Proof of Factorization for Diffractive Hard Scattering
John C. Collins
TL;DR
This work establishes a rigorous hard-scattering factorization theorem for diffractive deep-inelastic scattering and related target-fragmentation processes, showing that diffractive cross sections factorize into convolutions of process-dependent hard coefficients with diffractive parton densities, which obey DGLAP evolution. The proof adapts the Collins-Soper-Wise/CS framework to diffractive settings by a careful treatment of soft-gluon cancellations, employing contour deformations to validate Ward-identity factorization for jets and treating initial-state soft exchanges via longitudinal contour analysis. It further extends the result to fracture-function formalisms, arguing that non-perturbative final-state interactions do not spoil factorization under the stated conditions. The conclusions emphasize that while the theorem underpins diffractive lepton-induced processes, it does not generally apply to hadron-hadron diffraction due to absorptive corrections, and it clarifies the role of the pomeron as a labeling device rather than a fundamental dynamical exchange within QCD.
Abstract
A proof is given that hard-scattering factorization is valid for deep-inelastic processes which are diffractive or which have some other condition imposed on the final state in the target fragmentation region.