The BFKL Equation from the Wilson Renormalization Group

Abstract

We discuss the Wilson renormalization group approach to the effective action for low $x$ physics. It is shown that in the linearized, weak field regime the RG equation reduces to the BFKL equation for the evolution of the unintegrated gluon density. We discuss the relation of this approach with that of Lipatov.

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• CGC formalism with two sources
• Lattice Gauge Description of Colliding Nuclei
• Exclusive and dissociative J/$\psi$ photoproduction, and exclusive dimuon production, in p$-$Pb collisions at $\sqrt{s_{\mathrm{NN}}}=8.16$ TeV
• Measurement of inclusive very forward jet cross sections in proton-lead collisions at $\sqrt{s_{\mathrm{NN}}}=$ 5.02 TeV
• Predictions for net-proton and net-kaon distributions at LHC energies
• R-Current DIS on a Shock Wave: Beyond the Eikonal Approximation
• Liouville field theory for gluon saturation in QCD at high energy
• High energy asymptotic behavior of the $S$-matrix in the saturation region with the smallest dipole running coupling prescription
• Low-x QCD physics from RHIC and HERA to the LHC
• CGC/saturation approach for soft interactions at high energy: a two channel model
• QCD Saturation Equations including Dipole-Dipole Correlation
• Dipole evolution: perspectives for collectivity and ${\gamma }^{\ast }$A collisions
• JIMWLK Evolution, Lindblad Equation and Quantum-Classical Correspondence
• Uncovering the triple pomeron vertex from Wilson line formalism
• Hot and dense matter: from RHIC to LHC: Theoretical overview
• Solution to the evolution equation at NLL for high parton density QCD
• Charged Hadron Multiplicity Distribution at Relativistic Heavy Ion Colliders
• Reggeon Field Theory and Self Duality: Making Ends Meet
• Total gluon shadowing due to fluctuation effects
• Perturbative QCD and beyond: azimuthal angle correlations in deuteron-deuteron scattering from Bose-Einstein correlations
• Cubic color charge correlator in a proton made of three quarks and a gluon
• Non-linear evolution in CCFM: The interplay between coherence and saturation
• Extended collinearly-improved Balitsky-Kovchegov evolution equation in target rapidity
• General formulae for dipole Wilson line correlators with the Color Glass Condensate
• First Saturation Correction in High Energy Proton-Nucleus Collisions: I. Time evolution of classical Yang-Mills fields beyond leading order
• Non-Gaussian Correlations in the McLerran-Venugopalan Model
• Running Coupling Corrections to Nonlinear Evolution for Diffractive Dissociation
• QCD motivated approach to soft interactions at high energy: inclusive production
• Incoherent diffractive dijet production in electron DIS off nuclei at high energy
• Real Time Dynamics of Colliding Gauge Fields and the ''Glue Burst''
• The JIMWLK evolution and the s-channel unitarity
• Travelling waves and impact-parameter correlations
• Nonlinear dynamics of soft boson excitations in hot QCD plasma I: plasmon-plasmon scattering
• CGC/saturation approach for high energy soft interactions: `soft' Pomeron structure and $v_n$ in hadron and nucleus collisions from Bose-Einstein correlation
• Deep Inelastic Scattering in the Exponentially Small Bjorken Parameter Regime from the Holographic Softwall Model
• CGC/saturation approach for high energy soft interactions: ${\mathbf{v}}_2$ in proton-proton collisions
• Using dileptons to probe the Color Glass Condensate
• Diffractive dissociation including pomeron loops in zero transverse dimensions
• The BFKL Pomeron Calculus in zero transverse dimensions: diffractive processes and survival probability for central diffractive production
• Stronger $C$-odd color charge correlations in the proton at higher energy
• Looking for the gluon condensation signature in proton using the Earth limb gamma-ray spectra
• Geometric Scaling in Mueller-Navelet Jets
• A simple model for the nuclear unintegrated gluon distribution
• Shadowing of gluons in perturbative QCD: A comparison of different models
• Wilson lines - color charge densities correlators and the production of eta' in the CGC for pp and pA collisions
• Nuclei in the toy world: beyond the Pomeron in zero transverse dimensions
• Inclusive Gluon Production in the QCD Reggeon Field Theory: Pomeron Loops Included
• DPS in CGC: HBT correlations in double inclusive photon production
• BFKL and CCFM evolutions with saturation boundary
• Color Glass Condensate and its relation to HERA physics
• Strongly Interacting Matter at High Energy Density
• Multiparticle azimuthal angular correlations in $pA$ collisions
• CGC/saturation approach: soft interaction at the LHC energies
• On the Dipole Swing and the Search for Frame Independence in the Dipole Model
• Non linear evolution: revisiting the solution in the saturation region
• Solution of the Fan Diagram Equation in 2+1 Dimensional QCD
• 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
• Gluon saturation and inclusive production at low transverse momenta
• Particle multiplicities at LHC and deviations from limiting fragmentation
• Compatibility of phenomenological dipole cross sections with the Balitsky-Kovchegov equation
• Soft interaction at high energy and N=4 SYM
• Unifying approaches: derivation of Balitsky hierarchy from the Lipatov effective action
• Fluctuations of the gluon distribution from the small-x effective action
• Probing the Frontiers of QCD
• From EMC- and Cronin-effects to signals of quark-gluon plasma
• 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
• D-instantons and multiparticle production in N=4 SYM
• Coherent and incoherent diffractive hadron production in pA collisions and gluon saturation
• 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
• A CGC/saturation approach for angular correlations in proton-proton scattering
• Semiclassical solution to the BFKL equation with massive gluons
• Diffraction Production in a Soft Interaction Model: Mass Distributions
• Collective Phenomena in the Non-Equilibrium Quark-Gluon Plasma
• Forward trijet production in p-p and p-Pb collisions at LHC
• Geometric scaling behavior of the scattering amplitude for DIS with nuclei
• Small-$x$ QCD evolution of $2n$ Wilson line correlator: the weak field limit
• QCD at small x and nucleus-nucleus collisions
• Asymptotics of QCD traveling waves with fluctuations and running coupling effects
• Small-x QCD studies with CMS at the LHC
• 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
• CGC, QCD Saturation and RHIC data (Kharzeev-Levin-McLerran-Nardi point of view)
• Rare fluctuations of the $S$-matrix at NLO in QCD
• Inclusive production in a QCD and N=4 SYM motivated model for soft interactions
• DIS and the effects of fluctuations: a momentum space analysis
• On QCD RFT corrections to the propagator of reggeized gluons
• Quark TMDs from back-to-back dijet production at forward rapidities in pA collisions beyond eikonal accuracy in the CGC
• Gluon recombination in high parton density QCD: inclusive pion production
• 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 multiplicity in coherent diffraction of onium on a heavy nucleus
• Saturation and Wilson Line Distributions
• Analytic solution of Balitsky-Kovchegov equation with running coupling constant using homogeneous balance method
• Exclusive vector meson productions with the analytical solution of Balitsky-Kovchegov Equation
• Spectrum of diffractively produced gluons in onium-nucleus collisions
• Saturation and linear transport equation
• High energy scattering in Einstein-Cartan gravity
• The two-loop Higgs impact factor
• The Status of Parton Saturation and the CGC
• Non-Abelian color fields from relativistic color charge configurations in the classical limit
• Symplectic approach to lightcone QCD
• Probing gluon number fluctuation effects in future electron-hadron colliders
• A parton shower generator based on the GLR equation
• Sudakov effects and the dipole amplitude
• CGC/saturation approach for soft interactions at high energy: long range rapidity correlations
• Gauge invariant source terms in QCD
• Dipole-dipole scattering amplitude in CGC approach
• An analytical solution of Balitsky-Kovchegov equation using homotopy perturbation method
• Complete calculation of exclusive heavy vector meson production at next-to-leading order in the dipole picture
• Solution to the Sudakov suppressed Balitsky-Kovchegov equation and its application to the HERA data
• 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
• Proton and anti-proton production in the forward region of d+Au collisions at RHIC from the color glass condensate
• Non-linear equation in the re-summed next-to-leading order of perturbative QCD: the leading twist approximation
• Probing Gluons in Nuclei: the Case of ${\eta }^{\prime }$
• Soft interactions at high energies: QCD motivated approach
• Longitudinal Rescaling and High-Energy Effective Actions
• Prediction for unintegrated parton distributions
• Rapidity dependence of the photon to pion production ratio in high energy collisions
• Non-perturbative renormalization of the average color charge and multi-point correlators of color charge from a non-Gaussian small-$x$ action
• Long range rapidity correlations in soft interaction at high energies
• Inside looking out: probing JIMWLK with BFKL calculations
• Simple Mechanism of Softening Structure Functions at Low Transverse Momentum Region
• The Weizsäcker-Williams distribution of linearly polarized gluons (and its fluctuations) at small x
• Next-to-Leading Order correction to inclusive particle spectra in the Color Glass Condensate framework
• Color Glass Condensate meets High Twist Expansion
• Near-integrability and confinement for high-energy hadron-hadron collisions
• High density QCD and nucleus-nucleus scattering deeply in the saturation region
• Large distance behaviour of light cone operator product in perturbative and nonperturbative QCD regimes
• Distribution of multiple scatterings in proton-nucleus collisions at high energy
• Quarkonium production at collider energies in Small-$x$ formalism
• Exclusive vector meson production with leading neutrons in a saturation model for the dipole amplitude in mixed space
• On the behaviour of single scale hard small $x$ processes in QCD near the black disc limit
• Taming of preasymptotic small x evolution within resummation framework
• Energy evolution of J/$\psi$ production in DIS on nuclei
• Low-x QCD with CMS at the LHC
• Impact-parameter-dependent solutions to the Balitsky-Kovchegov equation at next-to-leading order
• Saturation scale fluctuations and multi-particle rapidity correlations
• Forward Hadron Productions in Proton-Proton Collisions in Small-$x$ Formalism
• Tachyon dynamics of the black disc limit in the hard small $x$ processes in QCD
• Soft processes at high energy without soft Pomeron: a QCD motivated model
• Homotopy solution to non-linear evolution for heavy nuclei
• Unequal rapidity correlators in the dilute limit of JIMWLK
• High-energy QCD evolution from BRST symmetry
• Sudakov Factor in the Deep Inelastic Scattering of a Current off a Large Nucleus
• JIMWLK evolution and small-x asymptotics of 2n-tuple Wilson line correlators
• Scattering Amplitudes in High Energy QCD
• Gluon saturation: survival probability for leading neutrons in DIS
• CGC and saturation approach: Impact-parameter dependent model of perturbative QCD and combined HERA data
• Soft Pomeron in the Colour Glass Condensate approach
• Eikonal but not: a complementary view of high energy evolution
• On the Nuclear Modification Factor at RHIC and LHC
• A geometrizing higher twist effect on nuclear target
• Multiplicity and transverse energy of produced gluon in relativistic heavy ion collision
• Callan-Symanzik equations and low-energy theorems with trace anomalies
• Resummation of projectile-target multiple scatterings and parton saturation
• Low-$x$ Physics in $pA$ Collisions and at the EIC
• Azimuthal angle correlations in hadron-nucleus scattering: enhanced diagrams
• Remarks on Diffractive Dissociation within JIMWLK Evolution at NLO
• The BFKL Pomeron calculus: summing enhanced diagrams
• Evolution equation for elastic scattering of hadrons
• Classical information entropy of parton distribution functions and an application in searching gluon saturation
• Average $p_t$ as a probe of high energy QCD dynamics
• Mapping the internal structure of hadrons through color and spin effects
• Gluon saturation effects on J/Psi production in heavy ion collisions
• Photoproduction of ${\eta }_c\gamma$ pairs in CGC framework
• BFKL Pomeron calculus: nucleus-nucleus scattering
• Gluon Evolution and Saturation Proceedings
• Momentum space saturation model for deep inelastic scattering and single inclusive hadron production
• Can $1/N_c$ corrections destroy the saturation of dipole densities?
• What's new at small x
• Parton model contributions as next-to-eikonal corrections to the dipole factorization of DIS and SIDIS at low $x_{Bj}$
• Ekpyrosis and inflationary dynamics in heavy ion collisions: the role of quantum fluctuations
• Perturbative Corrections to Quark TMDPDFs in the Background-Field Method: Gauge Invariance, Equations of Motion, and Multiple Interactions
• Effective Field Theory Factorization for Diffraction
• Structure of the medium formed in heavy ion collisions
• Statistical properties of partonic configurations and diffractive dissociation in high-energy electron-nucleus scattering
• Compact construction algorithms for the singlets of SU(N) over mixed tensor product spaces
• From Classical to Quantum Saturation in the Nuclear Gluon Distribution
• First correction to JIMWLK evolution from the classical equations of motion
• Diffractive hadron production in DIS off heavy nuclei and gluon saturation
• Perturbative structure of two- and four-point functions of color charge in a non-Gaussian small-$x$ action
• Looking for quark saturation in proton and nuclei
• From RHIC to EIC: Nuclear Structure Functions
• A numerical implementation of the NLO DIS structure functions in the dipole picture
• Exploring the DGLAP resummation in the JIMWLK Hamiltonian
• Gluon imaging using azimuthal correlations in diffractive scattering at the Electron-Ion Collider
• Geometrical scaling of heavy-quark contributions in the low $x$ region
• High-energy factorization and evolution with improved kinematics
• On the low-x NLO evolution of 4 point colorless operators
• Investigation of proton structure function $F_2^p$ at HERA in light of an analytical solution to Balitsky-Kovchegov equation
• High energy scattering in QCD: dipole approach with Pomeron loops
• Statistical fluctuations of correlators in the Color Glass Condensate
• Single photon production in ppBar collision in the collinear and kt-factorisation framework and investigation of their differences
• Transverse Spin and Classical Gluon Fields: Combining Two Perspectives on Hadronic Structure
• Invariant color calculus and generalized Balitsky-Kovchegov hierarchy
• Four-pomeron vertex
• Dijet photoproduction at low $x$ at next-to-leading order and its back-to-back limit
• Scattering off the Color Glass Condensate
• Color-glass condensate beyond the Gaussian approximation
• Photoproduction of three jets in the CGC: gluon TMDs and dilute limit
• 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
• Diffraction 2006: Theoretical Summary
• Markov Chain Mote Carlo solution of BK equation through Newton-Kantorovich method
• Entanglement, Trace Anomaly and Confinement in QCD
• Classical initial conditions in high energy nucleus-nucleus collisions
• NNLO classical solution for Lipatov's effective action for reggeized gluons
• Small-x, Diffraction and Vector Mesons
• Local one-dimensional reggeon model of the interaction of several pomerons
• Finite volume effects in the McLerran-Venugopalan initial condition for the JIMWLK equation
• 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 $x$
• 3-D Glasma initial state from small-x evolution
• High Energy Collisions of Dense Hadrons in Quantum Chromodynamics : LHC Phenomenology and Universality of Parton Distributions
• Impact Factor for Exclusive Diffractive Dijet Production with NLO Accuracy
• A unified description of initial and final state interactions in heavy ion collisions
• Probing gluon saturation via diffractive jets in ultra-peripheral nucleus-nucleus collisions
• Tunneling through Color Glass Condensate and True Black Disks
• Properties of inclusive hadron production in Deep Inelastic Scattering on heavy nuclei at low x