NLO cross sections in 4 dimensions without DREG

TL;DR

This paper introduces a novel method for calculating NLO QCD cross sections directly in four dimensions using Loop-Tree Duality, avoiding Dimensional Regularisation, and demonstrates its application to a specific process.

Contribution

The paper presents a new Loop-Tree Duality based algorithm for NLO calculations in 4D without DREG, enabling direct phase-space integration of loop and real contributions.

Findings

Successfully computes NLO cross sections in 4D without DREG.

Applies the method to the $ o qar{q}(g)$ process.

Provides a framework for future NLO calculations in four dimensions.

Abstract

In this review, we present a new method for computing physical cross sections at NLO accuracy in QCD without using the standard Dimensional Regularisation. The algorithm is based on the Loop-Tree Duality theorem, which allow us to obtain loop integrals as a sum of phase-space integrals; in this way, transforming loop integrals into phase-space integrals, we propose a method to merge virtual and real contributions in order to find observables at NLO in $d=4$ space-time dimensions. In addition, the strategy described is used for computing the $\gamma^*\to q\bar{q}(g)$ process. A more detailed discussion related on this topic can be found in Ref [1].