Quantum chromodynamics factorization theorem in limit of the large x

The quantum chromodynamics (QCD) factorizatin theorem is considered for high-energy scattering in the limit of large x, with the main focus being deep inelastic scattering (DIS). Using the extensible parton distribution function (PDF) for large x, we derive the QCD factorization theorem for DIS. The PDF in the limited x → 1 consists of collinear and soft interactions, which are not factrorizable further because subleading spectator soft-collinear interactions are indispensable. This fact also indicates that the PDF at large x should be suppressed by some powers of (1 - x). With the extensible PDF, we considered the factorization theorem for the Drell-Yan process in the limit of large x, which might break down because of the nonfactorizable soft interactions.