Evolution of transverse-distance dependent parton densities at large-$x_B$ and geometry of the loop space

TL;DR

This paper explores how the geometrical evolution of Wilson loops relates to the behavior of transverse-distance dependent parton densities at large Bjorken-x, with implications for upcoming experimental programs at Jefferson Lab and the Electron-Ion Collider.

Contribution

It introduces a novel connection between Wilson loop equations of motion and the evolution of TDD parton densities at large-x, relevant for future experimental analyses.

Findings

Wilson loop evolution corresponds to rapidity and RG equations of TDDs.

Geometrical evolution provides insights into large-x parton dynamics.

Applicable to upcoming Jefferson Lab and Electron-Ion Collider experiments.

Abstract

We discuss possible applications of the equations of motion in the generalized Wilson loop space to the phenomenology of the three-dimensional parton distribution functions in the large-$x_B$ approximation. This regime is relevant for future experimental programs to be launched at the (approved) Jefferson Lab 12 GeV upgrade and the (planned) Electron-Ion Collider. We show that the geometrical evolution of the Wilson loops corresponds to the combined rapidity and renormalization-group equation of the transverse-distance dependent parton densities in the large-$x_B$ factorization scheme.