Transverse Structure of Nucleon Parton Distributions from Lattice QCD

TL;DR

Using lattice QCD, the authors compute the first three moments (n=1–3) of spin-averaged and spin-polarized generalized parton distributions in the proton by extracting generalized form factors A_{n0}(t) and \tilde{A}_{n0}(t). They apply Burkardt's impact-parameter interpretation at xi=0 to relate t-dependence to the transverse spatial distribution q(x,b_perp) and demonstrate that the slope of these form factors decreases substantially with increasing n, implying the transverse size of the light-cone quark distribution shrinks as x grows. The results, obtained on unquenched SESAM lattices with heavy pion masses, reveal strong x- and flavor- and spin-dependent transverse structure and argue against a simple factorization H(x,0,t)=Q(x)F(t). The study sets the stage for future work at lighter quark masses, incorporating disconnected contributions, and performing controlled chiral extrapolations to connect first-principles moments to physical nucleon structure.

Abstract

This work presents the first calculation in lattice QCD of three moments of spin-averaged and spin-polarized generalized parton distributions in the proton. It is shown that the slope of the associated generalized form factors decreases significantly as the moment increases, indicating that the transverse size of the light-cone quark distribution decreases as the momentum fraction of the struck parton increases.

Figures (1)

• Figure 1: Normalized lattice results for generalized form factors $A_{n0}$ and $\tilde{A}_{n0}$ as a function of momentum transfer squared, $-t$, for n=1 (circles), 2 (triangles), and 3 (squares).