Feynman's Tree Theorem and Loop-Tree Dualities

TL;DR

This paper explores the duality theorem linking loop integrals to phase space integrals, extending it to higher loops and demonstrating its application to complex scalar master integrals.

Contribution

It rederives the duality relation for one-loop integrals and extends it to two and higher loops, providing new insights into the structure of loop integrals.

Findings

Extended duality relation to multi-loop integrals

Applied duality to two- and three-loop scalar master integrals

Analyzed the structure of cuts in loop integrals

Abstract

We discuss the duality theorem, which provides a relation between loop integrals and phase space integrals. We rederive the duality relation for the one-loop case and extend it to two and higher-order loops. We explicitly show its application to two- and three-loop scalar master integrals and discuss the structure of the occurring cuts.