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In this talk, we review the basis of the loop-tree duality theorem, whichallows to rewrite loop scattering amplitudes in terms of tree-level likeobjects. Since the loop measure is converted into a phase-space one, bothvirtual and real contributions are expressible using the same integrationvariables. A physically motivated momentum mapping allows to generate the realemission process starting from the Born kinematics and the loop momenta. Theintegrand-level combination leads to regular functions, which can be integratedwithout using dimensional regularization (DREG) and correctly reproduce thefinite higher-order corrections to physical observables. We explain theimplementation of this novel approach to compute some benchmark physicalprocesses, and we show how to deal with both infrared and ultravioletdivergences in four space-time dimensions.

Towards regularized higher-order computations in QFT without DREG