Towards a Loop-Tree Duality at Two Loops and Beyond

TL;DR

This paper extends the duality theorem relating loop integrals to tree-level phase-space integrals from one loop to higher loops, providing a framework for more complex quantum field theory calculations.

Contribution

It introduces a method to generalize the loop-tree duality theorem to two and more loops, enhancing computational techniques in quantum field theory.

Findings

Extended duality theorem to two loops and beyond

Detailed analysis of the two-loop master diagram

Discussion of three-loop master diagrams

Abstract

We present an extension of the duality theorem, previously defined by S. Catani et al. on the one-loop level, to higher loop orders. The duality theorem provides a relation between loop integrals and tree-level phase-space integrals. Here, the one-loop relation is rederived in a way which is more suitable for its extension to higher loop orders. This is shown in detail by considering the two-loop N-leg master diagram and by a short discussion of the four master diagrams at three loops, in this sketching the general structure of the duality theorem at even higher loop orders.