On the singular behaviour of scattering amplitudes in quantum field theory

TL;DR

This paper investigates the singularities in one-loop scattering amplitudes in quantum field theory, revealing partial cancellations and finite regions for remaining divergences, which can be managed with real correction phase-space mapping.

Contribution

It demonstrates a novel partial cancellation of singularities at the integrand level using the loop--tree duality approach, linking causality to singularity structure.

Findings

Partial cancellation of singularities among dual integrand components

Remaining divergences confined to finite loop momentum regions

Mapping of these regions to real correction phase-space for divergence cancellation

Abstract

We analyse the singular behaviour of one-loop integrals and scattering amplitudes in the framework of the loop--tree duality approach. We show that there is a partial cancellation of singularities at the loop integrand level among the different components of the corresponding dual representation that can be interpreted in terms of causality. The remaining threshold and infrared singularities are restricted to a finite region of the loop momentum space, which is of the size of the external momenta and can be mapped to the phase-space of real corrections to cancel the soft and collinear divergences.