Impact Parameter Dependent Parton Distributions and Off-Forward Parton Distributions for $ζ\to 0$

TL;DR

This work analyzes off-forward parton distributions at ζ=0 and shows they encode a simultaneous distribution of light-cone momentum and transverse position, accessible via the Fourier transform with respect to transverse momentum transfer. By examining both nonrelativistic and infinite-momentum-frame limits, the authors show that f(x,b_perp) emerges as the impact-parameter dependent density, with a clean interpretation in the IMF where only diagonal Fock-space overlaps contribute. The Q^2 evolution reduces to standard DGLAP for ζ=0, preserving the impact-parameter structure under scale changes. The results provide a practical link between measurable t-dependence and three-dimensional parton structure, aiding modeling, phenomenology, and lattice studies, and extend naturally to spin-dependent distributions.

Abstract

It is shown that off-forward parton distributions for $ζ=0$, i.e. where the initial and final state differ only in their transverse momenta, can be interpreted as a simultaneous measurement of the longitudinal momentum and transverse position (impact parameter) of partons in the infinite momentum frame.