Non-Abelian Weizsacker-Williams field and a two-dimensional effective color charge density for a very large nucleus

Abstract

We consider a very large ultra-relativistic nucleus. Assuming a simple model of the nucleus and weak coupling we find a classical solution for the gluon field of the nucleus and construct the two-dimensional color charge density for McLerran-Venugopalan model out of it. We prove that the density of states distribution, as a function of color charge density, is Gaussian, confirming the assumption made by McLerran and Venugopalan.

9 pages, REVTeX, 1 figure, some minor changes included

References in corpus (4)

• Computing Quark and Gluon Distribution Functions for Very Large Nuclei
• Gluon Distribution Functions for Very Large Nuclei at Small Transverse Momentum
• Green's Functions in the Color Field of a Large Nucleus
• Gluon Production from Non-Abelian Weizsäcker-Williams Fields in Nucleus-Nucleus Collisions

Cited by in corpus (310)

• Small-x F_2 Structure Function of a Nucleus Including Multiple Pomeron Exchanges
• Nonlinear Gluon Evolution in the Color Glass Condensate: I
• Nonlinear Gluon Evolution in the Color Glass Condensate: II
• Unitarization of the BFKL Pomeron on a Nucleus
• The Renormalization Group Equation for the Color Glass Condensate
• The Intrinsic Glue Distribution at Very Small x
• Hadron production in nuclear collisions at RHIC and high density QCD
• Fluctuating Glasma initial conditions and flow in heavy ion collisions
• The Physics of Ultraperipheral Collisions at the LHC
• Manifestations of high density QCD in the first RHIC data
• Parton-Based Gribov-Regge Theory
• Saturation Physics and Deuteron--Gold Collisions at RHIC
• Evolution at small x_bj: The Color Glass Condensate
• Gluon production in current-nucleus and nucleon-nucleus collisions in a quasi-classical approximation
• Event-by-event gluon multiplicity, energy density and eccentricities at RHIC and LHC
• Glasma flux tubes and the near side ridge phenomenon at RHIC
• The Energy Dependence of the Saturation Momentum
• Geometric Scaling above the Saturation Scale
• Cronin Effect and High-p_T Suppression in pA Collisions
• The initial energy density of gluons produced in very high energy nuclear collisions
• Triumvirate of Running Couplings in Small-x Evolution
• The Color Glass Condensate and hadron production in the forward region
• Event-by-Event Simulation of the Three-Dimensional Hydrodynamic Evolution from Flux Tube Initial Conditions in Ultrarelativistic Heavy Ion Collisions
• Hydrodynamic Models for Heavy Ion Collisions
• Fock Space Distributions, Structure Functions, Higher Twists and Small x
• Non-perturbative computation of gluon mini-jet production in nuclear collisions at very high energies
• Parton Saturation at Small x and in Large Nuclei
• Solution to the evolution equation for high parton density QCD
• Inclusive Gluon Production in DIS at High Parton Density
• Parton saturation and N_part scaling of semi--hard processes in QCD
• High energy pA collisions in the color glass condensate approach II. Quark production
• Coherent gluon production in very high energy heavy ion collisions
• Color Glass Condensate at the LHC: hadron multiplicities in $pp$, $pA$ and $AA$ collisions
• The Unstable Glasma
• High energy pA collisions in the color glass condensate approach I. Gluon production and the Cronin effect
• Forward inclusive dijet production and azimuthal correlations in pA collisions
• Quantum structure of the non-Abelian Weizsacker-Williams field for a very large nucleus
• Nuclear Modification Factor in d+Au Collisions: Onset of Suppression in the Color Glass Condensate
• Forward Quark Jets from Protons Shattering the Colored Glass
• Solving The High Energy Evolution Equation Including Running Coupling Corrections
• The Energy Dependence of the Saturation Momentum from RG Improved BFKL Evolution
• The onset of classical QCD dynamics in relativistic heavy ion collisions
• Distribution of linearly polarized gluons inside a large nucleus
• Universal features of JIMWLK and BK evolution at small x
• Energy Dependence of the Cronin Effect from Non-Linear QCD Evolution
• Classical Gluon Radiation in Ultrarelativistic Nucleus-Nucleus Collisions
• Running the gamut of high energy nuclear collisions
• From Color Glass Condensate to Quark Gluon Plasma through the event horizon
• Wilson line correlator in the MV model: relating the glasma to deep inelastic scattering
• Toward Equilibration in the Early Stages After a High Energy Heavy Ion Collision
• Inclusive Two-Gluon and Valence Quark-Gluon Production in DIS and pA
• Classical Gluodynamics of High Energy Nuclear Collisions: an Erratum and an Update
• Eikonal Evolution and Gluon Radiation
• QCD Saturation and Deuteron-Nucleus Collisions
• Gluon production in the Color Glass Condensate model of collisions of ultrarelativistic finite nuclei
• Energy density of the Glasma
• Yang-Mills Radiation in Ultra-relativistic Nuclear Collisions
• A Langevin equation for high energy evolution with pomeron loops
• Color Glass Condensate and Glasma
• Anomalous chirality fluctuations in the initial stage of heavy ion collisions and parity odd bubbles
• Heavy quark pair production in high energy pA collisions: Quarkonium
• High energy factorization in nucleus-nucleus collisions
• Heavy quark pair production in high energy pA collisions: Open heavy flavors
• Long-Range Rapidity Correlations in Heavy-Light Ion Collisions
• Quark pair production in high energy pA collisions: General features
• Relativistic hydrodynamics in heavy-ion collisions: general aspects and recent developments
• Glittering Glasmas
• From Color Glass to Color Dipoles in high-energy onium--onium scattering
• Effective Hamiltonian for QCD evolution at high energy
• The Boltzmann equation for gluons at early times after a heavy ion collision
• Saturation and parton level Cronin effect: enhancement vs suppression of gluon production in p-A and A-A collisions
• Perturbative Odderon in the Dipole Model
• Subleading-N_c corrections in non-linear small-x evolution
• Angular and long range rapidity correlations in particle production at high energy
• Last Call for RHIC Predictions
• QCD Plasma Instabilities and Isotropization
• Particle production in field theories coupled to strong external sources I. Formalism and main results
• Geometric scaling violations in the central rapidity region of d+Au collisions at RHIC
• A Linear Evolution for Non-Linear Dynamics and Correlations in Realistic Nuclei
• Universality of the saturation scale and the initial eccentricity in heavy ion collisions
• Large mass Q-Qbar production from the Color Glass Condensate
• Running coupling and power corrections in nonlinear evolution at the high--energy limit
• Non linear gluon evolution in path-integral form
• Jet Azimuthal Correlations and Parton Saturation in the Color Glass Condensate
• Diffractive Structure Function in a Quasi-Classical Approximation
• The Cronin Effect, Quantum Evolution and the Color Glass Condensate
• Long Range Forward-Backward Correlations and the Color Glass Condensate
• Quark loop contribution to BFKL evolution: Running coupling and leading-N_f NLO intercept
• 3-D Glasma initial state for relativistic heavy ion collisions
• From DIS to proton-nucleus collisions in the Color Glass Condensate model
• Classical Initial Conditions for Ultrarelativistic Heavy Ion Collisions
• A Gaussian effective theory for gluon saturation
• Helicity Evolution at Small $x$: Flavor Singlet and Non-Singlet Observables
• Small-$x$ Helicity Evolution: an Operator Treatment
• Early Time Dynamics in Heavy Ion Collisions from AdS/CFT Correspondence
• Dilepton production from the Color Glass Condensate
• High Gluon Densities in Heavy Ions Collisions
• Asymmetric Collision of Two Shock Waves in AdS_5
• Scattering of Gluons from the Color Glass Condensate
• Early Time Dynamics of Gluon Fields in High Energy Nuclear Collisions
• Signatures of the Color Glass Condensate in J/Psi production off nuclear targets
• High energy scattering in Quantum Chromodynamics
• A New Mechanism for Generating a Single Transverse Spin Asymmetry
• A classical Odderon in QCD at high energies
• Generalized scaling of the transverse mass spectrum at the Relativistic Heavy-Ion Collider
• Small-$x$ Asymptotics of the Gluon Helicity Distribution
• Baryon Stopping and the Valence Quark Distribution at Small x
• Nonlinear corrections to the DGLAP equations in view of the HERA data
• Cronin effect and high-p_T suppression in the nuclear gluon distribution at small x
• Evidence for Hydrodynamic Evolution in Proton-Proton Scattering at LHC Energies
• Random walks of partons in SU(N_c) and classical representations of color charges in QCD at small x
• Helicity-dependent generalization of the JIMWLK evolution
• Azimuthal asymmetries for quark pair production in pA collisions
• Broadening of Transverse Momentum of Partons Propagating through a Medium
• Open charm production in heavy ion collisions and the Color Glass Condensate
• Heavy quark production by a quasi-classical color field in proton-nucleus collisions
• Saturation and shadowing in high-energy proton-nucleus dilepton production
• Multiplicity distributions in p+p, p+A and A+A collisions from Yang-Mills dynamics
• From colored glass condensate to gluon plasma: equilibration in high energy heavy ion collisions
• New observables to test the Color Glass Condensate beyond the large-N_c limit
• Relativistic Fluid Dynamics In and Out of Equilibrium -- Ten Years of Progress in Theory and Numerical Simulations of Nuclear Collisions
• Large Scale Rapidity Correlations in Heavy Ion Collisions
• Diffractive Gluon Production in Proton-Nucleus Collisions and in DIS
• Geometric Scaling at RHIC and LHC
• Anisotropy of the semi-classical gluon field of a large nucleus at high energy
• Scale Anomaly and "Soft" Pomeron in QCD
• Diffractive dijet production in impact parameter dependent saturation models
• The elliptic gluon GTMD inside a large nucleus
• Elliptic Flow from Minijet Production in Heavy Ion Collisions
• Medium Induced Transverse Momentum Broadening in Hard Processes
• Elliptic flow of colored glass in high energy heavy ion collisions
• Non-linear evolution and parton distributions at LHC and THERA energies
• The non-linear Glasma
• Event engineering studies for heavy flavor production and hadronization in high multiplicity hadron-hadron and hadron-nucleus collisions
• Helicity-dependent extension of the McLerran-Venugopalan model
• Parton densities and saturation scale from non-linear evolution in DIS on nuclei
• Long range rapidity correlations as seen in the STAR experiment
• HERA-data in the light of small x evolution with state of the art NLO input
• Quark Sivers Function at Small $x$: Spin-Dependent Odderon and the Sub-Eikonal Evolution
• Forward Rapidity Hadron Production in Deuteron Gold Collisions from Valence Quarks
• Can Thermalization in Heavy Ion Collisions be Described by QCD Diagrams?
• Calculating TMDs of a Large Nucleus: Quasi-Classical Approximation and Quantum Evolution
• Multiplicity and Pseudorapidity Distributions of Charged Particles and Photons at Forward Pseudorapidity in Au + Au Collisions at sqrt{s_NN} = 62.4 GeV
• Two-Gluon Correlations in Heavy-Light Ion Collisions: Energy and Geometry Dependence, IR Divergences, and $k_T$-Factorization
• The cathode tube effect: heavy quarks probing the Glasma in p-Pb collisions
• Ultra-High Energy Neutrino-Nucleon Scattering and Parton Distributions at Small $x$
• Initial energy density and gluon distribution from the Glasma in heavy-ion collisions
• Color Glass Condensate and Glasma
• Heavy Ion Collisions with Transverse Dynamics from Evolving AdS Geometries
• Onium-Onium scattering at fixed impact parameter: exact equivalence between the color dipole model and the BFKL Pomeron
• Gluon saturation effects on J/Psi production in heavy ion collisions
• Wong's equations and the small x effective action in QCD
• $\psi (2S)$ versus $J/\psi$ suppression in proton-nucleus collisions from factorization violating soft color exchanges
• Initial fields and instability in the classical model of the heavy-ion collision
• Hard Probes in Heavy Ion Collisions at the LHC: Jet Physics
• Running Coupling Corrections to High Energy Inclusive Gluon Production
• Helicity Evolution at Small $x$: the Single-Logarithmic Contribution
• Particle production in high-energy collisions beyond the shockwave limit
• Gluon Distributions and Color Charge Correlations in a Saturated Light-cone Wavefunction
• Color charge correlations in the proton at NLO: beyond geometry based intuition
• Boost covariant gluon distributions in large nuclei
• Extracting many-body color charge correlators in the proton from exclusive DIS at large Bjorken x
• The initial state of heavy-ion collisions
• Hadrons and direct photon in pp and pA collisions at LHC and saturation effects
• When gluons go odd: how classical gluon fields generate odd azimuthal harmonics for the two-gluon correlation function in high-energy collisions
• Multi-quark matrix elements in the proton and three gluon exchange for exclusive ${\eta }_c$ production in photon-proton diffractive scattering
• Intrinsic Broadening of the Transverse Momentum Spectra in Ultrarelativistic Heavy-Ion Collisions?
• Light projectile scattering off the Color Glass Condensate
• Color Neutrality and the Gluon Distribution in a Very Large Nucleus
• Longitudinal Resolution in a Large Relativistic Nucleus: Adding a Dimension to the McLerran-Venugopalan Model
• Comparing AdS/CFT Calculations to HERA F_2 Data
• Diffractive dissociation from non-linear evolution in DIS on nuclei
• QCD Saturation in the Semi-classical Approach
• The role of the chiral anomaly in polarized deeply inelastic scattering II: Topological screening and transitions from emergent axion-like dynamics
• Evolution to the Quark-Gluon Plasma
• Webs and Posets
• Initial conditions for dipole evolution beyond the McLerran-Venugopalan model
• Enhancement and Suppression of the Neutrino-Nucleon Total Cross Section at Ultra-High Energies
• A Pomeron Approach to Hadron-Nucleus and Nucleus-Nucleus "Soft" Interactions at High Energy
• T-odd Leading-Twist Quark TMDs at Small $x$
• Extracting many-body correlators of saturated gluons with precision from inclusive photon+dijet final states in deeply inelastic scattering
• Hard probes in heavy ion collisions at the LHC: PDFs, shadowing and $pA$ collisions
• Limiting fragmentation from the Color Glass Condensate
• Unitarity Corrections and High Field Strengths in High Energy Hard Collisions
• Electromagnetic Signatures of the Color Glass Condensate: Dileptons
• Collinear Singularities and Running Coupling Corrections to Gluon Production in CGC
• Gluon saturation effects on the color singlet J/Psi production in high energy dA and AA collisions
• Diffusion of heavy quarks in the early stage of high-energy nuclear collisions at energies available at the BNL Relativistic Heavy Ion Collider and at the CERN Large Hadron Collider
• Randomness in infinitesimal extent in the McLerran-Venugopalan model
• Proton breakup in high-energy pA collisions from perturbative QCD
• Ballistic diffusion of heavy quarks in the early stage of relativistic heavy ion collisions at RHIC and LHC
• Instantons in the Saturation Environment
• Photon from the annihilation process with CGC in the $pA$ collision
• Searching Evidence for the Color Glass Condensate at RHIC
• Measuring Color Memory in a Color Glass Condensate at Electron-Ion Colliders
• Gluon Radiation and Coherent States in Ultrarelativistic Nuclear Collisions
• High-density QCD and Cosmic Ray Air Showers
• Nonlinear GLR-MQ evolution equation and Q^2-evolution of gluon distribution function
• Classical Gluon Radiation in Ultrarelativistic Nuclear Collisions: Space-Time Structure, Instabilities, and Thermalization
• Color Glass Condensate in Schwinger-Keldysh QCD
• High Pt Hadron Spectra at High Rapidity
• Non-equilibrium QCD: Interplay of hard and soft dynamics in high-energy multi-gluon beams
• The Mini-Jet Scale and Energy Loss at RHIC in the HIJING and RQMD Models
• Initial state and thermalization in the Color Glass Condensate framework
• Prompt photon - jet angular correlations at central rapidities in p+A collisions
• Initial State Quantum Fluctuations in the Little Bang
• Classical Computation of Elliptic Flow at Large Transverse Momentum
• Theoretical overview: towards understanding the quark-gluon plasma
• 3-D structure of the Glasma initial state -- Breaking boost-invariance by collisions of extended shock waves in classical Yang-Mills theory
• Classical Gluon Production Amplitude for Nucleus-Nucleus Collisions: First Saturation Correction in the Projectile
• The Yin and Yang of High Energy Chromodynamics: Scattering in Black and White
• Sub-femtometer scale color charge correlations in the proton
• Higher twists and maxima for DIS on nuclei in high density QCD region
• The high energy behavior of QCD: The effective action and the triple-Pomeron-vertex
• Schwinger Model and String Percolation in Hadron-Hadron and Heavy Ion Collisions
• Decoherence and Entropy Production in Relativistic Nuclear Collisions
• Higgs boson production in high energy proton-nucleus collisions
• The medium-modified $g\to c\bar{c}$ splitting function in the BDMPS-Z formalism
• From Glasma to Quark Gluon Plasma in heavy ion collisions
• Forward Heavy Quarkonium Productions at the LHC
• Two-Gluon Production and Longitudinal Correlations in the Color Glass Condensate
• Correlation Functions and Cumulants in Elliptic Flow Analysis
• Leptons from heavy-quark semileptonic decay in pA collisions within the CGC framework
• Lensing Mechanism Meets Small-$x$ Physics: Single Transverse Spin Asymmetry in $p^{\uparrow }+p$ and $p^{\uparrow }+A$ Collisions
• O(α_s^2)-corrections to JIMWLK evolution from the classical equations of motion
• Thoughts on Non-Perturbative Thermalization and Jet Quenching in Heavy Ion Collisions
• Quark production in high energy proton-nucleus collisions
• Early Time Evolution of High Energy Heavy Ion Collisions
• Has HERA reached a new QCD regime?
• Structure functions at small x from world-lines. I: Unpolarized distributions
• Triple- and Quadruple-Gluon Azimuthal Correlations from Glasma and Higher-Dimensional Ridges
• Lattice Gauge Description of Colliding Nuclei
• Modified Kolmogorov Wave Turbulence in QCD matched onto "Bottom-up" Thermalization
• Baryon Stopping in Proton-Nucleus Collisions
• Anomalous ANITA air shower events and tau decays
• The Color Glass Condensate: an overview
• The saturation scale and its x-dependence from Lambda polarization studies
• Magnetic flux loop in high-energy heavy-ion collisions
• R-Current DIS on a Shock Wave: Beyond the Eikonal Approximation
• In-medium QCD and Cherenkov gluons
• Evolution of pressures and correlations in the Glasma produced in high energy nuclear collisions
• Rapidity Profile of the Initial Energy Density in Heavy-Ion Collisions
• Center of mass energy and system-size dependence of photon production at forward rapidity at RHIC
• Pressure Anisotropy in Heavy Ion Collisions from Color Glass Condensate
• Total gluon shadowing due to fluctuation effects
• Ioffe Time in Double Logarithmic Approximation
• Non-Gaussian Correlations in the McLerran-Venugopalan Model
• Multiparticle Production at Mid-Rapidity in the Color-Glass Condensate
• General formulae for dipole Wilson line correlators with the Color Glass Condensate
• Initial Angular Momentum and Flow in High Energy Nuclear Collisions
• Color-neutral heavy particle production in nucleus-nucleus collisions in the quasi-classical approximation
• Regularization of the Light-Cone Gauge Gluon Propagator Singularities Using Sub-Gauge Conditions
• Shadowing of gluons in perturbative QCD: A comparison of different models
• Density saturation and the decrease of the normalised width of the multiplicity distribution in high energy pp collisions
• First Saturation Correction in High Energy Proton-Nucleus Collisions: II. Single Inclusive Semi-Hard Gluon Production
• Determination of the Parameters of a Color Neutral 3D Color Glass Condensate Model
• Generalized parton distributions and Deeply Virtual Compton Scattering in Color Glass Condensate model
• Magnetic screening in high-energy heavy-ion collisions
• Compatibility of phenomenological dipole cross sections with the Balitsky-Kovchegov equation
• Fluctuations of the gluon distribution from the small-x effective action
• Collective Phenomena in the Non-Equilibrium Quark-Gluon Plasma
• The small-x gluon distribution in centrality biased pA and pp collisions
• Study of the behavior of nuclear modification factor in freeze-out state
• Coherent and incoherent diffractive hadron production in pA collisions and gluon saturation
• Introduction to the Physics of Saturation
• Higher Twist Corrections and Maxima for DIS on a Proton in the High Density QCD Region
• Gauge-Invariant Quantities Characterizing Gauge Fields in Chromodynamics
• Time-Dependent Observables in Heavy Ion Collisions I: Setting up the Formalism
• QCD in the nuclear medium and effects due to Cherenkov gluons
• Quark and Gluon Production from a Boost-invariantly Expanding Color Electric Field
• Multi-photon interactions in lepton photo-production on nuclei at high energies
• A geometrical estimation of saturation of partonic densities
• Probing Gluons in Nuclei: the Case of ${\eta }^{\prime }$
• Sudakov effects and the dipole amplitude
• Scattering from an external field in quantum chromodynamics at high energies: from foundations to interdisciplinary connections
• Long Range Azimuthal Correlations of Multiple Gluons in Gluon Saturation Limit
• Proton and anti-proton production in the forward region of d+Au collisions at RHIC from the color glass condensate
• Longitudinal Rescaling and High-Energy Effective Actions
• Fluctuations of topological charge and chiral density in the early stage of high energy nuclear collisions
• Near-integrability and confinement for high-energy hadron-hadron collisions
• Chaos in the Color Glass Condensate
• Quarkonium production at collider energies in Small-$x$ formalism
• Coulomb corrections to photon and dilepton production in high energy pA collisions
• Multiplicity and transverse energy of produced gluon in relativistic heavy ion collision
• Open and hidden charm production in pA collisions
• Forward Hadron Productions in Proton-Proton Collisions in Small-$x$ Formalism
• BRAHMS results in the context of saturation and quantum evolution
• Review of Recent Developments in the CGC
• Cumulant Expansion in Gluon Saturation, and Five and Six-Gluon Azimuthal Correlations
• Gluon saturation effects on J/Psi production in heavy ion collisions
• Low-x Physics
• Low-$x$ Physics in $pA$ Collisions and at the EIC
• The Semiclassical Gluon Distribution at Next-to-Leading Order
• Structure of the medium formed in heavy ion collisions
• Initial Conditions and Global Event Properties from Color Glass Condensate
• Spatial Wilson loops in the classical field of high-energy heavy-ion collisions
• Quantum collisions of finite-size ultrarelativistic nuclei
• First correction to JIMWLK evolution from the classical equations of motion
• Diffractive hadron production in DIS off heavy nuclei and gluon saturation
• Elliptic Flow from Color Glass Condensate
• From Classical to Quantum Saturation in the Nuclear Gluon Distribution
• Double inclusive small-x gluon production and their azimuthal correlations in a biased ensemble
• BRAHMS Overview
• The gluon field of a fast moving nucleus and the effective langrangian for QCD at high energy
• Energy dependence of Cronin momentum in saturation model for $p+A$ and $A+A$ collisions
• Saturation Physics in Heavy Ion Collisions
• Suppressing the Background Process to QED Compton Scattering for Delineating the Photon Content of the Proton
• Properties of inclusive hadron production in Deep Inelastic Scattering on heavy nuclei at low x
• Gluon saturation and pseudo-rapidity distributions of charged hadrons at RHIC energy regions
• Tunneling through Color Glass Condensate and True Black Disks