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

J Jesús Aguilera-Verdugo,Germán F.R Sborlini,Félix Driencourt-Mangin,Selomit Ramírez-Uribe,Szymon Tracz,Judith Plenter,Germán Rodrigo,William J Torres Bobadilla

doi:10.1007/jhep12(2019)163

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.

Highlights

We show how non-causal unphysical thresholds cancel locally in the forest defined by the sum of dual cuts thanks to the momentum dependent ı0 prescription of the dual propagators
The vector η is mostly arbitrary — it only has to be future-like — the most convenient choice is η = (1, 0)
We present the first comprehensive analysis of the unitarity thresholds and anomalous thresholds of scattering amplitudes at two loops and beyond based on the looptree 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

Summary

Introduction

We show how non-causal unphysical thresholds cancel locally in the forest defined by the sum of dual cuts thanks to the momentum dependent ı0 prescription of the dual propagators. In the space-like case, kj2i < 0, unphysical thresholds occur in the intersection of the two forward on-shell hyperboloids and in the intersection of the two backward on-shell hyperboloids.

Results

Conclusion