The Renormalization Group Equation for the Color Glass Condensate

Abstract

We present an explicit and simple form of the renormalization group equation which governs the quantum evolution of the effective theory for the Color Glass Condensate (CGC). This is a functional Fokker-Planck equation for the probability density of the color field which describes the CGC in the covariant gauge. It is equivalent to the Euclidean time evolution equation for a second quantized current-current Hamiltonian in two spatial dimensions. The quantum corrections are included in the leading log approximation, but the equation is fully non-linear with respect to the generally strong background field. In the weak field limit, it reduces to the BFKL equation, while in the general non-linear case it generates the evolution equations for Wilson-line operators previously derived by Balitsky and Kovchegov within perturbative QCD.

14 pages, more details on intermediate calculations. Final version, to appear in Physics Letters B

References in corpus (1)

• Nonlinear Gluon Evolution in the Color Glass Condensate: II

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• Semiclassical solution to the BFKL equation with massive gluons
• On asymptotic solutions of RFT in zero transverse dimensions
• Small-$x$ QCD evolution of $2n$ Wilson line correlator: the weak field limit
• QCD at small x and nucleus-nucleus collisions
• Geometric scaling behavior of the scattering amplitude for DIS with nuclei
• Diffraction Production in a Soft Interaction Model: Mass Distributions
• From EMC- and Cronin-effects to signals of quark-gluon plasma
• Large $\mathbf{b}$ behaviour in the CGC/saturation approach: BFKL equation with pion loops
• A CGC/saturation approach for angular correlations in proton-proton scattering
• The small-x gluon distribution in centrality biased pA and pp collisions
• QCD motivated approach to soft interactions at high energies: nucleus-nucleus and hadron-nucleus collisions
• Collective Phenomena in the Non-Equilibrium Quark-Gluon Plasma
• D-instantons and multiparticle production in N=4 SYM
• Study of the behavior of nuclear modification factor in freeze-out state
• The BEST framework for the search for the QCD critical point and the chiral magnetic effect
• The Colour Glass Condensate
• Violation of the geometric scaling behaviour of the amplitude for running QCD coupling in the saturation region
• Asymptotics of QCD traveling waves with fluctuations and running coupling effects
• Time-Dependent Observables in Heavy Ion Collisions II: in Search of Pressure Isotropization in the ${\phi }^4$ Theory
• CGC, QCD Saturation and RHIC data (Kharzeev-Levin-McLerran-Nardi point of view)
• Inclusive production in a QCD and N=4 SYM motivated model for soft interactions
• Brief Review of Saturation Physics
• The Phase Diagram of QCD and Some Issues of Large Nc
• Analytic solution of Balitsky-Kovchegov equation with running coupling constant using homogeneous balance method
• Off-shell amplitudes as boundary integrals of analytically continued Wilson line slope
• Gluon multiplicity in coherent diffraction of onium on a heavy nucleus
• Hadronization of correlated gluon fields
• Beyond DGLAP improved saturation model
• On QCD RFT corrections to the propagator of reggeized gluons
• Non-linear evolution in the re-summed next-to-leading order of perturbative QCD:\confronting the experimental data
• On the odderon mechanism for transverse single spin asymmetry in the Wandzura-Wilczek approximation
• Gluon recombination in high parton density QCD: inclusive pion production
• Spectrum of diffractively produced gluons in onium-nucleus collisions
• High energy scattering in Einstein-Cartan gravity
• Dynamical behavior connection of the gluon distribution and the proton structure function at small $x$
• Saturation and linear transport equation
• Saturation and Wilson Line Distributions
• Renormalization Group Equation and QCD Coupling Constant in the Presence of SU(3) Chromo-Electric Field
• Quark TMDs from back-to-back dijet production at forward rapidities in pA collisions beyond eikonal accuracy in the CGC
• The Status of Parton Saturation and the CGC
• Dipole-dipole scattering amplitude in CGC approach
• Soft interactions at high energies: QCD motivated approach
• Structure functions from renormalization group improved small $x$ evolution
• Complete calculation of exclusive heavy vector meson production at next-to-leading order in the dipole picture
• Investigating the broadening phenomenon in two-particle correlations induced by gluon saturation
• Longitudinal Rescaling and High-Energy Effective Actions
• Fluctuations of topological charge and chiral density in the early stage of high energy nuclear collisions
• CGC/saturation approach for soft interactions at high energy: long range rapidity correlations
• Proton and anti-proton production in the forward region of d+Au collisions at RHIC from the color glass condensate
• Sudakov effects and the dipole amplitude
• Deriving the Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner equation with classical and quantum source terms
• Non-perturbative renormalization of the average color charge and multi-point correlators of color charge from a non-Gaussian small-$x$ action
• Rapidity dependence of the photon to pion production ratio in high energy collisions
• Gauge invariant source terms in QCD
• Probing Gluons in Nuclei: the Case of ${\eta }^{\prime }$
• Probing gluon number fluctuation effects in future electron-hadron colliders
• Prediction for unintegrated parton distributions
• Scattering from an external field in quantum chromodynamics at high energies: from foundations to interdisciplinary connections
• Impact-parameter-dependent solutions to the Balitsky-Kovchegov equation at next-to-leading order
• Infrared instability from nonlinear QCD evolution
• Long range rapidity correlations in soft interaction at high energies
• Chaos in the Color Glass Condensate
• Inside looking out: probing JIMWLK with BFKL calculations
• Distribution of multiple scatterings in proton-nucleus collisions at high energy
• Energy evolution of J/$\psi$ production in DIS on nuclei
• High density QCD and nucleus-nucleus scattering deeply in the saturation region
• Exclusive vector meson production with leading neutrons in a saturation model for the dipole amplitude in mixed space
• Heavy quark structure functions from unifying the color dipole picture and double asymptotic scaling approaches
• Single inclusive jet transverse momentum and energy spectra at very forward rapidity in proton-proton collisions with $\sqrt{s}=7$ and 13 TeV
• Color Glass Condensate meets High Twist Expansion
• Quarkonium production at collider energies in Small-$x$ formalism
• Next-to-Leading Order correction to inclusive particle spectra in the Color Glass Condensate framework
• Soft processes at high energy without soft Pomeron: a QCD motivated model
• Unequal rapidity correlators in the dilute limit of JIMWLK
• High-energy QCD evolution from BRST symmetry
• Soft Pomeron in the Colour Glass Condensate approach
• Gluon saturation: survival probability for leading neutrons in DIS
• CGC and saturation approach: Impact-parameter dependent model of perturbative QCD and combined HERA data
• On the Nuclear Modification Factor at RHIC and LHC
• The energy dependence of exclusive heavy vector meson photoproduction cross-sections and NLO BFKL evolution
• Homotopy solution to non-linear evolution for heavy nuclei
• JIMWLK evolution and small-x asymptotics of 2n-tuple Wilson line correlators
• Forward Hadron Productions in Proton-Proton Collisions in Small-$x$ Formalism
• A geometrizing higher twist effect on nuclear target
• Eikonal but not: a complementary view of high energy evolution
• Gluon saturation effects on J/Psi production in heavy ion collisions
• Analytic structure of the high-energy gravitational amplitude: multi-H diagrams and classical 5PM logarithms
• Photoproduction of ${\eta }_c\gamma$ pairs in CGC framework
• Remarks on Diffractive Dissociation within JIMWLK Evolution at NLO
• Fine structures of azimuthal correlations of two gluons in the glasma
• Bulk quantities in nuclear collisions from running coupling $k_T$-factorization and hybrid simulations
• Gluon Evolution and Saturation Proceedings
• Twist decomposition of non-linear effects in Balitsky-Kovchegov evolution of proton structure functions
• Dijet impact factor in DIS at next-to-leading order in the Color Glass Condensate
• Resummation of projectile-target multiple scatterings and parton saturation
• Effective Field Theory Factorization for Diffraction
• The BFKL Pomeron calculus: summing enhanced diagrams
• BFKL Pomeron calculus: nucleus-nucleus scattering
• Classical information entropy of parton distribution functions and an application in searching gluon saturation
• Rapidity dependence of saturation in inclusive HERA data with the rcBK equation
• Average $p_t$ as a probe of high energy QCD dynamics
• Callan-Symanzik equations and low-energy theorems with trace anomalies
• Can $1/N_c$ corrections destroy the saturation of dipole densities?
• Mapping the internal structure of hadrons through color and spin effects
• Azimuthal angle correlations in hadron-nucleus scattering: enhanced diagrams
• Parton model contributions as next-to-eikonal corrections to the dipole factorization of DIS and SIDIS at low $x_{Bj}$
• First correction to JIMWLK evolution from the classical equations of motion
• Perturbative structure of two- and four-point functions of color charge in a non-Gaussian small-$x$ action
• Rapidity window dependence of ridge correlations in the glasma
• Gluon imaging using azimuthal correlations in diffractive scattering at the Electron-Ion Collider
• Looking for quark saturation in proton and nuclei
• Spin-glass model of QCD near saturation
• Balitsky-Kovchegov equation at next-to-leading order accuracy with a resummation of large logarithms
• Two-Particle Correlations in Heavy-Light Ion Collisions
• From RHIC to EIC: Nuclear Structure Functions
• Exploring the DGLAP resummation in the JIMWLK Hamiltonian
• Effects of heavy quarks in the dipole cross section with the KLN model
• Improving the solver for the Balitsky-Kovchegov evolution equation with Automatic Differentiation
• Color dipole cross-section from unifying the color dipole picture and improved saturation models
• Elliptic Flow from Color Glass Condensate
• Structure of the medium formed in heavy ion collisions
• High-energy factorization and evolution with improved kinematics
• Color Glass Condensate and BFKL dynamics in deep inelastic scattering at small x
• High energy scattering in QCD: dipole approach with Pomeron loops
• Multi-gluon correlations in the Color Glass Condensate
• Scattering off the Color Glass Condensate
• QCD Beyond Leading Power
• Glauber quark and gluon contributions to quark energy loss at next-to-leading order and next-to-leading twist
• Reconstruction of the Dipole Amplitude in the Dipole Picture as a mathematical Inverse Problem
• Entanglement, Trace Anomaly and Confinement in QCD
• CGC-induced longitudinal ridge in p-Pb collisions
• Dijet photoproduction at low $x$ at next-to-leading order and its back-to-back limit
• BFKL Pomeron calculus: solution to equations for nucleus-nucleus scattering in the saturation domain
• Local one-dimensional reggeon model of the interaction of several pomerons
• Four-pomeron vertex
• High Energy Collisions of Dense Hadrons in Quantum Chromodynamics : LHC Phenomenology and Universality of Parton Distributions
• Small-x, Diffraction and Vector Mesons
• Photoproduction of three jets in the CGC: gluon TMDs and dilute limit
• 3-D Glasma initial state from small-x evolution
• NNLO classical solution for Lipatov's effective action for reggeized gluons
• Impact Factor for Exclusive Diffractive Dijet Production with NLO Accuracy
• Transverse Spin and Classical Gluon Fields: Combining Two Perspectives on Hadronic Structure