[Paper Review] Small-x Physics, High Parton Densities and Parton Saturation in QCD

A.H. Mueller|ArXiv.org|Nov 9, 1999

Quantum Chromodynamics and Particle Interactions4 citations

TL;DR

This paper develops a theoretical framework for parton saturation in QCD at small x, using the Weizsäcker-Williams approximation and a large-Nc dipole formalism to derive the BFKL equation. It demonstrates that high gluon densities lead to saturation, with evidence suggested by HERA data, providing a non-perturbative mechanism to unitarize high-energy scattering amplitudes in deep inelastic scattering and hadronic collisions.

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.

Motivation & Objective

• To understand the dynamics of partons at small Bjorken-x, where parton densities become large.
• To develop a theoretical description of parton saturation in high-energy QCD processes.
• To connect the BFKL and DGLAP evolution equations within a large-Nc dipole formalism.
• To assess experimental signatures of saturation in deep inelastic scattering at HERA.
• To provide a framework for unitarizing high-energy scattering amplitudes via gluon saturation.

Proposed method

• Uses the Weizsäcker-Williams approximation for a large nucleus to model high parton density states.
• Applies the large-Nc limit to derive the BFKL equation in a dipole formalism, linking it to high-energy scattering.
• Formulates parton saturation in terms of dipole-nucleon or dipole-nucleus scattering amplitudes.
• Integrates DGLAP and BFKL evolution equations to describe parton density evolution at small x.
• Analyzes the saturation scale Qs(x) as a function of x, predicting a rise in gluon density until saturation occurs.
• Compares theoretical predictions with HERA data to search for signatures of saturation.

Experimental results

Research questions

• RQ1 How does parton saturation emerge in high-energy QCD at small x?
• RQ2 What is the role of the dipole formalism in describing saturation in the large-Nc limit?
• RQ3 How do DGLAP and BFKL evolution equations relate to the onset of saturation?
• RQ4 What experimental evidence for saturation can be found in HERA deep inelastic scattering data?
• RQ5 How does the saturation scale Qs(x) evolve with decreasing x?

Key findings

• The BFKL equation is derived in the large-Nc dipole formalism, providing a consistent framework for high-energy evolution.
• Parton saturation is shown to unitarize scattering amplitudes in high-energy hadronic and deep inelastic scattering.
• The saturation scale Qs(x) increases as x decreases, signaling the onset of high gluon density effects.
• Evidence for saturation is suggested by a flattening of the structure function F2 at small x in HERA data, consistent with saturation models.
• The dipole picture provides a unified description of saturation in both nucleon and nuclear targets.
• The Weizsäcker-Williams approximation successfully models the initial state of a large nucleus with high parton density.