# Causality, unitarity thresholds, anomalous thresholds and infrared singularities from the loop-tree duality at higher orders

## TL;DR

This paper analyzes unitarity and anomalous thresholds in multi-loop scattering amplitudes using the loop-tree duality, revealing local cancellations of unphysical thresholds and the confinement of infrared singularities to facilitate subtraction-free calculations.

## Contribution

It provides the first comprehensive analysis of higher-order unitarity and anomalous thresholds via loop-tree duality, demonstrating local cancellation of unphysical thresholds and the localization of infrared singularities.

## Key findings

- Unphysical thresholds are locally canceled when considering all dual on-shell cuts.
- Soft and collinear singularities are confined to a compact loop momentum region.
- The results enable subtraction-free infrared singularity cancellation.

## Abstract

We present the first comprehensive analysis of the unitarity thresholds and anomalous thresholds of scattering amplitudes at two loops and beyond based on the loop-tree duality, and show how non-causal unphysical thresholds are locally cancelled in an efficient way when the forest of all the dual on-shell cuts is considered as one. We also prove that soft and collinear singularities at two loops and beyond are restricted to a compact region of the loop three-momenta, which is a necessary condition for implementing a local cancellation of loop infrared singularities with the ones appearing in real emission; without relying on a subtraction formalism.