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High-Energy QCD and Wilson Lines

I. Balitsky

TL;DR

This work develops a Wilson-line, shock-wave framework for high-energy QCD, arguing that fast gluons are naturally described by gauge-invariant Wilson lines along their nearly light-like trajectories. It formulates a high-energy operator product expansion in rapidity, derives the BFKL kernel from Wilson-line evolution, and explains how nonlinear evolution unitarizes the pomeron, including dipole and large-N_c Reggeon dynamics. The paper also introduces an explicit factorization formula and an effective action for a given rapidity interval, and develops both perturbative and semiclassical approaches in sQCD for collisions of shock waves. Together, these results provide a unified, gauge-invariant description of forward and diffractive high-energy scattering, linking perturbative BFKL dynamics to nonlinear saturation phenomena with potential applications to heavy-ion collisions and small-x physics.

Abstract

At high energies the particles move very fast so their trajectories can be approximated by straight lines collinear to their velocities. The proper degrees of freedom for the fast gluons moving along the straight lines are the Wilson-line operators -- infinite gauge factors ordered along the straight line. I review the study of the high-energy scattering in terms of Wilson-line degrees of freedom.

High-Energy QCD and Wilson Lines

TL;DR

This work develops a Wilson-line, shock-wave framework for high-energy QCD, arguing that fast gluons are naturally described by gauge-invariant Wilson lines along their nearly light-like trajectories. It formulates a high-energy operator product expansion in rapidity, derives the BFKL kernel from Wilson-line evolution, and explains how nonlinear evolution unitarizes the pomeron, including dipole and large-N_c Reggeon dynamics. The paper also introduces an explicit factorization formula and an effective action for a given rapidity interval, and develops both perturbative and semiclassical approaches in sQCD for collisions of shock waves. Together, these results provide a unified, gauge-invariant description of forward and diffractive high-energy scattering, linking perturbative BFKL dynamics to nonlinear saturation phenomena with potential applications to heavy-ion collisions and small-x physics.

Abstract

At high energies the particles move very fast so their trajectories can be approximated by straight lines collinear to their velocities. The proper degrees of freedom for the fast gluons moving along the straight lines are the Wilson-line operators -- infinite gauge factors ordered along the straight line. I review the study of the high-energy scattering in terms of Wilson-line degrees of freedom.

Paper Structure

This paper contains 30 sections, 321 equations, 40 figures.

Table of Contents

  1. Introduction
  2. The hard pomeron in pQCD
  3. High-energy $\gamma^\ast\gamma^\ast$ scattering
  4. The BFKL kernel
  5. Bare pomeron in the LLA
  6. Diffusion in the transverse momentum and the BFKL equation with running coupling constant
  7. Reggeized gluons and unitarization of the pomeron
  8. Operator expansion for high-energy scattering
  9. High-energy OPE vs light-cone expansion
  10. High-energy asymptotics as a scattering from the shock-wave field.
  11. Regularized Wilson-line operators
  12. One-loop evolution of Wilson-line operators.
  13. BFKL pomeron from the evolution of the Wilson-line operators
  14. Non-linear evolution of Wilson lines
  15. Operator expansion for diffractive high-energy scattering
  16. ...and 15 more sections

Figures (40)

  • Figure 1: Propagator of a fast "A" gluon in the slow "B" background.
  • Figure 2: Gluon of "B" type viewed from the rest frame of "A" gluons.
  • Figure 3: A typical Feynman diagram for the high-energy $\gamma^*\gamma^*$ scattering.
  • Figure 4: Lowest-order diagrams for the high-energy scattering of virtual photons.
  • Figure 5: Photon impact factor.
  • ...and 35 more figures