QED and QCD self-energy corrections through the loop-tree duality

TL;DR

This paper develops a method to compute self-energy corrections in QED and QCD using the loop-tree duality formalism, enabling local cancellation of singularities and facilitating more efficient scattering amplitude calculations.

Contribution

It provides explicit calculations of scalar functions for self-energy corrections in QED and QCD within the LTD framework, including their UV behavior.

Findings

Explicit LTD representations of self-energy corrections in QED and QCD.

Demonstration of UV behavior of the scalar functions.

Facilitation of local singularity cancellation in scattering amplitudes.

Abstract

The loop-tree duality (LTD) theorem establishes that loop contributions to scattering amplitudes can be computed through dual integrals, which are build from single cuts of the virtual diagrams. In order to build a complete LTD representation of a cross section and to achieve a local cancellation of singularities, it is crucial to include the renormalized self-energy corrections in an unintegrated form. In this document, we calculate the scalar functions related to the self-energy corrections in QED and QCD in the LTD formalism and extract explicitly their UV behaviour.