The Wilson renormalization group for low x physics: towards the high density regime

Abstract

We continue the study of the effective action for low $x$ physics based on a Wilson renormalization group approach. We express the full nonlinear renormalization group equation in terms of the average value and the average fluctuation of extra color charge density generated by integrating out gluons with intermediate values of $x$. This form clearly exhibits the nature of the phenomena driving the evolution and should serve as the basis of the analysis of saturation effects at high gluon density at small $x$.

14 pages, latex

References in corpus (1)

• The BFKL Equation from the Wilson Renormalization Group

Cited by in corpus (737)

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• Saturation effects in SIDIS at very forward rapidities
• Soft Fragmentation on the Celestial Sphere
• On parton number fluctuations at various stages of the rapidity evolution
• Decoherence and Entropy Production in Relativistic Nuclear Collisions
• KLWMIJ Reggeon Field Theory beyond the large $N_c$ limit
• Improvement for Color Glass Condensate factorization: single hadron production in pA collisions at next-to-leading order
• Probing colored glass via $q\bar{q}$ photoproduction II: diffraction
• Multipole scattering amplitudes in the Color Glass Condensate formalism
• The BFKL Pomeron Calculus in the dipole approach
• Inelastic processes in DIS and N=4 SYM
• Nonlinear evolution of pomeron and odderon in momentum space
• TMD gluon distributions for multiparton processes
• Helicity Evolution at Small $x$: Revised Asymptotic Results at Large $N_c\&N_f$
• Diphoton production in high-energy p+A collisions
• Testing the Gaussian Approximation to the JIMWLK Equation
• Resumming double non-global logarithms in the evolution of a jet
• How particles emerge from decaying classical fields in heavy ion collisions: towards a kinetic description of the Glasma
• Matching next-to-leading-order and high-energy-resummed calculations of heavy-quarkonium-hadroproduction cross sections
• Probing gluon number density with electron-dijet correlations at EIC
• The dipole representation of vector meson electroproduction beyond leading twist
• Saturation and geometric scaling in DIS at small x
• Conformal symmetry of JIMWLK Evolution at NLO
• $J/\psi$ production in hadron scattering: three-pomeron contribution
• Forward Neutrinos from Charm at Large Hadron Collider
• Sudakov suppression of the Balitsky-Kovchegov kernel
• CGC/saturation approach: a new impact-parameter dependent model
• Gluon saturation and Feynman scaling in leading neutron production
• Lensing Mechanism Meets Small-$x$ Physics: Single Transverse Spin Asymmetry in $p^{\uparrow }+p$ and $p^{\uparrow }+A$ Collisions
• Non-linear equation: energy conservation and impact parameter dependence
• Impact Parameter Dependence in the Balitsky-Kovchegov Equation
• CGC/saturation approach for soft interactions at high energy: survival probability of the central exclusive production
• O(α_s^2)-corrections to JIMWLK evolution from the classical equations of motion
• Heavy quark production at LHC in the color dipole formalism
• On systematic effects in the numerical solutions of the JIMWLK equation
• Regge Field Theory in zero transverse dimensions: loops versus "net" diagrams
• Deeply virtual Compton scattering at small-$x$ in future Electron - Ion Colliders
• QCD saturation in the dipole sector with correlations
• Has HERA reached a new QCD regime?
• The dimensionally reduced description of the high energy scattering and the effective action for the reggeized gluons
• Langevin equation in effective theory of interacting QCD pomerons in the limit of large $N_c$
• Nuclear effects in Drell-Yan pair production in high-energy $pA$ collisions
• A model for strong interactions at high energy based on the CGC/saturation approach
• QCD resummation of dijet azimuthal decorrelations in pp and pA collisions
• Forward Inclusive Jet Productions in pA Collisions
• Quark production in high energy proton-nucleus collisions
• Thoughts on Non-Perturbative Thermalization and Jet Quenching in Heavy Ion Collisions
• Structure functions at small x from world-lines. I: Unpolarized distributions
• Exclusive photoproduction of vector meson at next-to-leading order from Color Glass Condensate
• Correlations in impact-parameter space in a hierarchical saturation model for QCD at high energy
• On perturbative limits of quadrupole evolution in QCD at high energy
• Decisive test of color coherence in proton-nucleus collisions at the LHC
• Diffractive deep inelastic scattering in an AdS/CFT inspired model: A phenomenological study
• CGC formalism with two sources
• S-matrix and productions amplitudes in high energy QCD
• Soft photon and two hard jets forward production in proton-nucleus collisions
• On the Wess-Zumino term in high energy QCD
• CGC/saturation approach for soft interactions at high energy: inclusive production
• Particle distribution in intense fields in a light-front Hamiltonian approach
• Baryon Stopping in Proton-Nucleus Collisions
• Baryon stopping in the Color Glass Condensate formalism: A phenomenological study
• Triple- and Quadruple-Gluon Azimuthal Correlations from Glasma and Higher-Dimensional Ridges
• The Description of $F_2$ at Very High Parton Densities
• Global analysis of polarized DIS & SIDIS data with improved small-$x$ helicity evolution
• High energy QCD: multiplicity dependence of quarkonia production
• CGC/saturation approach for soft interactions at high energy: a two channel model
• Uncovering the triple pomeron vertex from Wilson line formalism
• QCD Saturation Equations including Dipole-Dipole Correlation
• On correlations and discreteness in non-linear QCD evolution
• Exclusive processes with a leading neutron in $ep$ collisions
• Hot and dense matter: from RHIC to LHC: Theoretical overview
• Liouville field theory for gluon saturation in QCD at high energy
• R-Current DIS on a Shock Wave: Beyond the Eikonal Approximation
• JIMWLK Evolution, Lindblad Equation and Quantum-Classical Correspondence
• Fully coherent energy loss effects on light hadron production in pA collisions
• Solution to the evolution equation at NLL for high parton density QCD
• High energy asymptotic behavior of the $S$-matrix in the saturation region with the smallest dipole running coupling prescription
• 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
• Cubic color charge correlator in a proton made of three quarks and a gluon
• Pressure Anisotropy in Heavy Ion Collisions from Color Glass Condensate
• Total gluon shadowing due to fluctuation effects
• Charged Hadron Multiplicity Distribution at Relativistic Heavy Ion Colliders
• Single inclusive jet production and the nuclear modification ratio at very forward rapidity in proton-lead collisions with $\sqrt{s_{NN}}$ = 5.02 TeV
• On the rapidity dependence of the average transverse momentum in hadronic collisions
• 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
• Multiparticle Production at Mid-Rapidity in the Color-Glass Condensate
• CGC/saturation approach for high energy soft interactions: `soft' Pomeron structure and $v_n$ in hadron and nucleus collisions from Bose-Einstein correlation
• Running Coupling Corrections to Nonlinear Evolution for Diffractive Dissociation
• A phenomenological analysis of the nonperturbative QCD contributions for the photon wave function
• Testing the running coupling $k_T$-factorization formula for the inclusive gluon production
• QCD motivated approach to soft interactions at high energy: inclusive production
• The JIMWLK evolution and the s-channel unitarity
• Dipole model for double meson production in two-photon interactions at high energies
• Diffractive dissociation including pomeron loops in zero transverse dimensions
• First Saturation Correction in High Energy Proton-Nucleus Collisions: I. Time evolution of classical Yang-Mills fields beyond leading order
• Using dileptons to probe the Color Glass Condensate
• Incoherent diffractive dijet production in electron DIS off nuclei at high energy
• Travelling waves and impact-parameter correlations
• Nonlinear dynamics of soft boson excitations in hot QCD plasma I: plasmon-plasmon scattering
• Non-Gaussian Correlations in the McLerran-Venugopalan Model
• BFKL and CCFM evolutions with saturation boundary
• Wilson lines - color charge densities correlators and the production of eta' in the CGC for pp and pA collisions
• The BFKL Pomeron Calculus in zero transverse dimensions: diffractive processes and survival probability for central diffractive production
• Evolution of initial stage fluctuations in the glasma
• DPS in CGC: HBT correlations in double inclusive photon production
• Multiparticle azimuthal angular correlations in $pA$ collisions
• Nuclei in the toy world: beyond the Pomeron in zero transverse dimensions
• Stronger $C$-odd color charge correlations in the proton at higher energy
• Geometric Scaling in Mueller-Navelet Jets
• Ultra-forward particle production from CGC+Lund fragmentation
• Inclusive Gluon Production in the QCD Reggeon Field Theory: Pomeron Loops Included
• Estimating non-linear QCD effects in ultrahigh energy neutrino events at IceCube
• Quantum corrections to the Classical Statistical Approximation for the expanding quantum field
• Solution of the Fan Diagram Equation in 2+1 Dimensional QCD
• On the Dipole Swing and the Search for Frame Independence in the Dipole Model
• Non linear evolution: revisiting the solution in the saturation region
• CGC/saturation approach: soft interaction at the LHC energies
• Heavy quark production in deep inelastic electron-nucleus scattering
• Strongly Interacting Matter at High Energy Density
• Probing the Color Glass Condensate in $pp$ collisions at forward rapidities and very low transverse momenta
• Gluon saturation and inclusive production at low transverse momenta
• Soft interaction at high energy and N=4 SYM
• Fluctuations of the gluon distribution from the small-x effective action
• Gluon density fluctuations in dilute hadrons
• The color dipole model bounds with the gluon-gluon recombination correction
• High-Energy QCD factorization from DIS to pA collisions
• On correlators of Reggeon fields and operators of Wilson lines in high energy QCD
• Novel Cross Section Ratios as Possible Signals of Saturation in UPCs
• Probing the Frontiers of QCD
• Violation of Geometrical Scaling in pp Collisions at NA61/SHINE
• Baryon scattering at high energies: wave function, impact factor, and gluon radiation
• Unifying approaches: derivation of Balitsky hierarchy from the Lipatov effective action
• Compatibility of phenomenological dipole cross sections with the Balitsky-Kovchegov equation
• Small-$x$ QCD evolution of $2n$ Wilson line correlator: the weak field limit
• Geometric scaling behavior of the scattering amplitude for DIS with nuclei
• Collective Phenomena in the Non-Equilibrium Quark-Gluon Plasma
• On asymptotic solutions of RFT in zero transverse dimensions
• Semiclassical solution to the BFKL equation with massive gluons
• Forward trijet production in p-p and p-Pb collisions at LHC
• 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
• From EMC- and Cronin-effects to signals of quark-gluon plasma
• 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
• Diffraction Production in a Soft Interaction Model: Mass Distributions
• A CGC/saturation approach for angular correlations in proton-proton scattering
• Coherent and incoherent $J/\Psi$ photoproduction in $PbPb$ collisions at the LHC, HE -- LHC and FCC
• Coherent and incoherent diffractive hadron production in pA collisions and gluon saturation
• The small-x gluon distribution in centrality biased pA and pp collisions
• Diffractive $\rho$ production at small $x$ in future Electron - Ion Colliders
• Higher Twist Corrections and Maxima for DIS on a Proton in the High Density QCD Region
• Introduction to the Physics of Saturation
• CGC, QCD Saturation and RHIC data (Kharzeev-Levin-McLerran-Nardi point of view)
• Rare fluctuations of the $S$-matrix at NLO in QCD
• Time-Dependent Observables in Heavy Ion Collisions II: in Search of Pressure Isotropization in the ${\phi }^4$ Theory
• Asymptotics of QCD traveling waves with fluctuations and running coupling effects
• Violation of the geometric scaling behaviour of the amplitude for running QCD coupling in the saturation region
• Spectrum of diffractively produced gluons in onium-nucleus collisions
• Brief Review of Saturation Physics
• Tensor Meson Production in Proton-Proton Collisions from the Color Glass Condensate
• Long range rapidity correlations and the ridge in A+A collisions
• Enhancement of prompt photons in ultrarelativistic proton-proton collisions from nonlinear gluon evolution at small-$x$
• High energy scattering in Einstein-Cartan gravity
• Analytic solution of Balitsky-Kovchegov equation with running coupling constant using homogeneous balance method
• Gluon recombination in high parton density QCD: inclusive pion production
• Off-shell amplitudes as boundary integrals of analytically continued Wilson line slope
• On QCD RFT corrections to the propagator of reggeized gluons
• Gluon multiplicity in coherent diffraction of onium on a heavy nucleus
• Saturation and linear transport equation
• Saturation and Wilson Line Distributions
• Inclusive production in a QCD and N=4 SYM motivated model for soft interactions
• Non-linear evolution in the re-summed next-to-leading order of perturbative QCD:\confronting the experimental data
• Quark TMDs from back-to-back dijet production at forward rapidities in pA collisions beyond eikonal accuracy in the CGC
• Probing Gluons in Nuclei: the Case of ${\eta }^{\prime }$
• Solution to the Sudakov suppressed Balitsky-Kovchegov equation and its application to the HERA data
• Longitudinal Rescaling and High-Energy Effective Actions
• Proton and anti-proton production in the forward region of d+Au collisions at RHIC from the color glass condensate
• Complete calculation of exclusive heavy vector meson production at next-to-leading order in the dipole picture
• Non-linear equation in the re-summed next-to-leading order of perturbative QCD: the leading twist approximation
• Rapidity dependence of the photon to pion production ratio in high energy collisions
• AAMQS: a non-linear QCD description of new HERA data at small-x
• Dipole-dipole scattering amplitude in CGC approach
• Pseudo and quasi gluon PDF in the BFKL approximation
• QCD Evolution Workshop: Introduction
• Scattering from an external field in quantum chromodynamics at high energies: from foundations to interdisciplinary connections
• Probing gluon number fluctuation effects in future electron-hadron colliders
• Symplectic approach to lightcone QCD
• Nuclear shadowing in deep inelastic scattering on nuclei: a closer look
• Structure functions from renormalization group improved small $x$ evolution
• Deriving the Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner equation with classical and quantum source terms
• A unitarized model of inclusive and diffractive DIS with Q2-evolution
• Heavy Quark Production in Ultra High Energy Cosmic Ray Interactions
• Non-perturbative renormalization of the average color charge and multi-point correlators of color charge from a non-Gaussian small-$x$ action
• A parton shower generator based on the GLR equation
• The Status of Parton Saturation and the CGC
• Prediction for unintegrated parton distributions
• Gauge invariant source terms in QCD
• Near-integrability and confinement for high-energy hadron-hadron collisions
• Inside looking out: probing JIMWLK with BFKL calculations
• The Emerging QCD Frontier: The Electron Ion Collider
• Next-to-Leading Order correction to inclusive particle spectra in the Color Glass Condensate framework
• Long range rapidity correlations in soft interaction at high energies
• On the behaviour of single scale hard small $x$ processes in QCD near the black disc limit
• Classicalization and unitarization of wee partons in QCD and Gravity: The CGC-Black Hole correspondence
• Distribution of multiple scatterings in proton-nucleus collisions at high energy
• Chaos in the Color Glass Condensate
• Exclusive $\rho$ and $J/\Psi$ photoproduction in ultraperipheral $pO$ and $OO$ collisions at energies available at the CERN Large Hadron Collider
• Double vector meson production in the International Linear Collider
• Large distance behaviour of light cone operator product in perturbative and nonperturbative QCD regimes
• Low-x QCD with CMS at the LHC
• Probing QCD dynamics in two-photon interactions at high energies
• Color Glass Condensate meets High Twist Expansion
• Energy evolution of J/$\psi$ production in DIS on nuclei
• Impact-parameter-dependent solutions to the Balitsky-Kovchegov equation at next-to-leading order
• Exclusive vector meson production with leading neutrons in a saturation model for the dipole amplitude in mixed space
• Quarkonium production at collider energies in Small-$x$ formalism
• Single inclusive jet transverse momentum and energy spectra at very forward rapidity in proton-proton collisions with $\sqrt{s}=7$ and 13 TeV
• High density QCD and nucleus-nucleus scattering deeply in the saturation region
• Saturation scale fluctuations and multi-particle rapidity correlations
• Taming of preasymptotic small x evolution within resummation framework
• Exclusive heavy quark photoproduction in $pp$, $pPb$ and $PbPb$ collisions at the LHC and FCC energies
• Thermal radiation and inclusive production in the running coupling $k_T$ -- factorization approach
• JIMWLK evolution and small-x asymptotics of 2n-tuple Wilson line correlators
• Homotopy solution to non-linear evolution for heavy nuclei
• Unequal rapidity correlators in the dilute limit of JIMWLK
• Single inclusive jet photoproduction at very forward rapidities in $pp$ and $pPb$ collisions at the LHC
• Eikonal but not: a complementary view of high energy evolution
• Scattering Amplitudes in High Energy QCD
• Inclusive gauge boson production in the color dipole formalism
• Open and hidden charm production in pA collisions
• Gluon saturation: survival probability for leading neutrons in DIS
• Soft Pomeron in the Colour Glass Condensate approach
• CGC and saturation approach: Impact-parameter dependent model of perturbative QCD and combined HERA data
• High-energy QCD evolution from BRST symmetry
• Sudakov Factor in the Deep Inelastic Scattering of a Current off a Large Nucleus
• On the Nuclear Modification Factor at RHIC and LHC
• Tachyon dynamics of the black disc limit in the hard small $x$ processes in QCD
• Forward Hadron Productions in Proton-Proton Collisions in Small-$x$ Formalism
• Gluon Evolution and Saturation Proceedings
• Evolution equation for elastic scattering of hadrons
• Non-linear evolution of unintegrated gluon density at large values of coupling constant
• Effective Field Theory Factorization for Diffraction
• Low-x Physics
• Parton model contributions as next-to-eikonal corrections to the dipole factorization of DIS and SIDIS at low $x_{Bj}$
• Rapidity dependence of saturation in inclusive HERA data with the rcBK equation
• The BFKL Pomeron calculus: summing enhanced diagrams
• Low-$x$ Physics in $pA$ Collisions and at the EIC
• Can $1/N_c$ corrections destroy the saturation of dipole densities?
• Gluon saturation effects on J/Psi production in heavy ion collisions
• Resummation of projectile-target multiple scatterings and parton saturation
• Mapping the internal structure of hadrons through color and spin effects
• BFKL Pomeron calculus: nucleus-nucleus scattering
• SPIN Effects, QCD, and Jefferson Laboratory with 12 GeV electrons
• Average $p_t$ as a probe of high energy QCD dynamics
• Remarks on Diffractive Dissociation within JIMWLK Evolution at NLO
• Photoproduction of ${\eta }_c\gamma$ pairs in CGC framework
• Callan-Symanzik equations and low-energy theorems with trace anomalies
• BRAHMS results in the context of saturation and quantum evolution
• Fine structures of azimuthal correlations of two gluons in the glasma
• Unequal rapidity correlators in the dilute limit of JIMWLK
• Two-Particle Correlations in Heavy-Light Ion Collisions
• Perturbative structure of two- and four-point functions of color charge in a non-Gaussian small-$x$ action
• Improving the solver for the Balitsky-Kovchegov evolution equation with Automatic Differentiation
• Exploring the DGLAP resummation in the JIMWLK Hamiltonian
• Small $x$ behavior in QCD from maximal entanglement and conformal invariance
• The spin-flip amplitude in the impact-parameter representation
• Statistical fluctuations of correlators in the Color Glass Condensate
• High energy scattering in QCD: dipole approach with Pomeron loops
• Rapidity window dependence of ridge correlations in the glasma
• Gluon imaging using azimuthal correlations in diffractive scattering at the Electron-Ion Collider
• First correction to JIMWLK evolution from the classical equations of motion
• Probing Saturation Physics in the Real Compton Scattering at Ultraperipheral $pPb$ Collisions
• Quantum collisions of finite-size ultrarelativistic nuclei
• Statistical properties of partonic configurations and diffractive dissociation in high-energy electron-nucleus scattering
• From RHIC to EIC: Nuclear Structure Functions
• Structure of the medium formed in heavy ion collisions
• High-energy factorization and evolution with improved kinematics
• Diffractive hadron production in DIS off heavy nuclei and gluon saturation
• Markov Chain Mote Carlo solution of BK equation through Newton-Kantorovich method
• Probing gluon saturation via diffractive jets in ultra-peripheral nucleus-nucleus collisions
• 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
• Transverse Spin and Classical Gluon Fields: Combining Two Perspectives on Hadronic Structure
• High energy DVCS on a photon and related meson exclusive production
• Entanglement, Trace Anomaly and Confinement in QCD
• High Energy Collisions of Dense Hadrons in Quantum Chromodynamics : LHC Phenomenology and Universality of Parton Distributions
• CGC-induced longitudinal ridge in p-Pb collisions
• Scattering off the Color Glass Condensate
• BRAHMS Overview
• A predictive phenomenological tool at small Bjorken-x
• Properties of inclusive hadron production in Deep Inelastic Scattering on heavy nuclei at low x
• Four-pomeron vertex
• QCD Beyond Leading Power
• Tunneling through Color Glass Condensate and True Black Disks
• Dijet photoproduction at low $x$ at next-to-leading order and its back-to-back limit
• Invariant color calculus and generalized Balitsky-Kovchegov hierarchy
• 3-D Glasma initial state from small-x evolution
• Photoproduction of three jets in the CGC: gluon TMDs and dilute limit
• Diffraction 2006: Theoretical Summary
• Finite volume effects in the McLerran-Venugopalan initial condition for the JIMWLK equation
• The Color Glass Condensate and some applications
• NNLO classical solution for Lipatov's effective action for reggeized gluons
• Local one-dimensional reggeon model of the interaction of several pomerons
• Nonlinear corrections to the nuclear heavy flavor structure functions
• Small-x, Diffraction and Vector Mesons
• Impact Factor for Exclusive Diffractive Dijet Production with NLO Accuracy
• Hot Quarks and Gluons at an Electron-Ion Collider