# Causality and loop-tree duality at higher loops

## TL;DR

This paper establishes a connection between higher-loop Feynman integrals and phase space integrals using spanning trees, providing a simple formula for the modified causality-preserving $i\, extdelta$-prescription.

## Contribution

It introduces a novel method linking $l$-loop integrals to phase space sums via spanning trees, with a straightforward formula for the causality-consistent $i\, extdelta$-prescription.

## Key findings

- Derived a relation between $l$-loop integrals and phase space integrals.
- Provided a simple formula for the modified $i\, extdelta$-prescription.
- Clarified the role of spanning trees in loop integral analysis.

## Abstract

We relate a $l$-loop Feynman integral to a sum of phase space integrals, where the integrands are determined by the spanning trees of the original $l$-loop graph. Causality requires that the propagators of the trees have a modified $i\delta$-prescription and we present a simple formula for the correct $i\delta$-prescription.