Solution to the Balitsky-Kovchegov equation in the saturation domain

Abstract

The solution to the Balitsky-Kovchegov equation is found in the deep saturation domain. The controversy between different approaches regarding the asymptotic behaviour of the scattering amplitude is solved. It is shown that the dipole amplitude behaves as $1-\exp (-z+\ln z)$ with $z=\ln (r^2{Q}_s^2)$ ($r$ -size of the dipole, $Q_s$ is the saturation scale) in the deep saturation region. This solution is developed from the scaling solution to the homogeneous Balitsky-Kovchegov equation. The dangers associated with making simplifications in the BFKL kernel, to investigate the asymptotic behaviour of the scattering amplitude, is pointed out . In particular, the fact that the Balitsky-Kovchegov equation belongs to the Fisher-Kolmogorov-Petrovsky-Piscounov -type of equation, needs further careful investigation.

19 pages, 3 figures

References in corpus (29)

• Computing Quark and Gluon Distribution Functions for Very Large Nuclei
• Operator expansion for high-energy scattering
• Gluon Distribution Functions for Very Large Nuclei at Small Transverse Momentum
• Small-x F_2 Structure Function of a Nucleus Including Multiple Pomeron Exchanges
• Green's Functions in the Color Field of a Large Nucleus
• The Energy Dependence of the Saturation Momentum
• Geometric Scaling above the Saturation Scale
• Geometric scaling as traveling waves
• Fock Space Distributions, Structure Functions, Higher Twists and Small x
• Solution to the evolution equation for high parton density QCD
• Traveling wave fronts and the transition to saturation
• The Energy Dependence of the Saturation Momentum from RG Improved BFKL Evolution
• Quantum Corrections to the Weizsäcker--Williams Distribution Function as Small x
• Universal behavior of QCD amplitudes at high energy from general tools of statistical physics
• On solutions of the Balitsky-Kovchegov equation with impact parameter
• New Scaling at High Energy DIS
• Studies of Unitarity at Small~$x$ Using the Dipole Formulation
• Large multiplicity fluctuations and saturation effects in onium collisions
• Universality and tree structure of high energy QCD
• Nonlinear QCD Evolution: Saturation without Unitarization
• Nonlinear evolution and saturation for heavy nuclei in DIS
• Froissart Bound from Gluon Saturation
• No Froissart Bound from Gluon Saturation
• Perturbative Saturation and the Soft Pomeron
• The spread of the gluon k_t-distribution and the determination of the saturation scale at hadron colliders in resummed NLL BFKL
• Froissart boundary for deep inelastic structure functions
• QCD Saturation in the Semi-classical Approach
• QCD Saturation and ${\gamma }^{\ast }-{\gamma }^{\ast }$ Scattering
• Taming the BFKL Intercept via Gluon Saturation

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• Treading on the cut: Semi inclusive observables at high energy
• Solution for the BFKL Pomeron Calculus in zero transverse dimensions
• An approximate approach to the nonlinear DGLAP evaluation equation
• QCD traveling waves at non-asymptotic energies
• The BFKL Pomeron Calculus in the dipole approach
• Compatibility of phenomenological dipole cross sections with the Balitsky-Kovchegov equation
• The behavior of the heavy-quarks structure functions at small-$x$
• A geometrical scaling solution to the BFKL Pomeron Calculus in the saturation domain