Partonic Picture of Nuclear Shadowing at Small x

TL;DR

This work develops a coherent, perturbative QCD-based picture of nuclear shadowing at small $x$ by combining the Glauber multiple-scattering framework with a double-logarithm approximation (DLA) for the nucleon gluon density, constrained by HERA data on $F_2^N$. It demonstrates that quark shadowing results from an interplay of soft and semihard QCD dynamics, while gluon shadowing is largely perturbative and becomes robust for $Q^2$ above a semihard scale $Q_{ m SH}^2\approx 3$ GeV$^2$, largely independent of initial conditions. The paper provides explicit formulas for both quark and gluon shadowing in the Glauber model, clarifies the role of coherence length, and analyzes the impact-parameter dependence, highlighting non-linear modifications to the nuclear parton densities. These results have practical implications for predicting minijet and quarkonium production in central nucleus–nucleus collisions, where accurate, parameter-free gluon shadowing is essential.

Abstract

We investigate the nuclear shadowing mechanism in the context of perturbative QCD and the Glauber multiple scattering model. Using recent HERA data on nucleon structure function at small $x$, we put stringent constrains on the nucleon gluon density in the double-logarithm approximation. We suggest that the scaling violation of the nucleon structure function in the region of small $x$ and semihard scale $Q^2$ can be reliably described by perturbative QCD which is a central key to the understanding of the scale dependence of the nuclear shadowing effect. Our results indicate that while the shadowing of the quark density arises from an interplay between the ``soft'' and semihard QCD processes, the gluon shadowing is largely driven by a perturbative shadowing mechanism. We demonstrate that the gluon shadowing is a robust phenomenon at large $Q^2$ and can be unambiguously predicted by perturbative QCD.

Figures (9)

• Figure 1: The perturbative diagrams giving rise to the $q\bar{q}$ pair fluctuation.
• Figure 2: The $Q^2$-dependence of the nucleon structure function calculated using the DLA and compared with experiment data [24].
• Figure 3: The $x$-dependence of the nucleon structure function calculated using the DLA and compared with the experiment data.
• Figure 4: The $x$-dependence of nuclear quark shadowing ratio $R_q=F_2^A/(AF_2^N)$ at various $Q^2$ for $^{208}$Pb and $^{40}$Ca. The lower panels represent the parameterizations of initial shadowing ratios evolved to the experimental $\langle Q^2\rangle_{\rm exp}$ values. The non-saturation of $R_q(x)$ as $x$ decreases at large $Q^2$ is the feature of the perturbative shadowing mechanism.
• Figure 5: The $Q^2$-dependence of nuclear quark shadowing ratio $R_q=F_2^A/(AF_2^N)$ at $x=10^{-4}$ for $^{208}$Pb.