From dimensional regularization to NLO computations in four dimensions

TL;DR

This paper reviews the Loop-tree duality method, which simplifies NLO computations by expressing virtual contributions as phase-space integrals, enabling four-dimensional regularization and clearer understanding of infrared singularities.

Contribution

It introduces a novel application of LTD to regularize Feynman integrals at integrand level, facilitating four-dimensional NLO calculations and physical interpretation of infrared divergences.

Findings

LTD expresses virtual contributions as phase-space integrals.

The method allows four-dimensional limit of regularized integrals.

Infrared singularities are naturally interpreted and canceled.

Abstract

Loop-tree duality (LTD) allows to express virtual contributions in terms of phase-space integrals, thus leading to a direct mapping with real radiation terms. We review the basis of the method and describe its application to regularize Feynman integrals. Performing an integrand-level combination of real and virtual terms, we show how to recover physical results by simply taking the four-dimensional limit of $d$-dimensional expressions. Moreover, this method provides a natural physical interpretation of infrared singularities, their origin and the way that they cancel in the complete computation.