Effective Hamiltonian for QCD evolution at high energy

Abstract

We construct the effective Hamiltonian which governs the renormalization group flow of the gluon distribution with increasing energy and in the leading logarithmic approximation. This Hamiltonian defines a two-dimensional field theory which involves two types of Wilson lines: longitudinal Wilson lines which describe gluon recombination (or merging) and temporal Wilson lines which account for gluon bremsstrahlung (or splitting). The Hamiltonian is self-dual, i.e., it is invariant under the exchange of the two types of Wilson lines. In the high density regime where one can neglect gluon number fluctuations, the general Hamiltonian reduces to that for the JIMWLK evolution. In the dilute regime where gluon recombination becomes unimportant, it reduces to the dual partner of the JIMWLK Hamiltonian, which describes bremsstrahlung.

44 pages, 3 figures. More clarifications added on the Hamiltonian structure of the effective theory

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• The Color Glass Condensate
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• Quark contribution to the small-$x$ evolution of color dipole
• Color Glass Condensate and Glasma
• High energy factorization in nucleus-nucleus collisions
• Deep inelastic scattering at strong coupling from gauge/string duality : the saturation line
• Diffusive scaling and the high-energy limit of deep inelastic scattering in QCD at large N_c
• NLO evolution of color dipoles in N=4 SYM
• Multiparton Interactions with an x-dependent Proton Size
• High-enegy effective action from scattering of QCD shock waves
• Odderon and seven Pomerons: QCD Reggeon field theory from JIMWLK evolution
• One gluon, two gluon: multigluon production via high energy evolution
• Summing Pomeron loops in the dipole approach
• Neutrino mixing matrix in the 3-3-1 model with heavy leptons and $A_4$ symmetry
• Treading on the cut: Semi inclusive observables at high energy
• More Remarks on High Energy Evolution
• Solution for the BFKL Pomeron Calculus in zero transverse dimensions
• Higher-twist corrections to gluon TMD factorization
• The BFKL Pomeron Calculus in zero transverse dimensions: summation of Pomeron loops and generating functional for the multiparticle production processes
• Reggeon Field Theory for Large Pomeron Loops
• Color Glass Condensate and Glasma
• Pomeron loop and running coupling effects in high energy QCD evolution
• Pomeron loops in zero transverse dimensions
• Inclusive Gluon Production In High Energy Onium-Onium Scattering
• On the Probabilistic Interpretation of the Evolution Equations with Pomeron Loops in QCD
• QCD Reggeon Field Theory for every day: Pomeron loops included
• Quantum chromodynamics at high energy and statistical physics
• Forward gluon production in hadron-hadron scattering with Pomeron loops
• High energy amplitude in the dipole approach with Pomeron loops: asymptotic solution
• A zero-dimensional model for high-energy scattering in QCD
• Evolution to the Quark-Gluon Plasma
• AntiBRST symmetry and Background Field Method
• From bubbles to foam: dilute to dense evolution of hadronic wave function at high energy
• Solving effective field theory of interacting QCD pomerons in the semi-classical approximation
• Parton distribution function for quarks in an s-channel approach
• One-dimensional model for QCD at high energy
• On the Projectile-Target Duality of the Color Glass Condensate in the Dipole Picture
• Color dipoles from Bremsstrahlung in QCD evolution at high energy
• Color Glass Condensate in Schwinger-Keldysh QCD
• The Color Glass Condensate formalism, Balitsky-JIMWLK evolution and Lipatov's high energy effective action
• Effective action for reggeized gluons, classical gluon field of relativistic color charge and color glass condensate approach
• The Yin and Yang of High Energy Chromodynamics: Scattering in Black and White
• One loop light-cone QCD, effective action for reggeized gluons and QCD RFT calculus
• The energy-momentum tensor at the earliest stage of relativistic heavy ion collisions
• The BFKL Pomeron Calculus in the dipole approach
• Boundary conditions in the QCD nucleus-nucleus scattering problem
• O(α_s^2)-corrections to JIMWLK evolution from the classical equations of motion
• Regge Field Theory in zero transverse dimensions: loops versus "net" diagrams
• Non-linear equation: energy conservation and impact parameter dependence
• QCD unitarity constraints on Reggeon Field Theory
• Langevin equation in effective theory of interacting QCD pomerons in the limit of large $N_c$
• The dimensionally reduced description of the high energy scattering and the effective action for the reggeized gluons
• On the Wess-Zumino term in high energy QCD
• S-matrix and productions amplitudes in high energy QCD
• CGC formalism with two sources
• On correlations and discreteness in non-linear QCD evolution
• Reggeon Field Theory and Self Duality: Making Ends Meet
• First Saturation Correction in High Energy Proton-Nucleus Collisions: I. Time evolution of classical Yang-Mills fields beyond leading order
• The JIMWLK evolution and the s-channel unitarity
• Diffractive dissociation including pomeron loops in zero transverse dimensions
• Travelling waves and impact-parameter correlations
• Color Glass Condensate and its relation to HERA physics
• The BFKL Pomeron Calculus in zero transverse dimensions: diffractive processes and survival probability for central diffractive production
• Nuclei in the toy world: beyond the Pomeron in zero transverse dimensions
• On correlators of Reggeon fields and operators of Wilson lines in high energy QCD
• Unifying approaches: derivation of Balitsky hierarchy from the Lipatov effective action
• On the High Energy Behaviour of The Total Cross Section in the QCD Dipole Model
• Asymptotics of QCD traveling waves with fluctuations and running coupling effects
• On QCD RFT corrections to the propagator of reggeized gluons
• High energy scattering in Einstein-Cartan gravity
• Dipole-dipole scattering amplitude in CGC approach
• On the anomalous dimensions of the multiple pomeron exchanges
• Longitudinal Rescaling and High-Energy Effective Actions
• Gauge invariant source terms in QCD
• Canonical Flow in the Space of Gauge Parameters
• Deriving the Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner equation with classical and quantum source terms
• Near-integrability and confinement for high-energy hadron-hadron collisions
• High density QCD and nucleus-nucleus scattering deeply in the saturation region
• More on eikonal approximation for high energy scattering
• High-energy QCD evolution from BRST symmetry
• Soft Pomeron in the Colour Glass Condensate approach
• The BFKL Pomeron calculus: summing enhanced diagrams
• Can $1/N_c$ corrections destroy the saturation of dipole densities?
• BFKL Pomeron calculus: nucleus-nucleus scattering
• Wave function derivation of the JIMWLK equation
• The role of AGK theorem in QCD
• First correction to JIMWLK evolution from the classical equations of motion
• High energy scattering in QCD: dipole approach with Pomeron loops