A zero-dimensional model for high-energy scattering in QCD

2006/06/30 by Jean-Paul Blaizot, J. -P. Blaizot, Edmond Iancu +3 · 2 citations
Physics and Astronomy · #Color-glass condensate #Gluon #Hadron #High-Energy Particle Collisions Research #Mathematical physics #Matrix (chemical analysis) #Particle physics #Particle physics theoretical and experimental studies #Physics #Pomeron #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum electrodynamics #Quantum mechanics #Rapidity #Saturation (graph theory) #Scattering #hep-ph

paper · pdf · doi:10.1016/j.nuclphysa.2006.11.127

published as Nucl.Phys.A784:227-258,2007 · 34 pages, 9 figures. Some explanations added on the frame-dependence of the relevant configurations (new section 3.3)

arxiv created 2006/08/02 · openalex publication_date 2006/12/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We investigate a zero-dimensional toy model originally introduced by Mueller and Salam which mimics high-energy scattering in QCD in the presence of both gluon saturation and gluon number fluctuations, and hence of Pomeron loops. Unlike other toy models of the reaction-diffusion type, the model studied in this paper is consistent with boost invariance and, related to that, it exhibits a mechanism for particle saturation close to that of the JIMWLK equation in QCD, namely the saturation of the emission rate due to high-density effects. Within this model, we establish the dominant high-energy behaviour of the S-matrix element <Sⁿ> for the scattering between a target obtained by evolving one particle and a projectile made with exactly n particles. Remarkably, we find that all such matrix elements approach the black disk limit S=0 at high rapidity Y, with the same exponential law: <Sⁿ> ~ exp(-Y) for all values of n. This is so because the S-matrix is dominated by rare target configurations which involve only few particles. We also find that the bulk distribution for a saturated system is of the Poisson type.

Citations

• Nucleus–nucleus scattering in perturbative QCD with Nc→∞
• Solution for the BFKL pomeron calculus in zero transverse dimensions
• Wilson renormalization group for lowxphysics: Towards the high density regime
• Non linear gluon evolution in path-integral form
• Studies of unitarity at small x using the dipole formulation
• Universality and tree structure of high-energy QCD
• Traveling wave fronts and the transition to saturation
• The BFKL equation from the Wilson renormalization group
• Gluon distributions and color charge correlations in a saturated light-cone wavefunction
• High-energy effective action from scattering of QCD shock waves
• Unitarity at small Bjorken x
• Small-x physics beyond the Kovchegov equation
• Saturation and universality in QCD at small x
• Dense-dilute duality at work: Dipoles of the target
• Algebraic models for the hierarchy structure of evolution equations at small x
• The energy dependence of the saturation momentum
• Geometric Scaling as Traveling Waves
• On the projectile-target duality of the color glass condensate in the dipole picture
• Relating different approaches to nonlinear QCD evolution at finite gluon density
• Diffusive scaling and the high-energy limit of deep inelastic scattering in QCD at large
• Effective field theory for the small-x evolution

Cited by

• QCD unitarity constraints on Reggeon Field Theory
• Effects of gluon number fluctuations onγγcollisions at high energies