Higher twist parton distributions from light-cone wave functions

TL;DR

The paper develops a framework to generate higher-twist parton distributions from overlaps of light-cone wave functions, focusing on valence qqq and qqqg Fock states with zero total orbital angular momentum and normalizing these WFs via QCD sum rules. It demonstrates that the resulting parton densities reproduce large-x behavior for both polarized and unpolarized gluons and constructs twist-3 quark–antiquark–gluon correlators, predicting the correct sign for g2 at large x and showing that gluon-pole contributions emerge only after QCD evolution. The analysis shows that twist-3 observables are sensitive to the interference between Fock sectors and that radiative evolution can generate soft-pole contributions consistent with GRV-type dynamics, though magnitudes depend on the starting scale and Fock-content. While offering valuable insight into higher-twist structure, the study acknowledges limitations from truncating the Fock space and hints at extensions with additional partonic components to improve small-x behavior and phenomenology.

Abstract

We explore the possibility to construct higher-twist parton distributions in a nucleon at some low reference scale from convolution integrals of the light-cone wave functions (WFs). To this end we introduce simple models for the four-particle nucleon WFs involving three valence quarks and a gluon with total orbital momentum zero, and estimate their normalization (WF at the origin) using QCD sum rules. We demonstrate that these WFs provide one with a reasonable description of both polarized and unpolarized gluon parton densities at large values of Bjorken variable x > 0.5. Twist-three parton distributions are then constructed as convolution integrals of qqqg and usual three-quark WFs. The cases of the polarized structure function g_2(x,Q^2) and single transverse spin asymmetries are considered in detail. We find that the so-called gluon-pole contribution to twist-three distributions relevant for single spin asymmetry vanishes in this model, but is generated perturbatively at higher scales by the evolution, in the spirit of GRV parton distributions.

Figures (10)

• Figure 1: Quark and gluon parton distributions. The black curves correspond to the existing parametrizations: GRV Gluck:1998xa (short dashes), DSSV deFlorian:2009vb (long dashes) and LSS'10 Leader:2010rb (dash-dotted) at the scale $\mu^2=1GeV^2$Cafarella:2003jr. The solid blue curve is our model prediction taking into account the contributions of the valence three-quark state and the state involving one additional gluon. The contribution of the valence state alone is shown by dots for comparison.
• Figure 2: The quark transversity distribution $\delta q(x)$. The solid blue curve is our model prediction taking into account the contributions of the valence three-quark state and the state involving one additional gluon. The contribution of the valence state alone is shown by dots for comparison. The Soffer bound (\ref{['eq:Soffer']}) is indicated by the (magenta) dashed curve.
• Figure 3: Twist-three correlation functions from the overlap of light-cone wave functions.
• Figure 4: Support properties of twist-three correlation functions in barycentric coordinates. For the explanation of different regions see text.
• Figure 5: The quark-antiquark-gluon twist-three correlation function $\mathcal{Q}_{d}^+(x)$ at the reference scale 1 GeV.