#### Local Unitarity

Local Unitarity provides an order-by-order representation of perturbative cross-sections that realises at the local level the cancellation of final-state collinear and soft singularities predicted by the KLN theorem. The representation is obtained by manipulating the real and virtual interference diagrams contributing to transition probabilities using general local identities. As a consequence, the Local Unitarity representation can be directly integrated using Monte Carlo methods and without the need of infrared counter-terms. I will start by presenting the Cross-Free Family representation of loop integrals, a close relative of the Time-Ordered Perturbation Theory and Loop-Tree Duality representations, which reveals with unmatched clarity the singularity structure of Feynman diagrams. I will use this representation and the causal flow, a construct that allows to bypass the mappings common to subtraction methods, to obtain the Local Unitarity representation. Finally, I will show first results from this new approach with examples up to N3LO accuracy. I will conclude by giving an outlook on future generalisations of the method applicable to hadronic collisions.

*Wednesday, 14th December 2022, 14:30 — Sala Wataghin *