Non linear gluon evolution in path-integral form

Abstract

We explore and clarify the connections between two different forms of the renormalisation group equations describing the quantum evolution of hadronic structure functions at small $x$. This connection is established via a Langevin formulation and associated path integral solutions that highlight the statistical nature of the quantum evolution, pictured here as a random walk in the space of Wilson lines. The results confirm known approximations, form the basis for numerical simulations and widen the scope for further analytical studies.

32 pages

References in corpus (4)

• Geometric Scaling above the Saturation Scale
• Diffusion into infra-red and unitarization of the BFKL pomeron
• A Simple Derivation of the JIMWLK Equation
• Nonlinear evolution in high-density QCD

Cited by in corpus (79)

• The Color Glass Condensate
• QCD thermalization: Ab initio approaches and interdisciplinary connections
• Universal features of JIMWLK and BK evolution at small x
• Universal behavior of QCD amplitudes at high energy from general tools of statistical physics
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• Renormalization group evolution of multi-gluon correlators in high energy QCD
• Color Glass Condensate and Glasma
• Numerical analysis of the Balitsky-Kovchegov equation with running coupling: dependence of the saturation scale on nuclear size and rapidity
• Extension of the JIMWLK Equation in the Low Gluon Density Region
• The distribution of linearly polarized gluons and elliptic azimuthal anisotropy in DIS dijet production at high energy
• Resummation of non-global logarithms at finite $N_c$
• From Color Glass to Color Dipoles in high-energy onium--onium scattering
• Effective Hamiltonian for QCD evolution at high energy
• Subleading-N_c corrections in non-linear small-x evolution
• Non-Global Logarithms, Factorization, and the Soft Substructure of Jets
• High energy factorization in nucleus-nucleus collisions III. Long range rapidity correlations
• Non-global jet evolution at finite N_c
• The initial spectrum of fluctuations in the little bang
• 3-D Glasma initial state for relativistic heavy ion collisions
• Confronting impact parameter dependent JIMWLK evolution with HERA data
• A Gaussian effective theory for gluon saturation
• The shape of the proton at high energies
• High Gluon Densities in Heavy Ions Collisions
• On the running coupling in the JIMWLK equation
• Measuring the Weizsaecker-Williams distribution of linearly polarized gluons at an EIC through dijet azimuthal asymmetries
• Higher-point correlations from the JIMWLK evolution
• Small x physics and RHIC data
• The importance of kinematic twists and genuine saturation effects in dijet production at the Electron-Ion Collider
• Anisotropy of the semi-classical gluon field of a large nucleus at high energy
• High Energy QCD at NLO: from light-cone wave function to JIMWLK evolution
• JIMWLK evolution in the Gaussian approximation
• Hemisphere jet mass distribution at finite $N_c$
• Gluon splitting in a shockwave
• TMD gluon distributions at small x in the CGC theory
• Non-global logarithms in hadron collisions at $N_c=3$
• Extracting many-body color charge correlators in the proton from exclusive DIS at large Bjorken x
• On the Probabilistic Interpretation of the Evolution Equations with Pomeron Loops in QCD
• High energy amplitude in the dipole approach with Pomeron loops: asymptotic solution
• QCD Saturation in the Semi-classical Approach
• JIMWLK evolution of the odderon
• Structure of longitudinal chromomagnetic fields in high energy collisions
• A zero-dimensional model for high-energy scattering in QCD
• Accessing the gluonic structure of light nuclei at the Electron Ion Collider
• Rapidity dependence of initial state geometry and momentum correlations in p+Pb collisions
• Collinearly improved JIMWLK evolution in Langevin form
• On the Projectile-Target Duality of the Color Glass Condensate in the Dipole Picture
• Forward trijet production in proton-nucleus collisions
• A simple evolution equation for rapidity distributions in nucleus-nucleus collisions
• JIMWLK evolution for multi-particle production in Langevin form
• Initial State Quantum Fluctuations in the Little Bang
• Rapidity distribution of gluons in the classical field model for heavy ion collisions
• Some Aspects of the Theory of Heavy Ion Collisions
• The BFKL Pomeron Calculus in the dipole approach
• Testing the Gaussian Approximation to the JIMWLK Equation
• Finite-size effects on small-$x$ evolution and saturation in proton and nuclear targets
• O(α_s^2)-corrections to JIMWLK evolution from the classical equations of motion
• How Pomerons Meet in Coloured Glass
• QCD saturation in the dipole sector with correlations
• On the Wess-Zumino term in high energy QCD
• On perturbative limits of quadrupole evolution in QCD at high energy
• JIMWLK Evolution, Lindblad Equation and Quantum-Classical Correspondence
• On correlations and discreteness in non-linear QCD evolution
• Solution of the Fan Diagram Equation in 2+1 Dimensional QCD
• Stronger $C$-odd color charge correlations in the proton at higher energy
• Fluctuations of the gluon distribution from the small-x effective action
• Structure of chromomagnetic fields in the glasma
• The small-x gluon distribution in centrality biased pA and pp collisions
• Small-$x$ QCD evolution of $2n$ Wilson line correlator: the weak field limit
• Proposal for a running coupling JIMWLK equation
• Stochastic quantization and diffusion models
• Deriving the Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner equation with classical and quantum source terms
• Unequal rapidity correlators in the dilute limit of JIMWLK
• High-energy QCD evolution from BRST symmetry
• Double inclusive small-x gluon production and their azimuthal correlations in a biased ensemble
• JIMWLK evolution for multi-particle production with rapidity correlations
• Gluon imaging using azimuthal correlations in diffractive scattering at the Electron-Ion Collider
• JIMWLK evolution: from color charges to rapidity correlations
• Color-glass condensate beyond the Gaussian approximation
• 3-D Glasma initial state from small-x evolution