Paper
QCD Factorization for Deep-Inelastic Scattering At Large Bjorken $x_B \sim 1-{\cal O}(Λ_{\rm QCD}/Q$
Authors
Abstract
We study deep-inelastic scattering factorization on a nucleon in the end-point regime where the traditional operator product expansion is supposed to fail. We argue, nevertheless, that the standard result holds to leading order in due to the absence of the scale dependence on . Refactorization of the scale 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 introduces the spurious scale in various factors, which drives them nonperturbative in the region of our interest. We show how to improve the situation by introducing a rapidity cut-off scheme, and how to recover the effective theory refactorization by choosing appropriately the cut-off 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.