Matching collinear factorization with color-glass condensate for inclusive and exclusive deep inelastic scattering

Collinear factorization and color-glass condensate (CGC) effective field theory are generally treated as separate approaches for calculating scattering amplitudes, valid in different kinematic regimes. For deep inelastic scattering at high photon virtuality and high center-of-mass energy, however, both of these approaches should be applicable. By expressing collinear parton distributions and generalized parton distributions in the shockwave approximation, we show that the resulting collinear-factorization amplitudes exactly reproduce the large-$Q^2$ expansion of CGC amplitudes for inclusive deep inelastic scattering, deeply virtual Compton scattering, and deeply virtual meson production. The matching holds directly at the amplitude level and includes both logarithmically enhanced and finite contributions. Our results establish the consistency between collinear factorization and the CGC in their common region of validity, clarify the origin of large momentum logarithms within the CGC framework, and provide a path toward combining high-energy and collinear evolution in a unified description of hadronic structure at small $x$ and large momentum scales.