Infrared Scales and Factorization in QCD

Abstract

Effective field theory methods are used to study factorization of the deep inelastic scattering cross-section. The cross-section is shown to factor in QCD, even though it does not factor in perturbation theory for some choices of the infrared regulator. Messenger modes are not required in soft-collinear effective theory for deep inelastic scattering as x -> 1.

Figures (2)

• Figure 1: Box diagram contributing to deep-inelastic photon-gluon scattering via the process $\gamma^* + g \to q + \bar{q}$. The total cross-section is given by the imaginary part of the diagram. The wavy lines are the high-$Q^2$ virtual photon, and the helical lines are the gluon target.
• Figure 2: Graph contributing to the gluon matrix element of the quark distribution function. The two $\otimes$ and the dashed line denote the insertion of the bilocal operator $O_{\Delta q}$ defined in Eq. (\ref{['6']}). Graphs where the gluons connect to the Wilson line (the dashed line) vanish for the polarized parton distribution function.