Analysis of singularities and the four-dimensional representation of physical observables within the LTD formalism

TL;DR

This paper explores the application of the loop-tree duality theorem within the Four-Dimensional Unsubtraction formalism to analyze singularities in scattering amplitudes, aiming to improve calculations of physical observables.

Contribution

It introduces a novel approach combining LTD with FDU to better understand and handle singularities in loop amplitudes for higher-order computations.

Findings

Identification of regions responsible for infrared singularities

Analysis of threshold singularities in loop amplitudes

Framework extension towards NNLO calculations

Abstract

In the past years, we have been developing a novel technique, called Four-Dimensional Unsubtraction (FDU) which aims to obtain purely four-dimensional representations of the matrix elements contributing to physical observables. In this talk, we describe the application of the loop-tree duality (LTD) theorem to represent loop amplitudes in terms of tree-level like objects, focusing on the origin of possible singularities of scattering amplitudes. In particular, we analyze the regions responsible of infrared and threshold singularities. With this information, we aim to extend the FDU formalism to NNLO and beyond.