Next-to-soft factorization and unitarity in Drell-Yan processes

The Drell-Yan process is considered as a case study to investigate two different aspects of perturbative Quantum Chromodynamics: the search for a next-to-soft factorization formalism to organize next-to-leading-power (NLP) threshold logarithms to all orders, and the development of new methods based on unitarity to efficiently compute fixed-order cross-sections of single-particle inclusive processes.
Specifically, considering the abelian part of the real-virtual interference diagrams of the two-loop Drell-Yan K-factor, next-to-soft corrections are studied with three different approaches: the use of diagrammatic techniques, the method of regions, and an approach based on the soft-collinear factorization formula. In this investigation special care is needed for collinear effects, which lead to the definition of a radiative jet function, computed here for the first time at one-loop. The final result of this analysis is a full control of abelian-like NLP logarithms that paves the way for a full resummation formalism.
For what concerns unitarity methods, the formulation in Mellin space of the optical theorem for Deep Inelastic Scattering is generalized to the Drell-Yan case through a diagram-by-diagram approach based on unitary cuts. Crucial to this analysis is the removal of unphysical cuts by means of diagram-independent prescriptions in Mellin space. This approach offers an alternative method to compute the NNLO Drell-Yan cross-section and seems a promising tool for the computation of inclusive cross-sections at NNNLO.