A Tree-Loop Duality Relation at Two Loops and Beyond
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.
Cite
@article{arxiv.1007.0194,
title = {A Tree-Loop Duality Relation at Two Loops and Beyond},
author = {Isabella Bierenbaum and Stefano Catani and Petros Draggiotis and German Rodrigo},
journal= {arXiv preprint arXiv:1007.0194},
year = {2011}
}
Comments
20 pages. Few typos corrected, some additional comments included, Appendix B and one reference added. Final version as published in JHEP