We present a new method to compute higher-order corrections to physical cross-sections, at Next-to-Leading Order and beyond. This method, based on the Loop Tree Duality, leads to locally integrable expressions in four dimensions. By introducing a physically motivated momentum mapping between the momenta involved in the real and the virtual contributions, infrared singularities naturally cancel at integrand level, without the need to introduce subtraction counter-terms. Ultraviolet singularities are dealt with by using dual representations of suitable counter-terms, with some subtleties regarding the self-energy contributions. As an example, we apply this method to compute the $1\to2$ decay rate in the context of a scalar toy model with massive particles.

Presented at Diffraction 2016 Workshop, 2-8 September 2016, Acireale. 4 pages, 1 figure