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arXiv · 1007.0194

A Tree-Loop Duality Relation at Two Loops and Beyond

Isabella Bierenbaum·Stefano Catani·Petros Draggiotis·German Rodrigo
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Abstract

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.

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Isabella Bierenbaum, Stefano Catani, Petros Draggiotis, German Rodrigo. 2010-10-27. A Tree-Loop Duality Relation at Two Loops and Beyond. https://doi.org/10.1007/jhep10(2010)073

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