Nonlinear QCD Evolution: Saturation without Unitarization

Abstract

We consider the perturbative description of saturation based on the nonlinear QCD evolution equation of Balitsky and Kovchegov (BK). Although the nonlinear corrections lead to saturation of the scattering amplitude locally in impact parameter space, we show that they do not unitarize the total cross section. The total cross section for the scattering of a strongly interacting probe on a hadronic target is found to grow exponentially with rapidity. The origin of this violation of unitarity is the presence of long range Coulomb fields away from the saturation region. The growth of these fields with rapidity is not tempered by the nonlinearity of the BK equation.

4 pages, RevTeX

References in corpus (1)

• Diffusion into infra-red and unitarization of the BFKL pomeron

Cited by in corpus (90)

• Saturation Physics and Deuteron--Gold Collisions at RHIC
• Evolution at small x_bj: The Color Glass Condensate
• Analysis of combined HERA data in the Impact-Parameter dependent Saturation model
• Impact-parameter dependent Color Glass Condensate dipole model and new combined HERA data
• On solutions of the Balitsky-Kovchegov equation with impact parameter
• Numerical analysis of the Balitsky-Kovchegov equation with running coupling: dependence of the saturation scale on nuclear size and rapidity
• Exclusive vector meson production at high energies and gluon saturation
• In pursuit of Pomeron loops: the JIMWLK equation and the Wess-Zumino term
• Color Glass Condensate at next-to-leading order meets HERA data
• CGC predictions for p+A collisions at the LHC and signature of QCD saturation
• Unintegrated gluon distribution from modified BK equation
• AdS black disk model for small-x DIS
• Froissart Bound from Gluon Saturation
• No Froissart Bound from Gluon Saturation
• Small x Phenomenology - summary of the 3rd Lund Small x Workshop in 2004
• Confronting impact parameter dependent JIMWLK evolution with HERA data
• Exclusive vector meson production at HERA from QCD with saturation
• The shape of the proton at high energies
• Balitsky's hierarchy from Mueller's dipole model and more about target correlations
• Numerical solution of the nonlinear evolution equation at small x with impact parameter and beyond the LL approximation
• Diffractive Dijet Production and Wigner Distributions from the Color Glass Condensate
• Gluon saturation and energy dependence of hadron multiplicity in pp and AA collisions at the LHC
• Odderon and seven Pomerons: QCD Reggeon field theory from JIMWLK evolution
• One gluon, two gluon: multigluon production via high energy evolution
• Small x nonlinear evolution with impact parameter and the structure function data
• Exact kinematics in the small x evolution of the color dipole and gluon cascade
• Diffractive dijet production in impact parameter dependent saturation models
• Treading on the cut: Semi inclusive observables at high energy
• Higher Order Effects in Non Linear Evolution from a Veto in Rapidities
• Two-Gluon Correlations in Heavy-Light Ion Collisions: Energy and Geometry Dependence, IR Divergences, and $k_T$-Factorization
• Glauber - Gribov approach for DIS on nuclei in N=4 SYM
• Next-to-leading and resummed BFKL evolution with saturation boundary
• Exclusive Higgs boson production at the LHC: hard rescattering corrections
• The Balitsky-Kovchegov equation in full momentum space
• Traveling waves and geometric scaling at non-zero momentum transfer
• Color confinement and screening in the $\theta$ -vacuum
• QCD Saturation in the Semi-classical Approach
• The Dipole Picture and Saturation in Soft Processes
• Accessing the gluonic structure of light nuclei at the Electron Ion Collider
• Scattering of color dipoles: from low to high energies
• Rapidity dependence of initial state geometry and momentum correlations in p+Pb collisions
• Solving effective field theory of interacting QCD pomerons in the semi-classical approximation
• Asymptotic neutrino-nucleon cross section and saturation effects
• Unitarisation of the hard pomeron and black-disk limit at the LHC
• CGC/saturation approach: a new impact-parameter dependent model in the next-to-leading order of perturbative QCD
• BFKL Pomeron with massive gluons
• Saturation in inclusive production beyond leading logarithm accuracy
• Gluon saturation and the Froissart bound: a simple approach
• Geometric Scaling in a Symmetric Saturation Model
• Classicalization and Unitarity
• CGC/saturation approach: a new impact-parameter dependent model
• Non-linear equation: energy conservation and impact parameter dependence
• Geometric scaling in exclusive processes
• Deeply virtual Compton scattering at small-$x$ in future Electron - Ion Colliders
• Finite-size effects on small-$x$ evolution and saturation in proton and nuclear targets
• Mutual boosting of the saturation scales in colliding nuclei
• Liouville field theory for gluon saturation in QCD at high energy
• Froissart bound and gluon number fluctuations
• Thermal radiation and inclusive production in the KLN model for ion-ion collisions
• QCD Saturation and ${\gamma }^{\ast }-{\gamma }^{\ast }$ Scattering
• BFKL Pomeron: modeling confinement
• Thermal radiation and inclusive production in the CGC/saturation approach at high energies
• Gluon Saturation Effects in Exclusive Heavy Vector Meson Photoproduction
• Geometric Scaling in Mueller-Navelet Jets
• Solution to the Balitsky-Kovchegov equation in the saturation domain
• CGC/saturation approach: soft interaction at the LHC energies
• Novel Cross Section Ratios as Possible Signals of Saturation in UPCs
• Gribov-Zwanziger confinement, high energy evolution and large impact parameter behaviour of the scattering amplitude
• Nonlinear corrections on the parameterization methods
• Large $\mathbf{b}$ behaviour in the CGC/saturation approach: BFKL equation with pion loops
• Semiclassical solution to the BFKL equation with massive gluons
• Geometric scaling behavior of the scattering amplitude for DIS with nuclei
• Violation of the geometric scaling behaviour of the amplitude for running QCD coupling in the saturation region
• BFKL equation in the next-to-leading order: solution at large impact parameters
• Large impact parameter behaviour in the CGC/saturation approach: a new non-linear equation
• Non-linear evolution in the re-summed next-to-leading order of perturbative QCD:\confronting the experimental data
• BFKL equation with running QCD coupling and HERA data
• Dipole-dipole scattering amplitude in CGC approach
• BFKL pomeron with massive gluons and running coupling
• High density QCD and nucleus-nucleus scattering deeply in the saturation region
• Inside looking out: probing JIMWLK with BFKL calculations
• CGC and saturation approach: Impact-parameter dependent model of perturbative QCD and combined HERA data
• CGC/saturation approach: an impact-parameter dependent model for diffraction production in DIS
• Soft Pomeron in the Colour Glass Condensate approach
• Gluon saturation: survival probability for leading neutrons in DIS
• Homotopy solution to non-linear evolution for heavy nuclei
• Soft processes at high energy without soft Pomeron: a QCD motivated model
• Can $1/N_c$ corrections destroy the saturation of dipole densities?
• High energy evolution for Gribov-Zwanziger confinement: solution to the equation
• `Effective' Pomeron model at large $\mathbf{b}$