Parton distributions in the shockwave formalism

Abstract

In this work, we calculate a broad class of parton distributions - including parton distribution functions (PDFs), transverse-momentum-dependent distributions (TMDs), generalized parton distributions (GPDs), generalized transverse-momentum-dependent distributions (GTMDs), and diffractive parton distributions - directly from their operator-level definition in the shockwave approximation for the target nucleon. This approximation is valid in the high-energy limit of scattering, corresponding to the small-$x$ regime. The shockwave framework allows us to employ the eikonal approximation and express the parton distributions in terms of Wilson-line correlators, naturally formulated within the color-glass condensate effective field theory. We present a comprehensive set of Feynman rules for evaluating parton distributions in this limit, and demonstrate how they can be systematically applied to calculate all phenomenologically relevant leading-twist parton distributions at leading order. This work establishes a unified starting point for future studies that aim to bridge the color-glass condensate approach with the partonic description of the nucleon.

Comments: 50 pages, 11 figures; v2: added clarifying discussion, fixed typos, matches published version