Factorisation and Subtraction beyond NLO
Lorenzo Magnea, Ezio Maina, Giovanni Pelliccioli, Chiara Signorile-Signorile, Paolo Torrielli, Sandro Uccirati
TL;DR
This work introduces a universal, all-orders framework for local infrared subtraction by exploiting the factorised structure of virtual IR corrections, defining radiative eikonal form factors and jet functions fully differential in the radiation phase space. By constructing soft and collinear local counterterms from gauge-invariant Wilson-line operators and employing completeness relations, it reproduces known NLO and NNLO results and lays out a principled path toward higher-order subtraction algorithms. The paper provides explicit soft- and collinear-counterterm structures and applies them to NLO and NNLO for massless final-state radiation, while outlining extensions to initial states, massive partons, Glauber issues, and N3LO. This approach promises a clearer, more efficient organization of subtraction schemes at future perturbative orders.
Abstract
We provide a general method to construct local infrared subtraction counterterms for unresolved radiative contributions to differential cross sections, to any order in perturbation theory. We start from the factorised structure of virtual corrections to scattering amplitudes, where soft and collinear divergences are organised in gauge-invariant matrix elements of fields and Wilson lines, and we define radiative eikonal form factors and jet functions which are fully differential in the radiation phase space, and can be shown to cancel virtual poles upon integration by using completeness relations and general theorems on the cancellation of infrared singularities. Our method reproduces known results at NLO and NNLO, and yields substantial simplifications in the organisation of the subtraction procedure, which will help in the construction of efficient subtraction algorithms at higher orders.