Local Unitarity: a representation of differential cross-sections that is locally free of infrared singularities at any order

• Ben Ruijl (ETH Zurich)

One of the major challenges in computing higher-order corrections of collider observables is the treatment of infrared singularities. Local Unitarity is a novel representation of differential scattering cross-sections that locally realises the direct cancellation of infrared singularities exhibited by its so-called real-emission and virtual degrees of freedom. We take advantage of the Loop-Tree Duality representation of each individual forward-scattering diagram and we prove that the ensuing expression is locally free of infrared divergences, applies at any perturbative order and for any process without initial-state collinear singularities. Our representation is especially suited for a numerical implementation and we demonstrate its practical potential by computing fully numerically and without any IR counterterm the next-to-leading order accurate differential cross-section for the process e+ e− -> d d. We also show first results beyond next-to-leading order by computing interference terms part of the N4LO-accurate inclusive cross-section of a 1 -> 2 + X scalar scattering process.