QCD Factorization for Deep-Inelastic Scattering At Large Bjorken x(B) ~ 1 - O (Lambda(QCD)/Q)

Jul, 2006
15 pages
Published in:
  • Nucl.Phys.B 763 (2007) 183-197
e-Print:

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Abstract:
We study deep-inelastic scattering factorization on a nucleon in the end-point regime xB1O(ΛQCD/Q)x_B \sim 1-{\cal O}(\Lambda_{\rm QCD}/Q) where the traditional operator product expansion is supposed to fail. We argue, nevertheless, that the standard result holds to leading order in 1xB1-x_B due to the absence of the scale dependence on (1xB)Q(1-x_B)Q. Refactorization of the scale (1xB)Q2(1-x_B)Q^2 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 (1xB)Q(1-x_B)Q 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.
  • lepton nucleon: deep inelastic scattering
  • nucleon: structure function
  • quantum chromodynamics: perturbation theory
  • factorization
  • effective Lagrangian
  • Feynman graph: higher-order
  • structure function: moment
  • parton: momentum spectrum
  • light cone
  • gluon: radiation