Quantum Corrections to the Weizsäcker--Williams Distribution Function as Small x

Abstract

We compute the quantum corrections to the gluon distribution function in the background of a non--Abelian Weizsäcker--Williams field. These corrections are valid to all orders in the effective coupling ${\alpha }_s\mu$, where ${\mu }^2$ denotes the average valence quark color charge squared per unit area. We find $\ln (1/x)$ logarithmic corrections to the classical gluon distribution function. The one loop corrections to the classical Weizsäcker-Williams field do not contribute to these singular terms in the distribution function. Their effect is to cause the running of ${\alpha }_s$.

Latex, 40 pages, 4 figures available upon request to the authors as postscript files

References in corpus (8)

• 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
• Single and Double BFKL Pomeron Exchange and a Dipole Picture of High Energy Hard Processes
• Gluon Production from Non-Abelian Weizsäcker-Williams Fields in Nucleus-Nucleus Collisions
• The Gluon Propagator in non-Abelian Weizsäcker-Williams fields
• A new evolution equation
• Quark and gluon distributions at the earliest stage of heavy ion collision

Cited by in corpus (143)

• The Wilson renormalization group for low x physics: towards the high density regime
• The BFKL Equation from the Wilson Renormalization Group
• The Wilson renormalization group for low x physics: Gluon evolution at finite parton density
• Relating different approaches to nonlinear QCD evolution at finite gluon density
• Manifestations of high density QCD in the first RHIC data
• Saturation Physics and Deuteron--Gold Collisions at RHIC
• Evolution at small x_bj: The Color Glass Condensate
• Non-perturbative computation of gluon mini-jet production in nuclear collisions at very high energies
• Solution to the evolution equation for high parton density QCD
• 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
• The initial gluon multiplicity in heavy ion collisions
• High energy pA collisions in the color glass condensate approach I. Gluon production and the Cronin effect
• Universal features of JIMWLK and BK evolution at small x
• Inclusive Two-Gluon and Valence Quark-Gluon Production in DIS and pA
• New Scaling at High Energy DIS
• Color Glass Condensate and Glasma
• Mining for Gluon Saturation at Colliders
• Photon production in high energy proton-nucleus collisions
• High energy factorization in nucleus-nucleus collisions
• Quark pair production in high energy pA collisions: General features
• Towards a symmetric approach to high energy evolution: generating functional with Pomeron loops
• Gluon saturation and inclusive hadron production at LHC
• A Linear Evolution for Non-Linear Dynamics and Correlations in Realistic Nuclei
• Multi-particle Production and Thermalization in High-Energy QCD
• The Cronin Effect, Quantum Evolution and the Color Glass Condensate
• From DIS to proton-nucleus collisions in the Color Glass Condensate model
• The Ridge from the BFKL evolution and beyond
• Dilepton production from the Color Glass Condensate
• A QCD motivated model for soft interactions at high energies
• Saturation and Scaling of Multiplicity, Mean p_T and p_T Distributions from 200 GeV < sqrt{s} < 7 TeV - Addendum
• S-Matrix Unitarity, Impact Parameter Profiles, Gluon Saturation and High-Energy Scattering
• Gluon saturation and energy dependence of hadron multiplicity in pp and AA collisions at the LHC
• Random walks of partons in SU(N_c) and classical representations of color charges in QCD at small x
• Hadron multiplicity in pp and AA collisions at LHC from the Color Glass Condensate
• Back-to-back inclusive dijets in DIS at small $x$: Sudakov suppression and gluon saturation at NLO
• 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
• From colored glass condensate to gluon plasma: equilibration in high energy heavy ion collisions
• Summing Pomeron loops in the dipole approach
• Transverse Energy Evolution as a Test of Parton Cascade Models
• Nuclear A-dependence near the Saturation Boundary
• NLO impact factor for inclusive photon$+$dijet production in $e+A$ DIS at small $x$
• Density matrix of a quantum field in a particle-creating background
• Production of q bar-q Pairs in Proton-Nucleus Collisions at High Energies
• Towards a New Global QCD Analysis: Solution to the Non-Linear Equation at Arbitrary Impact Parameter
• Forward Rapidity Hadron Production in Deuteron Gold Collisions from Valence Quarks
• Solution for the BFKL Pomeron Calculus in zero transverse dimensions
• Improved Geometrical Scaling at the LHC
• The BFKL Pomeron Calculus in zero transverse dimensions: summation of Pomeron loops and generating functional for the multiparticle production processes
• Glauber - Gribov approach for DIS on nuclei in N=4 SYM
• Color Glass Condensate and Glasma
• Production of Forward Rapidity Photons in High Energy Heavy Ion Collisions
• Wong's equations and the small x effective action in QCD
• Rapidity loss, spin and angular asymmetries in scattering of a quark from color field of a proton (nucleus)
• Inclusive prompt photon production in electron-nucleus scattering at small x
• General Solutions for Multispin Two-Time Correlation and Response Functions in the Glauber-Ising Chain
• Color Neutrality and the Gluon Distribution in a Very Large Nucleus
• High energy amplitude in the dipole approach with Pomeron loops: asymptotic solution
• A unitary model for structure functions and diffractive production at small x
• The Iancu-Mueller factorization and high energy asymptotic behaviour
• Diffractive dissociation from non-linear evolution in DIS on nuclei
• QCD Saturation in the Semi-classical Approach
• Inclusive gluon production in the dipole approach: AGK cutting rules
• A Pomeron Approach to Hadron-Nucleus and Nucleus-Nucleus "Soft" Interactions at High Energy
• Single Inclusive Hadron Production in DIS at Small $x$: Next to Leading Order Corrections
• Enhancement and Suppression of the Neutrino-Nucleon Total Cross Section at Ultra-High Energies
• Extracting many-body correlators of saturated gluons with precision from inclusive photon+dijet final states in deeply inelastic scattering
• Limiting fragmentation from the Color Glass Condensate
• Deep Inelastic Scattering Data and the Problem of Saturation in Small-x Physics
• Electromagnetic Signatures of the Color Glass Condensate: Dileptons
• A modified Balitsky-Kovchegov equation
• Color Glass Condensate in Schwinger-Keldysh QCD
• Single Inclusive Jet Production in $pA$ Collisions at NLO in the small-$x$ regime
• Initial state and thermalization in the Color Glass Condensate framework
• Dihadron Production in DIS at Small $x$ at Next to Leading Order: Transverse Photons
• Momentum Transfer Dependence of the Differential Cross Section for $J/\psi$ Production
• Small x Gluons in Nuclei and Hadrons
• Higher twists and maxima for DIS on nuclei in high density QCD region
• Gluon mini-jet production in nuclear collisions at high energies
• Some Aspects of the Theory of Heavy Ion Collisions
• BFKL Pomeron with massive gluons
• Multiparticle production in the mean field approximation of high density QCD
• Inelastic processes in DIS and N=4 SYM
• The BFKL Pomeron Calculus in the dipole approach
• Non-linear equation: energy conservation and impact parameter dependence
• CGC/saturation approach for soft interactions at high energy: survival probability of the central exclusive production
• Lattice Computations of Small-x Parton Distributions in a Model of Parton Densities in Very Large Nuclei
• A model for strong interactions at high energy based on the CGC/saturation approach
• Has HERA reached a new QCD regime?
• CGC/saturation approach for soft interactions at high energy: inclusive production
• Charged Hadron Multiplicity Distribution at Relativistic Heavy Ion Colliders
• Photons from thermalizing matter in heavy ion collisions
• Unitarity Corrections to the Drell-Yan Process in the Target Rest Frame
• BFKL Pomeron: modeling confinement
• Unitarity bound for gluon shadowing
• Non-Gaussian Correlations in the McLerran-Venugopalan Model
• Proton-proton cross-sections: the interplay between density and radius
• CGC/saturation approach for high energy soft interactions: ${\mathbf{v}}_2$ in proton-proton collisions
• QCD motivated approach to soft interactions at high energy: inclusive production
• Shadowing of gluons in perturbative QCD: A comparison of different models
• The BFKL Pomeron Calculus in zero transverse dimensions: diffractive processes and survival probability for central diffractive production
• Solution to the Balitsky-Kovchegov equation in the saturation domain
• Non linear evolution: revisiting the solution in the saturation region
• CGC/saturation approach: soft interaction at the LHC energies
• Scaling Violations in the $Q^2$ Logarithmic Derivative of $F_2$
• Direct quarkonium-plus-gluon production in DIS in the Color Glass Condensate
• Determination of the Parameters of a Color Neutral 3D Color Glass Condensate Model
• Soft interaction at high energy and N=4 SYM
• Gluon saturation and inclusive production at low transverse momenta
• D-instantons and multiparticle production in N=4 SYM
• QCD motivated approach to soft interactions at high energies: nucleus-nucleus and hadron-nucleus collisions
• Large $\mathbf{b}$ behaviour in the CGC/saturation approach: BFKL equation with pion loops
• Study of the behavior of nuclear modification factor in freeze-out state
• Diffraction Production in a Soft Interaction Model: Mass Distributions
• 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
• Time-Dependent Observables in Heavy Ion Collisions I: Setting up the Formalism
• Higher Twist Corrections and Maxima for DIS on a Proton in the High Density QCD Region
• Inclusive production in a QCD and N=4 SYM motivated model for soft interactions
• Rapidity dependence of the photon to pion production ratio in high energy collisions
• Two parton shower background for associate W Higgs production
• Probing Gluons in Nuclei: the Case of ${\eta }^{\prime }$
• Color Glass Condensate meets High Twist Expansion
• Energy evolution of J/$\psi$ production in DIS on nuclei
• Classicalization and unitarization of wee partons in QCD and Gravity: The CGC-Black Hole correspondence
• Long range rapidity correlations in soft interaction at high energies
• High density QCD and nucleus-nucleus scattering deeply in the saturation region
• Gluon saturation: survival probability for leading neutrons in DIS
• Testing the double-logarithm asymptotic gluon density in ultraperipheral heavy ion collisions at the Large Hadron Collider
• Homotopy solution to non-linear evolution for heavy nuclei
• On the Nuclear Modification Factor at RHIC and LHC
• BFKL Pomeron calculus: nucleus-nucleus scattering
• Dijet impact factor in DIS at next-to-leading order in the Color Glass Condensate
• Average $p_t$ as a probe of high energy QCD dynamics
• CGC/saturation approach: re-visiting the problem of odd harmonics in angular correlations
• The BFKL Pomeron calculus: summing enhanced diagrams
• Geometrical scaling of heavy-quark contributions in the low $x$ region
• Perturbative Vacuum Wavefunctional for Gauge Theories in the Milne Space
• A new parton model for the soft interactions at high energies
• Small $x$ behavior in QCD from maximal entanglement and conformal invariance
• From RHIC to EIC: Nuclear Structure Functions