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QCD evolution of the gluon density in a nucleus

A. L. Ayala, M. B. Gay Ducati, E. M. Levin

TL;DR

This work develops a QCD-based Glauber framework (Mueller formula) for the gluon density in a nucleus, quantifying shadowing corrections using the nucleon GRV gluon input. It demonstrates that shadowing is crucial at small x and significantly alters the nuclear gluon density and its anomalous dimension compared to the nucleon, while remaining under theoretical control in the double-log approximation. The authors derive a generalized evolution equation beyond the GLR approach, solve it in a semiclassical limit, and show that the resulting shadowing strengthens with A and x-dependence persists without true saturation, offering a potential bridge between soft high-energy phenomenology and hard QCD. They also discuss the limitations of the Glauber approach, the need for higher-order and nucleus-specific initial data, and the way forward to a more complete description including running coupling and all-parton correlations.

Abstract

The Glauber approach to the gluon density in a nucleus, suggested by A. Mueller, is developed and studied in detail. Using the GRV parameterization for the gluon density in a nucleon, the value as well as energy and $Q^2$ dependence of the gluon density in a nucleus is calculated. It is shown that the shadowing corrections are under theoretical control and are essential in the region of small $x$. They change crucially the value of the gluon density as well as the value of the anomalous dimension of the nuclear structure function, unlike of the nucleon one. The systematic theoretical way to treat the correction to the Glauber approach is developed and a new evolution equation is derived and solved. It is shown that the solution of the new evolution equation can provide a selfconsistent matching of ``soft" high energy phenomenology with ``hard" QCD physics.

QCD evolution of the gluon density in a nucleus

TL;DR

This work develops a QCD-based Glauber framework (Mueller formula) for the gluon density in a nucleus, quantifying shadowing corrections using the nucleon GRV gluon input. It demonstrates that shadowing is crucial at small x and significantly alters the nuclear gluon density and its anomalous dimension compared to the nucleon, while remaining under theoretical control in the double-log approximation. The authors derive a generalized evolution equation beyond the GLR approach, solve it in a semiclassical limit, and show that the resulting shadowing strengthens with A and x-dependence persists without true saturation, offering a potential bridge between soft high-energy phenomenology and hard QCD. They also discuss the limitations of the Glauber approach, the need for higher-order and nucleus-specific initial data, and the way forward to a more complete description including running coupling and all-parton correlations.

Abstract

The Glauber approach to the gluon density in a nucleus, suggested by A. Mueller, is developed and studied in detail. Using the GRV parameterization for the gluon density in a nucleon, the value as well as energy and dependence of the gluon density in a nucleus is calculated. It is shown that the shadowing corrections are under theoretical control and are essential in the region of small . They change crucially the value of the gluon density as well as the value of the anomalous dimension of the nuclear structure function, unlike of the nucleon one. The systematic theoretical way to treat the correction to the Glauber approach is developed and a new evolution equation is derived and solved. It is shown that the solution of the new evolution equation can provide a selfconsistent matching of ``soft" high energy phenomenology with ``hard" QCD physics.

Paper Structure

This paper contains 23 sections, 146 equations, 25 figures, 1 table.

Table of Contents

  1. Introduction.
  2. The Glauber approach in QCD .
  3. Passage of the $\bar{q} q$ ($G G$) pair through the target
  4. $\sigma(r_{t},q^2_{t})$ at $q_{t}$ = 0.
  5. The $b_{t}$ dependence of the scattering amplitude with a nucleon
  6. The $q_z$ dependence of nucleon density (gluon lifetime cutoff).
  7. The wave function of virtual gluon.
  8. The Mueller formula.
  9. An instructive example.
  10. Theory status of the Mueller formula.
  11. pQCD calculations from the Mueller formula.
  12. The gluon structure function for nucleon.
  13. The gluon structure function for nucleus.
  14. The behavior of $\alpha_s$.
  15. Beyond the Glauber Approach.
  16. ...and 8 more sections

Figures (25)

  • Figure 1: The structure of the parton cascade in the Glauber formula. $A$ denotes the nucleus, N - the nucleon, $G^{*}(Q^2)$ - the virtual gluon and $\sigma_N (r^2_t)$ is the nucleon cross section.
  • Figure 2:
  • Figure 3: The structure of parton cascade in the Glauber ( Mueller ) formula.
  • Figure 4: The vertex of a virtual colorless probe ( $Q^*$ ) to two gluons.
  • Figure 5: The interaction with nucleons that is not taken into account in the Glauber ( Mueller) formula.
  • ...and 20 more figures