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.
@article{arxiv.1904.08389,
title = {Causality, unitarity thresholds, anomalous thresholds and infrared singularities from the loop-tree duality at higher orders},
author = {J. Jesús Aguilera-Verdugo and Félix Driencourt-Mangin and Judith Plenter and Selomit Ramírez-Uribe and Germán Rodrigo and Germán F. R. Sborlini and William J. Torres Bobadilla and Szymon Tracz},
journal= {arXiv preprint arXiv:1904.08389},
year = {2019}
}