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NLO cross sections in 4 dimensions without DREG

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 $γ^*\to q\bar{q}(g)$ process. A more detailed discussion related on this topic can be found in Ref [1].