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Small-x Physics, High Parton Densities and Parton Saturation in QCD

A. H. Mueller

TL;DR

The paper investigates small-x QCD dynamics and gluon saturation by connecting a quantum light-cone parton description to a semi-classical non-Abelian Weizsäcker-Williams field. It develops DGLAP and BFKL evolution within a dipole framework and introduces the McLerran-Venugopalan model to describe saturated gluon fields in large nuclei, deriving a saturation scale Q_s that governs unitarity limits. The work then ties these concepts to phenomenology, showing how saturation can reconcile DIS data, diffractive processes, and nuclear scattering with unitarity constraints, and highlighting the Golec-Biernat-Wusthoff model as an effective phenomenological realization. Overall, it provides a coherent framework linking fundamental small-x dynamics to experimental observables and establishes saturation as a central organizing principle in high-density QCD.

Abstract

Partons are defined as the quanta in a Fock space description of a hadron. Gluon saturation is described in the Weizsäcker-Williams approximation for a large nucleus. The elements of DGLAP and BFKL evolution are given with the BFKL equation derived in a large-$N_c$ dipole formalism. A more general discussion of saturation is given in terms of a dipole scattering on a nucleon or nucleus. Possible evidence for saturation at HERA is discussed.

Small-x Physics, High Parton Densities and Parton Saturation in QCD

TL;DR

The paper investigates small-x QCD dynamics and gluon saturation by connecting a quantum light-cone parton description to a semi-classical non-Abelian Weizsäcker-Williams field. It develops DGLAP and BFKL evolution within a dipole framework and introduces the McLerran-Venugopalan model to describe saturated gluon fields in large nuclei, deriving a saturation scale Q_s that governs unitarity limits. The work then ties these concepts to phenomenology, showing how saturation can reconcile DIS data, diffractive processes, and nuclear scattering with unitarity constraints, and highlighting the Golec-Biernat-Wusthoff model as an effective phenomenological realization. Overall, it provides a coherent framework linking fundamental small-x dynamics to experimental observables and establishes saturation as a central organizing principle in high-density QCD.

Abstract

Partons are defined as the quanta in a Fock space description of a hadron. Gluon saturation is described in the Weizsäcker-Williams approximation for a large nucleus. The elements of DGLAP and BFKL evolution are given with the BFKL equation derived in a large- dipole formalism. A more general discussion of saturation is given in terms of a dipole scattering on a nucleon or nucleus. Possible evidence for saturation at HERA is discussed.

Paper Structure

This paper contains 18 sections, 104 equations, 13 figures.

Table of Contents

  1. Introduction: Partons,classical fields and a simple picture of saturation
  2. The field and gluon distribution in a quark
  3. The gluon field and distribution in a proton
  4. Non-Abelian Weizsäcker-Williams field and gluon saturation
  5. Interpreting saturation in the McLerran-Venugopalan modelMc
  6. DGLAP and BFKL evolution
  7. DGLAP evolution in the leading logarithnmic approximation
  8. The diple picture of BFKL evolution[10-12]
  9. Lowest order
  10. One soft gluon in the wavefunction
  11. Arbitrary numbers of soft gluons
  12. Scattering in the BFKL approximation
  13. Phenomenology
  14. Soft hadron-hadron scattering[14,15]
  15. Saturation of parton densities and unitarity
  16. ...and 3 more sections

Figures (13)

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  • ...and 8 more figures