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

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.

9 pages, 1 eps figure; needs ws-ijmpcs.cls (supplied). Invited talk presented at the QCD Evolution Workshop, May 6 -10, 2013, Thomas Jefferson National Accelerator Facility, Newport News (VA), USA