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

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 <S^n> 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: <S^n> ~ 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.

34 pages, 9 figures. Some explanations added on the frame-dependence of the relevant configurations (new section 3.3)

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• Diffractive dissociation including pomeron loops in zero transverse dimensions

Cited by in corpus (26)

• Small-x Dipole Evolution Beyond the Large-N_c Limit
• The BFKL Pomeron Calculus in zero transverse dimensions: summation of Pomeron loops and generating functional for the multiparticle production processes
• On possible implications of gluon number fluctuations in DIS data
• Pomeron loop and running coupling effects in high energy QCD evolution
• On the equivalence of Reggeon field theory in zero transverse dimensions and reaction-diffusion processes
• Quantum chromodynamics at high energy and statistical physics
• Reaction-diffusion processes in zero transverse dimensions as toy models for high-energy QCD
• QCD unitarity constraints on Reggeon Field Theory
• Regge Field Theory in zero transverse dimensions: loops versus "net" diagrams
• CGC formalism with two sources
• Total gluon shadowing due to fluctuation effects
• The JIMWLK evolution and the s-channel unitarity
• Nuclei in the toy world: beyond the Pomeron in zero transverse dimensions
• On the Dipole Swing and the Search for Frame Independence in the Dipole Model
• On asymptotic solutions of RFT in zero transverse dimensions
• On the High Energy Behaviour of The Total Cross Section in the QCD Dipole Model
• High energy scattering in Einstein-Cartan gravity
• On QCD RFT corrections to the propagator of reggeized gluons
• Dipole-dipole scattering amplitude in CGC approach
• On the anomalous dimensions of the multiple pomeron exchanges
• Nuclear scattering configurations of onia in different frames
• Running coupling and pomeron loop effects on inclusive and diffractive DIS cross sections
• Soft Pomeron in the Colour Glass Condensate approach
• Effects of gluon number fluctuations on photon - photon collisions at high energies
• Can $1/N_c$ corrections destroy the saturation of dipole densities?
• High energy QCD Lipatov's effective action in Euclidean space