Nonlinear Gluon Evolution in the Color Glass Condensate: II

Abstract

We complete the construction of the renormalization group equation (RGE) for the Color Glass Condenstate begun in Paper I. This is the equation which governs the evolution with rapidity of the statistical weight function for the color glass field. The coefficients in this equation --- one-loop real and virtual contributions --- are computed explicitly, to all orders in the color glass field. The resulting RGE can be interpreted as the imaginary-time evolution equation, with rapidity as the ``imaginary time'', for a quantum field theory in two spatial dimensions. In the weak field limit it reduces to the BFKL equation. In the general non-linear case, it is equivalent to an equation by Weigert which summarizes in functional form the evolution equations for Wilson line operators previously derived by Balitsky and Kovchegov.

52 pages

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• High energy QCD: multiplicity dependence of quarkonia production
• Parton Percolation and J/Psi Suppression
• Diffractive deep inelastic scattering in an AdS/CFT inspired model: A phenomenological study
• Triple- and Quadruple-Gluon Azimuthal Correlations from Glasma and Higher-Dimensional Ridges
• S-matrix and productions amplitudes in high energy QCD
• Global analysis of polarized DIS & SIDIS data with improved small-$x$ helicity evolution
• Baryon Stopping in Proton-Nucleus Collisions
• On perturbative limits of quadrupole evolution in QCD at high energy
• CGC formalism with two sources
• Baryon stopping in the Color Glass Condensate formalism: A phenomenological study
• Production of Secondaries in High Energy d+Au Collisions
• Liouville field theory for gluon saturation in QCD at high energy
• Lecture notes on "Quantum chromodynamics and statistical physics"
• R-Current DIS on a Shock Wave: Beyond the Eikonal Approximation
• High energy asymptotic behavior of the $S$-matrix in the saturation region with the smallest dipole running coupling prescription
• CGC/saturation approach for soft interactions at high energy: a two channel model
• Fully coherent energy loss effects on light hadron production in pA collisions
• JIMWLK Evolution, Lindblad Equation and Quantum-Classical Correspondence
• Uncovering the triple pomeron vertex from Wilson line formalism
• On correlations and discreteness in non-linear QCD evolution
• Hot and dense matter: from RHIC to LHC: Theoretical overview
• Exclusive processes with a leading neutron in $ep$ collisions
• Solution to the evolution equation at NLL for high parton density QCD
• The ratio of the beauty structure functions $R^b=F_L^b/F_2^b$ at low x
• Measurement of inclusive very forward jet cross sections in proton-lead collisions at $\sqrt{s_{\mathrm{NN}}}=$ 5.02 TeV
• Particle production and AGK relations in the Color Glass Condensate picture
• Cubic color charge correlator in a proton made of three quarks and a gluon
• Charged Hadron Multiplicity Distribution at Relativistic Heavy Ion Colliders
• Pressure Anisotropy in Heavy Ion Collisions from Color Glass Condensate
• Perturbative QCD and beyond: azimuthal angle correlations in deuteron-deuteron scattering from Bose-Einstein correlations
• Extended collinearly-improved Balitsky-Kovchegov evolution equation in target rapidity
• Non-linear evolution in CCFM: The interplay between coherence and saturation
• Photons from thermalizing matter in heavy ion collisions
• Geometrical scaling for energies available at the BNL Relativistic Heavy Ion Collider to those at the CERN Large Hadron Collider
• On the rapidity dependence of the average transverse momentum in hadronic collisions
• Nonlinear dynamics of soft boson excitations in hot QCD plasma I: plasmon-plasmon scattering
• The JIMWLK evolution and the s-channel unitarity
• A phenomenological analysis of the nonperturbative QCD contributions for the photon wave function
• Gluon Radiation from a classical point particle II: dense gluon fields
• Incoherent diffractive dijet production in electron DIS off nuclei at high energy
• General formulae for dipole Wilson line correlators with the Color Glass Condensate
• CGC/saturation approach for high energy soft interactions: ${\mathbf{v}}_2$ in proton-proton collisions
• Deep Inelastic Scattering in the Exponentially Small Bjorken Parameter Regime from the Holographic Softwall Model
• Running Coupling Corrections to Nonlinear Evolution for Diffractive Dissociation
• Testing the running coupling $k_T$-factorization formula for the inclusive gluon production
• CGC/saturation approach for high energy soft interactions: `soft' Pomeron structure and $v_n$ in hadron and nucleus collisions from Bose-Einstein correlation
• Dipole model for double meson production in two-photon interactions at high energies
• QCD motivated approach to soft interactions at high energy: inclusive production
• Non-Gaussian Correlations in the McLerran-Venugopalan Model
• First Saturation Correction in High Energy Proton-Nucleus Collisions: I. Time evolution of classical Yang-Mills fields beyond leading order
• Estimating non-linear QCD effects in ultrahigh energy neutrino events at IceCube
• DPS in CGC: HBT correlations in double inclusive photon production
• Nuclei in the toy world: beyond the Pomeron in zero transverse dimensions
• Inclusive Gluon Production in the QCD Reggeon Field Theory: Pomeron Loops Included
• Ultra-forward particle production from CGC+Lund fragmentation
• BFKL and CCFM evolutions with saturation boundary
• Stronger $C$-odd color charge correlations in the proton at higher energy
• Saturation and forward jets at HERA
• Solution of the Fan Diagram Equation in 2+1 Dimensional QCD
• Geometric Scaling in Mueller-Navelet Jets
• Quantum corrections to the Classical Statistical Approximation for the expanding quantum field
• The BFKL Pomeron Calculus in zero transverse dimensions: diffractive processes and survival probability for central diffractive production
• Multiparticle azimuthal angular correlations in $pA$ collisions
• Nonlinear dynamics of soft boson collective excitations in hot QCD plasma II: plasmon -- hard-particle scattering and energy losses
• Evolution of initial stage fluctuations in the glasma
• Color Glass Condensate and its relation to HERA physics
• CGC/saturation approach: soft interaction at the LHC energies
• Non linear evolution: revisiting the solution in the saturation region
• Wilson lines - color charge densities correlators and the production of eta' in the CGC for pp and pA collisions
• High-Energy QCD factorization from DIS to pA collisions
• Production of secondaries in soft p+pb collisions at LHC
• Gluon saturation and inclusive production at low transverse momenta
• Unifying approaches: derivation of Balitsky hierarchy from the Lipatov effective action
• Baryon scattering at high energies: wave function, impact factor, and gluon radiation
• Soft interaction at high energy and N=4 SYM
• Novel Cross Section Ratios as Possible Signals of Saturation in UPCs
• Direct quarkonium-plus-gluon production in DIS in the Color Glass Condensate
• Compatibility of phenomenological dipole cross sections with the Balitsky-Kovchegov equation
• Fluctuations of the gluon distribution from the small-x effective action
• On correlators of Reggeon fields and operators of Wilson lines in high energy QCD
• Computation of pion and kaon heavy ion multiplicities in a gluon-meson model
• Violation of Geometrical Scaling in pp Collisions at NA61/SHINE
• The color dipole model bounds with the gluon-gluon recombination correction
• Probing the Color Glass Condensate in $pp$ collisions at forward rapidities and very low transverse momenta
• Coherent and incoherent diffractive hadron production in pA collisions and gluon saturation
• Small-$x$ QCD evolution of $2n$ Wilson line correlator: the weak field limit
• The small-x gluon distribution in centrality biased pA and pp collisions
• Semiclassical solution to the BFKL equation with massive gluons
• QCD at small x and nucleus-nucleus collisions
• J/ψ and ψ' production in proton(deuteron)-nucleus collisions: lessons from RHIC for the proton-lead LHC run
• On asymptotic solutions of RFT in zero transverse dimensions
• Large $\mathbf{b}$ behaviour in the CGC/saturation approach: BFKL equation with pion loops
• QCD motivated approach to soft interactions at high energies: nucleus-nucleus and hadron-nucleus collisions
• Forward trijet production in p-p and p-Pb collisions at LHC
• Coherent and incoherent $J/\Psi$ photoproduction in $PbPb$ collisions at the LHC, HE -- LHC and FCC
• D-instantons and multiparticle production in N=4 SYM
• Exclusive processes in $ep$ collisions at the EIC and LHeC: A closer look on the predictions of saturation models
• A CGC/saturation approach for angular correlations in proton-proton scattering
• Geometric scaling behavior of the scattering amplitude for DIS with nuclei
• Introduction to the Physics of Saturation
• Asymptotics of QCD traveling waves with fluctuations and running coupling effects
• Diffractive $\rho$ production at small $x$ in future Electron - Ion Colliders
• NLO JIMWLK evolution with massive quarks
• The Colour Glass Condensate
• Violation of the geometric scaling behaviour of the amplitude for running QCD coupling in the saturation region
• Rare fluctuations of the $S$-matrix at NLO in QCD
• The BEST framework for the search for the QCD critical point and the chiral magnetic effect
• Inclusive production in a QCD and N=4 SYM motivated model for soft interactions
• Tensor Meson Production in Proton-Proton Collisions from the Color Glass Condensate
• Rapidity and energy dependence of average transverse momentum and particle density in saturation models
• Isolated photon production in $pp$ collisions at forward rapidities and high multiplicity events
• Colour strings vs. hard pomeron in perturbative QCD
• Non-linear evolution in the re-summed next-to-leading order of perturbative QCD:\confronting the experimental data
• On QCD RFT corrections to the propagator of reggeized gluons
• Analytic solution of Balitsky-Kovchegov equation with running coupling constant using homogeneous balance method
• High energy scattering in Einstein-Cartan gravity
• Gluon multiplicity in coherent diffraction of onium on a heavy nucleus
• Spectrum of diffractively produced gluons in onium-nucleus collisions
• Saturation and Wilson Line Distributions
• The Phase Diagram of QCD and Some Issues of Large Nc
• Hadronization of correlated gluon fields
• Quark TMDs from back-to-back dijet production at forward rapidities in pA collisions beyond eikonal accuracy in the CGC
• Dynamical behavior connection of the gluon distribution and the proton structure function at small $x$
• Pseudo and quasi gluon PDF in the BFKL approximation
• Solution to the Sudakov suppressed Balitsky-Kovchegov equation and its application to the HERA data
• Complete calculation of exclusive heavy vector meson production at next-to-leading order in the dipole picture
• Non-perturbative renormalization of the average color charge and multi-point correlators of color charge from a non-Gaussian small-$x$ action
• Dipole-dipole scattering amplitude in CGC approach
• Sudakov effects and the dipole amplitude
• A parton shower generator based on the GLR equation
• Scattering from an external field in quantum chromodynamics at high energies: from foundations to interdisciplinary connections
• CGC/saturation approach for soft interactions at high energy: long range rapidity correlations
• The two-loop Higgs impact factor
• Heavy Quark Production in Ultra High Energy Cosmic Ray Interactions
• Probing gluon number fluctuation effects in future electron-hadron colliders
• QCD Evolution Workshop: Introduction
• Nuclear shadowing in deep inelastic scattering on nuclei: a closer look
• AAMQS: a non-linear QCD description of new HERA data at small-x
• The Status of Parton Saturation and the CGC
• A unitarized model of inclusive and diffractive DIS with Q2-evolution
• Canonical Flow in the Space of Gauge Parameters
• Symplectic approach to lightcone QCD
• Gauge invariant source terms in QCD
• Deriving the Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner equation with classical and quantum source terms
• Soft interactions at high energies: QCD motivated approach
• Rapidity dependence of the photon to pion production ratio in high energy collisions
• The Emerging QCD Frontier: The Electron Ion Collider
• D meson production in d+Au process using a perturbative approach
• Probing QCD dynamics in two-photon interactions at high energies
• Impact-parameter-dependent solutions to the Balitsky-Kovchegov equation at next-to-leading order
• High density QCD and nucleus-nucleus scattering deeply in the saturation region
• Inside looking out: probing JIMWLK with BFKL calculations
• Taming of preasymptotic small x evolution within resummation framework
• Classicalization and unitarization of wee partons in QCD and Gravity: The CGC-Black Hole correspondence
• Exclusive heavy quark photoproduction in $pp$, $pPb$ and $PbPb$ collisions at the LHC and FCC energies
• Exclusive $\rho$ and $J/\Psi$ photoproduction in ultraperipheral $pO$ and $OO$ collisions at energies available at the CERN Large Hadron Collider
• Distribution of multiple scatterings in proton-nucleus collisions at high energy
• Long range rapidity correlations in soft interaction at high energies
• Energy evolution of J/$\psi$ production in DIS on nuclei
• Exclusive vector meson production with leading neutrons in a saturation model for the dipole amplitude in mixed space
• Infrared instability from nonlinear QCD evolution
• Color Glass Condensate meets High Twist Expansion
• Double vector meson production in the International Linear Collider
• More on eikonal approximation for high energy scattering
• Inclusive cross-sections for jet production in nucleus-nucleus collisions in perturbative QCD
• Soft Pomeron in the Colour Glass Condensate approach
• Single inclusive jet photoproduction at very forward rapidities in $pp$ and $pPb$ collisions at the LHC
• Soft processes at high energy without soft Pomeron: a QCD motivated model
• The energy dependence of exclusive heavy vector meson photoproduction cross-sections and NLO BFKL evolution
• Homotopy solution to non-linear evolution for heavy nuclei
• Thermal radiation and inclusive production in the running coupling $k_T$ -- factorization approach
• Eikonal but not: a complementary view of high energy evolution
• CGC and saturation approach: Impact-parameter dependent model of perturbative QCD and combined HERA data
• Gluon saturation: survival probability for leading neutrons in DIS
• Inclusive gauge boson production in the color dipole formalism
• Unequal rapidity correlators in the dilute limit of JIMWLK
• High-energy QCD evolution from BRST symmetry
• Azimuthal angle correlations in hadron-nucleus scattering: enhanced diagrams
• Average $p_t$ as a probe of high energy QCD dynamics
• Gluon Evolution and Saturation Proceedings
• Remarks on Diffractive Dissociation within JIMWLK Evolution at NLO
• The BFKL Pomeron calculus: summing enhanced diagrams
• BFKL Pomeron calculus: nucleus-nucleus scattering
• SPIN Effects, QCD, and Jefferson Laboratory with 12 GeV electrons
• Can $1/N_c$ corrections destroy the saturation of dipole densities?
• Parton model contributions as next-to-eikonal corrections to the dipole factorization of DIS and SIDIS at low $x_{Bj}$
• Perturbative Corrections to Quark TMDPDFs in the Background-Field Method: Gauge Invariance, Equations of Motion, and Multiple Interactions
• Photoproduction of ${\eta }_c\gamma$ pairs in CGC framework
• The MV Model of the Color Glass Condensate for a Finite Number of Sources Including Coulomb Interactions
• Callan-Symanzik equations and low-energy theorems with trace anomalies
• Low-$x$ Physics in $pA$ Collisions and at the EIC
• Twist decomposition of non-linear effects in Balitsky-Kovchegov evolution of proton structure functions
• Bulk quantities in nuclear collisions from running coupling $k_T$-factorization and hybrid simulations
• Higher twists effects in DIS on nuclei at the EIC and LHeC: A phenomenological analysis
• Evolution equation for elastic scattering of hadrons
• Dijet impact factor in DIS at next-to-leading order in the Color Glass Condensate
• 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
• Balitsky-Kovchegov equation at next-to-leading order accuracy with a resummation of large logarithms
• From RHIC to EIC: Nuclear Structure Functions
• Direct photons in d+Au collisions at s_(NN)**(1/2)=200GeV with STAR
• Perturbative structure of two- and four-point functions of color charge in a non-Gaussian small-$x$ action
• Compact construction algorithms for the singlets of SU(N) over mixed tensor product spaces
• Unequal rapidity correlators in the dilute limit of JIMWLK
• High energy scattering in QCD: dipole approach with Pomeron loops
• Probing Saturation Physics in the Real Compton Scattering at Ultraperipheral $pPb$ Collisions
• From Classical to Quantum Saturation in the Nuclear Gluon Distribution
• High-energy factorization and evolution with improved kinematics
• Geometrical scaling of heavy-quark contributions in the low $x$ region
• Diffractive hadron production in DIS off heavy nuclei and gluon saturation
• Spin-glass model of QCD near saturation
• Gluon imaging using azimuthal correlations in diffractive scattering at the Electron-Ion Collider
• Color Glass Condensate and BFKL dynamics in deep inelastic scattering at small x
• Wave function derivation of the JIMWLK equation
• Exploring the DGLAP resummation in the JIMWLK Hamiltonian
• On the low-x NLO evolution of 4 point colorless operators
• Properties of inclusive hadron production in Deep Inelastic Scattering on heavy nuclei at low x
• Dijet photoproduction at low $x$ at next-to-leading order and its back-to-back limit
• Reconstruction of the Dipole Amplitude in the Dipole Picture as a mathematical Inverse Problem
• Invariant color calculus and generalized Balitsky-Kovchegov hierarchy
• Characterizing the initial conditions of heavy-ion collisions at the LHC with mean transverse momentum and anisotropic flow correlations
• High energy DVCS on a photon and related meson exclusive production
• Local one-dimensional reggeon model of the interaction of several pomerons
• Entanglement, Trace Anomaly and Confinement in QCD
• Four-pomeron vertex
• Finite volume effects in the McLerran-Venugopalan initial condition for the JIMWLK equation
• A predictive phenomenological tool at small Bjorken-x
• Glauber quark and gluon contributions to quark energy loss at next-to-leading order and next-to-leading twist
• Photoproduction of three jets in the CGC: gluon TMDs and dilute limit
• Impact Factor for Exclusive Diffractive Dijet Production with NLO Accuracy
• The Color Glass Condensate and some applications
• Small-x, Diffraction and Vector Mesons
• Scattering off the Color Glass Condensate
• A unified description of initial and final state interactions in heavy ion collisions
• NNLO classical solution for Lipatov's effective action for reggeized gluons
• Probing gluon saturation via diffractive jets in ultra-peripheral nucleus-nucleus collisions
• Color strings, pomeron shadowing and Color Glass Condensate
• CGC-induced longitudinal ridge in p-Pb collisions
• BFKL Pomeron calculus: solution to equations for nucleus-nucleus scattering in the saturation domain
• Coherent energy loss effects in dihadron azimuthal angular correlations in Deep Inelastic Scattering at small $x$