QCD Constrains on the Shape of Polarized Quark and Gluon Distributions

TL;DR

The authors develop simple, constraint-driven analytic representations of polarized quark and gluon distributions at a bound-state scale, incorporating color-coherence at small x and helicity-retention at large x to fix the shapes with a minimal parameter set. By enforcing axial and SU(3) sum rules and PQCD counting rules, they produce explicit Δq(x), q(x), ΔG(x), and G(x) forms that predict sizable gluon polarization and strong correlations between nucleon helicity and its partonic constituents. The resulting distributions reproduce key moments (e.g., Δu, Δd, Δs, ΔΣ) and yield g1 structure functions compatible with polarized DIS data while providing consistent Bjorken sum-rule behavior. These low-Q^2 inputs can seed PQCD evolution and offer testable predictions for polarized structure functions and the x-dependence of spin fractions in the nucleon.

Abstract

We develop simple analytic representations of the polarized quark and gluon distributions in the nucleon at low $Q^2$ which incorporate general constraints obtained from the requirements of color coherence of gluon couplings at $x \sim 0$ and the helicity retention properties of perturbative QCD couplings at $x \sim 1.$ The unpolarized predictions are similar to the $D_0'$ distributions given by Martin, Roberts, and Stirling. The predictions for the quark helicity distributions are compared with polarized structure functions measured by the E142 experiment at SLAC and the SMC experiment at CERN.