Dense-dilute factorization for a class of stochastic processes and for high energy QCD

Abstract

Stochastic processes described by evolution equations in the universality class of the FKPP equation may be approximately factorized into a linear stochastic part and a nonlinear deterministic part. We prove this factorization on a model with no spatial dimensions and we illustrate it numerically on a one-dimensional toy model that possesses some of the main features of high energy QCD evolution. We explain how this procedure may be applied to QCD amplitudes, by combining Salam's Monte-Carlo implementation of the dipole model and a numerical solution of the Balitsky-Kovchegov equation.

9 pages. v2: Eq.(4) corrected, numerics improved, various clarifying comments added. Conclusions unchanged. v3: comments and references added, many misprints fixed

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Cited by in corpus (8)

• Summing Pomeron loops in the dipole approach
• 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
• Quantum chromodynamics at high energy and statistical physics
• Reaction-diffusion processes in zero transverse dimensions as toy models for high-energy QCD
• Correlations in impact-parameter space in a hierarchical saturation model for QCD at high energy
• Total gluon shadowing due to fluctuation effects
• Soft processes at high energy without soft Pomeron: a QCD motivated model