Effect of Orbital Angular Momentum on Valence-Quark Helicity Distributions

We study the quark helicity distributions at large $x$ in perturbative QCD, taking into account contributions from the valence Fock states of the nucleon which have nonzero orbital angular momentum. We find that the quark orbital angular momentum contributes a large logarithm to the negative helicity quark distributions in addition to its power behavior, scaling as $(1-x{)}^5{log}^2(1-x)$ in the limit of $x\to 1$. Our analysis shows that the ratio of the polarized over unpolarized down quark distributions, $\Delta d/d$, will still approach 1 in this limit. By comparing with the experimental data, we find that this ratio should cross zero at $x\approx 0.75$.

Figure 1

Examples of Feynman diagrams which contribute to the $q^{\pm }$ quark distributions at large $x$: (a) for $q^{+}$ with power contribution of $(1-x{)}^3$; (b) for $q^{-}$ with $(1-x{)}^5$; (c) for $q^{-}$ with $(1-x{)}^5{log}^2(1-x)$. The wave functions at the left and right sides of the cut line in (a) and (b) represent the leading Fock state expansion with zero quark orbital angular momentum, whereas those for (c) represent the valence Fock state with one-unit of quark orbital angular momentum.

Figure 2

Comparison of the quark helicity distributions Eq. (7) with the experimental data, plotted as functions of $x$ for up (the upper curves) and down (the lower curves) quarks. The circles are for HERMES data [11], the triangles up for SLAC [12], the triangles down for JLab Hall A data [9], the filled squares for CLAS [10]. The dashed curves are the predictions from [22], and the solid ones are our fit results (only the large-$x$ ($>0.3$) experimental data were used in the fit).