Random walks of partons in SU(N_c) and classical representations of color charges in QCD at small x

Abstract

The effective action for wee partons in large nuclei includes a sum over static color sources distributed in a wide range of representations of the SU(N_c) color group. The problem can be formulated as a random walk of partons in the N_c-1 dimensional space spanned by the Casimirs of SU(N_c). For a large number of sources, k >> 1, we show explicitly that the most likely representation is a classical representation of order O(\sqrt{k}). The quantum sum over representations is well approximated by a path integral over classical sources with an exponential weight whose argument is the quadratic Casimir operator of the group. The contributions of the higher N_c-2 Casimir operators are suppressed by powers of k. Other applications of the techniques developed here are discussed briefly.

arXiv comment51 pages, includes 3 eps files

References in corpus (33)

• Computing Quark and Gluon Distribution Functions for Very Large Nuclei
• Gluon Distribution Functions for Very Large Nuclei at Small Transverse Momentum
• Nonlinear Gluon Evolution in the Color Glass Condensate: I
• Green's Functions in the Color Field of a Large Nucleus
• The BFKL Equation from the Wilson Renormalization Group
• Nonlinear Gluon Evolution in the Color Glass Condensate: II
• The Intrinsic Glue Distribution at Very Small x
• Unitarity at small Bjorken x
• The Wilson renormalization group for low x physics: Gluon evolution at finite parton density
• The Quark-Gluon Plasma: Collective Dynamics and Hard Thermal Loops
• Non-Abelian Weizsacker-Williams field and a two-dimensional effective color charge density for a very large nucleus
• Geometric Scaling above the Saturation Scale
• Fock Space Distributions, Structure Functions, Higher Twists and Small x
• Quantum structure of the non-Abelian Weizsacker-Williams field for a very large nucleus
• Quantum Corrections to the Weizsäcker--Williams Distribution Function as Small x
• Classical Transport Theory and Hard Thermal Loops in the Quark-Gluon Plasma
• Classical Gluodynamics of High Energy Nuclear Collisions: an Erratum and an Update
• Yang-Mills Radiation in Ultra-relativistic Nuclear Collisions
• Semi-classical transport theory for non-Abelian plasmas
• Structure Functions of the Nucleon and their Interpretation
• Generalized Euler Angle Paramterization for SU(N)
• From Color Glass to Color Dipoles in high-energy onium--onium scattering
• Coherent States For SU(3)
• Volumes of Compact Manifolds
• Wong's equations and the small x effective action in QCD
• Coherent States of the SU(N) groups
• Gluon Distributions and Color Charge Correlations in a Saturated Light-cone Wavefunction
• Minding one's P's and Q's : from the one loop effective action in quantum field theory to classical transport theory
• Partons, Factorization and Resummation, TASI95
• QCD and Hadron Dynamics
• Optimally defined Racah-Casimir operators for su(n) and their eigenvalues for various classes of representations
• Charged Particle Multiplicity and Limiting Fragmentation in Au+Au Collisions at RHIC Energies Using the Phobos Detector
• Quasi-particle Model in hot QCD

Cited by in corpus (54)

• The Color Glass Condensate
• Event-by-event gluon multiplicity, energy density and eccentricities at RHIC and LHC
• The Unstable Glasma
• QCD thermalization: Ab initio approaches and interdisciplinary connections
• Mining for Gluon Saturation at Colliders
• Next-to-eikonal corrections in the CGC: gluon production and spin asymmetries in pA collisions
• Quark pair production in high energy pA collisions: General features
• Particle production in field theories coupled to strong external sources I. Formalism and main results
• Tracing the origin of azimuthal gluon correlations in the color glass condensate
• Prompt photon production and photon-hadron correlations at RHIC and the LHC from the Color Glass Condensate
• Dipole factorization for DIS at NLO: Combining the $q\bar{q}$ and $q\bar{q}g$ contributions
• Deeply inelastic scattering structure functions on a hybrid quantum computer
• A classical Odderon in QCD at high energies
• Quarkonium production in high energy proton-nucleus collisions: CGC meets NRQCD
• Multiplicity distributions in p+p, p+A and A+A collisions from Yang-Mills dynamics
• Transverse single spin asymmetries at small x and the anomalous magnetic moment
• Small x physics and RHIC data
• Anisotropy of the semi-classical gluon field of a large nucleus at high energy
• Two-gluon correlations and initial conditions for small-x evolution
• Gluon propagation inside a high-energy nucleus
• Constructing phase space distributions with internal symmetries
• Inclusive prompt photon production in electron-nucleus scattering at small x
• Extracting many-body color charge correlators in the proton from exclusive DIS at large Bjorken x
• Light projectile scattering off the Color Glass Condensate
• The quark-gluon medium
• Classical double copy from Color Kinematics duality: A proof in the soft limit
• The role of the chiral anomaly in polarized deeply inelastic scattering II: Topological screening and transitions from emergent axion-like dynamics
• Initial conditions for dipole evolution beyond the McLerran-Venugopalan model
• From Color Fields to Quark Gluon Plasma
• Extracting many-body correlators of saturated gluons with precision from inclusive photon+dijet final states in deeply inelastic scattering
• A Sommerfeld Toolbox for Colored Dark Sectors
• Measuring Color Memory in a Color Glass Condensate at Electron-Ion Colliders
• Sea quark Sivers distribution
• The spin dependent odderon in the diquark model
• Are the Angular Correlations in pA Collisions due to a Glasmion or Bose Condensation ?
• On the Wess-Zumino term in high energy QCD
• The Color Glass Condensate: an overview
• Large N limit of 2D Yang-Mills Theory and Instanton Counting
• Classical QGP : III. The free energy
• Nonlinear dynamics of soft fermion excitations in hot QCD plasma III: Soft-quark bremsstrahlung and energy losses
• Photon-Odderon interference in exclusive ${\chi }_c$ charmonium production at the Electron-Ion Collider
• Fluctuations of the gluon distribution from the small-x effective action
• Magnetic screening in high-energy heavy-ion collisions
• Gauge invariant source terms in QCD
• Non-perturbative renormalization of the average color charge and multi-point correlators of color charge from a non-Gaussian small-$x$ action
• Distribution of multiple scatterings in proton-nucleus collisions at high energy
• Hamiltonian formalism for Bose excitations in a plasma with a non-Abelian interaction I: plasmon -- hard particle scattering
• Mapping the internal structure of hadrons through color and spin effects
• Spatial Wilson loops in the classical field of high-energy heavy-ion collisions
• Perturbative structure of two- and four-point functions of color charge in a non-Gaussian small-$x$ action
• Color-glass condensate beyond the Gaussian approximation
• Invariant color calculus and generalized Balitsky-Kovchegov hierarchy
• Tunneling through Color Glass Condensate and True Black Disks
• Extremal black disks in QCD