QCD factorization for deep-inelastic scattering at large Bjorken xB∼1−O(ΛQCD/Q)

We study deep-inelastic scattering factorization on a nucleon in the end-point regime xB∼1−O(ΛQCD/Q) where the traditional operator product expansion is supposed to fail. We argue, nevertheless, that the standard result holds to leading order in 1−xB due to the absence of dependence on the scale Q2(1−xB)2. Refactorization at the scale Q2(1−xB) in the coefficient function can be made in the soft-collinear effective theory and remains valid in the end-point regime. On the other hand, the traditional refactorization approach that relies on gauge dependent quantities, introduces the spurious scale Q2(1−xB)2 in various factors, which drives them nonperturbative in the region of our interest. We show how to improve the situation by introducing a rapidity cutoff scheme, and how to recover the effective theory refactorization by choosing appropriately the cutoff parameter. Through a one-loop calculation, we demonstrate explicitly that the proper soft subtractions must be made in the collinear matrix elements to avoid double counting of soft contributions.