Unitarity at small Bjorken x

Abstract

This paper presents a solution to the nonlinear small x ``projectile side'' evolution equations as derived by Balitskii in 1996. The solution is based on functional Fokker-Planck methods. The fixed point at small x is explicitly calculated and all correlation functions in this limit are determined. They show clear saturation and unitarization properties. Scaling laws that hold during the saturation phase and throughout the whole course of the evolution are established. The corresponding Langevin equations are given as a basis for numerical simulations opening the field for future studies of dynamical issues of the evolution not analytically accessible. The methods used may be extended to the ``target side'' equations of Jalilian-Marian, Kovner, Leonidov and Weigert.

28 pages, several diagrams. Typos corrected, minor useful changes in notation

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• CGC and saturation approach: Impact-parameter dependent model of perturbative QCD and combined HERA data
• The energy dependence of exclusive heavy vector meson photoproduction cross-sections and NLO BFKL evolution
• High-energy QCD evolution from BRST symmetry
• Gluon saturation: survival probability for leading neutrons in DIS
• Forward Hadron Productions in Proton-Proton Collisions in Small-$x$ Formalism
• On the Nuclear Modification Factor at RHIC and LHC
• Inclusive gauge boson production in the color dipole formalism
• A geometrizing higher twist effect on nuclear target
• Soft processes at high energy without soft Pomeron: a QCD motivated model
• Eikonal but not: a complementary view of high energy evolution
• Soft Pomeron in the Colour Glass Condensate approach
• Resummation of projectile-target multiple scatterings and parton saturation
• BFKL Pomeron calculus: nucleus-nucleus scattering
• Mapping the internal structure of hadrons through color and spin effects
• Can $1/N_c$ corrections destroy the saturation of dipole densities?
• Remarks on Diffractive Dissociation within JIMWLK Evolution at NLO
• Evolution equation for elastic scattering of hadrons
• Classical information entropy of parton distribution functions and an application in searching gluon saturation
• Momentum space saturation model for deep inelastic scattering and single inclusive hadron production
• Parton model contributions as next-to-eikonal corrections to the dipole factorization of DIS and SIDIS at low $x_{Bj}$
• Rapidity dependence of saturation in inclusive HERA data with the rcBK equation
• Callan-Symanzik equations and low-energy theorems with trace anomalies
• Higher twists effects in DIS on nuclei at the EIC and LHeC: A phenomenological analysis
• The BFKL Pomeron calculus: summing enhanced diagrams
• Azimuthal angle correlations in hadron-nucleus scattering: enhanced diagrams
• Investigation of proton structure function $F_2^p$ at HERA in light of an analytical solution to Balitsky-Kovchegov equation
• Diffractive hadron production in DIS off heavy nuclei and gluon saturation
• High-energy factorization and evolution with improved kinematics
• Probing Saturation Physics in the Real Compton Scattering at Ultraperipheral $pPb$ Collisions
• First correction to JIMWLK evolution from the classical equations of motion
• On the low-x NLO evolution of 4 point colorless operators
• Looking for quark saturation in proton and nuclei
• Exploring the DGLAP resummation in the JIMWLK Hamiltonian
• Improving the solver for the Balitsky-Kovchegov evolution equation with Automatic Differentiation
• Structure of the medium formed in heavy ion collisions
• High energy scattering in QCD: dipole approach with Pomeron loops
• Gluon imaging using azimuthal correlations in diffractive scattering at the Electron-Ion Collider
• Spin-glass model of QCD near saturation
• From Classical to Quantum Saturation in the Nuclear Gluon Distribution
• Dijet photoproduction at low $x$ at next-to-leading order and its back-to-back limit
• Color-glass condensate beyond the Gaussian approximation
• Entanglement, Trace Anomaly and Confinement in QCD
• Diffraction 2006: Theoretical Summary
• Transverse Spin and Classical Gluon Fields: Combining Two Perspectives on Hadronic Structure
• Impact Factor for Exclusive Diffractive Dijet Production with NLO Accuracy
• 3-D Glasma initial state from small-x evolution
• High energy DVCS on a photon and related meson exclusive production
• The Color Glass Condensate and some applications
• BFKL Pomeron calculus: solution to equations for nucleus-nucleus scattering in the saturation domain
• Properties of inclusive hadron production in Deep Inelastic Scattering on heavy nuclei at low x
• Local one-dimensional reggeon model of the interaction of several pomerons
• Finite volume effects in the McLerran-Venugopalan initial condition for the JIMWLK equation
• Tunneling through Color Glass Condensate and True Black Disks
• NLO exclusive diffractive processes with saturation
• Photoproduction of three jets in the CGC: gluon TMDs and dilute limit
• Invariant color calculus and generalized Balitsky-Kovchegov hierarchy
• Four-pomeron vertex
• Small-x, Diffraction and Vector Mesons