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