Constraints on the Up-Quark Valence Distribution in the Proton

The high-$x$ data from the ZEUS Collaboration are used to extract parton density distributions of the proton deep in the perturbative regime of QCD. The data primarily constrain the up-quark valence distribution and new results are presented on its $x$ dependence as well as on the momentum carried by the up quark. The results were obtained using Bayesian analysis methods which can serve as a model for future parton density extractions.

Figure 1

Predictions of event numbers calculated from sampling the posterior probability distribution of the fitted parameters (shaded bands) compared to the ZEUS data (filled dots) for $e^{-}p$ (left) and $e^{+}p$ scattering (right). The predictions and data are displayed at the center of the bins in which events are recorded. For clarity the boxes at large $x$ are shown enlarged in the insets.

Figure 2

Joint probability contours of the up-valence parameters $K_u$ and ${\mathrm{\Delta }}_u$ (lower left) and the marginal distributions of $K_u$ (top) and ${\mathrm{\Delta }}_u$ (lower right). Shown are the 68% and 95% smallest credible intervals for both the prior (light shaded) and posterior (dark shaded) distributions.

Figure 3

The valence distribution $x{u}^v$ and the effective ($1-x$) power $\beta$ from this analysis at a value of $Q^2=100{\mathrm{GeV}}^2$. The 68% smallest probability contour is depicted. The vertical range plotted in the inset summarizes the results on $\beta$ reported in [12].