualityrelation is realized by a modification of the customary +i0 prescription of theFeynman propagators, which compensates for the absence of the multiple-cutcontributions that appear in the Feynman tree theorem. We rederive the dualitytheorem at one-loop order in a form that is more suitable for its iterativeextension to higher-loop orders. We explicitly show its application to two- andthree-loop scalar master integrals, and we discuss the structure of theoccurring cuts and the ensuing results in detail.

A Tree-Loop Duality Relation at Two Loops and Beyond