Four-dimensional regularization of higher-order computations: FDU approach

TL;DR

This paper introduces a novel four-dimensional regularization method for higher-order computations using the loop-tree duality theorem, enabling local cancellation of divergences without counter-terms or dimensional regularization.

Contribution

It presents a new regularization framework that combines real and virtual contributions at the integrand level, simplifying divergence handling in quantum field theory calculations.

Findings

Achieves local infrared divergence cancellation without counter-terms.

Handles both infrared and ultraviolet divergences without dimensional regularization.

Demonstrates implementation on physical processes.

Abstract

We have recently proposed a new regularization framework based on the loop-tree duality theorem. This theorem allows to rewrite loop level amplitudes in terms of tree-level structures and phase-space integrations. In consequence, it is possible to combine naturally real and virtual contributions at integrand level. Moreover, through the introduction of a proper momentum-mapping, a complete local cancellation of infrared singularities is achieved, by-passing the necessity of counter-terms. In this article, we briefly explain the implementation of this novel approach to compute some physical processes, and we show how to deal with both infrared and ultraviolet divergences without using DREG.