Numerical solution of the nonlinear evolution equation at small x with impact parameter and beyond the LL approximation

Abstract

Nonlinear evolution equation at small x with impact parameter dependence is analyzed numerically. Saturation scales and the radius of expansion in impact parameter are extracted as functions of rapidity. Running coupling is included in this evolution, and it is found that the solution is sensitive to the infrared regularization. Kinematical effects beyond leading logarithmic approximation are taken partially into account by modifying the kernel which includes the rapidity dependent cuts. While the local nonlinear evolution is not very sensitive to these effects, the kinematical constraints cannot be neglected in the evolution with impact parameter.

22 pages, 37 figures, RevTex

References in corpus (9)

• NLO evolution of color dipoles
• Quark contribution to the small-$x$ evolution of color dipole
• Triumvirate of Running Couplings in Small-x Evolution
• Solving The High Energy Evolution Equation Including Running Coupling Corrections
• A momentum Space Analysis of the Triple Pomeron Vertex in pQCD
• Correlation of small-x gluons in impact parameter space
• Non-linear equation: energy conservation and impact parameter dependence
• Correlations in impact-parameter space in a hierarchical saturation model for QCD at high energy
• On the Dipole Swing and the Search for Frame Independence in the Dipole Model

Cited by in corpus (62)

• AAMQS: A non-linear QCD analysis of new HERA data at small-x including heavy quarks
• Single inclusive particle production at high energy from HERA data to proton-nucleus collisions
• Impact-parameter dependent Color Glass Condensate dipole model and new combined HERA data
• Improving the kinematics for low-x QCD evolution equations in coordinate space
• Exclusive vector meson production at high energies and gluon saturation
• Towards the Test of Saturation Physics Beyond Leading Logarithm
• NLO corrections for the dipole factorization of DIS structure functions at low x
• Confronting impact parameter dependent JIMWLK evolution with HERA data
• The shape of the proton at high energies
• Diffractive Dijet Production in Deep Inelastic Scattering and Photon-Hadron Collisions in the Color Glass Condensate
• Implementing the exact kinematical constraint in the saturation formalism
• Diffractive Dijet Production and Wigner Distributions from the Color Glass Condensate
• Gluon saturation and energy dependence of hadron multiplicity in pp and AA collisions at the LHC
• Small x nonlinear evolution with impact parameter and the structure function data
• Hadron production in pA collisions at the LHC from the Color Glass Condensate
• Nucleon Energy Correlators for the Color Glass Condensate
• Wigner, Husimi and GTMD distributions in the Color Glass Condensate
• Diffractive $\rho$ and $\varphi$ production at HERA using an AdS/QCD holographic light-front meson wavefunction
• Collinearly improved kernel suppresses Coulomb tails in the impact-parameter dependent Balitsky-Kovchegov evolution
• Solution to the Balitsky-Kovchegov equation with the collinearly improved kernel including impact-parameter dependence
• Sub-femtometer scale color charge fluctuations in a proton made of three quarks and a gluon
• Pursuing the Precision Study for Color Glass Condensate in Forward Hadron Productions
• Color charge correlations in the proton at NLO: beyond geometry based intuition
• Charged particle multiplicities in pA interactions at the LHC from the Color Glass Condensate
• On theoretical uncertainty of color dipole phenomenology in the J/Psi and Upsilon photoproduction in pA and AA collisions at the CERN Large Hadron Collider
• Extracting the Distribution Amplitudes of the rho meson from the Color Glass Condensate
• Harmonics of Parton Saturation in Lepton-Jet Correlations at the EIC
• Selected topics in diffraction with protons and nuclei: past, present, and future
• Sub-femtometer scale color charge correlations in the proton
• BFKL Pomeron with massive gluons
• Saturation in inclusive production beyond leading logarithm accuracy
• Exclusive ${\eta }_c$ production from small-$x$ evolved Odderon at a electron-ion collider
• Deeply virtual Compton scattering at small-$x$ in future Electron - Ion Colliders
• Finite-size effects on small-$x$ evolution and saturation in proton and nuclear targets
• Nuclear effects in Drell-Yan pair production in high-energy $pA$ collisions
• Predictions for nuclear structure functions from the impact-parameter dependent Balitsky-Kovchegov equation
• Cubic color charge correlator in a proton made of three quarks and a gluon
• BFKL Pomeron: modeling confinement
• Testing the running coupling $k_T$-factorization formula for the inclusive gluon production
• Photon-Odderon interference in exclusive ${\chi }_c$ charmonium production at the Electron-Ion Collider
• Gribov-Zwanziger confinement, high energy evolution and large impact parameter behaviour of the scattering amplitude
• Novel Cross Section Ratios as Possible Signals of Saturation in UPCs
• Large $\mathbf{b}$ behaviour in the CGC/saturation approach: BFKL equation with pion loops
• Particle multiplicities in the central region of high-energy collisions from $k_T$-factorization with running coupling corrections
• Solutions to the Balitsky-Kovchegov equation including the dipole orientation
• Large impact parameter behaviour in the CGC/saturation approach: a new non-linear equation
• BFKL equation in the next-to-leading order: solution at large impact parameters
• Probing proton structure with $c\bar{c}$ correlations in ultraperipheral $pA$ collisions
• Non-linear evolution in the re-summed next-to-leading order of perturbative QCD:\confronting the experimental data
• Complete calculation of exclusive heavy vector meson production at next-to-leading order in the dipole picture
• Azimuthal instabilities of the Gribov-Levin-Ryskin equation
• A parton shower generator based on the GLR equation
• Impact-parameter-dependent solutions to the Balitsky-Kovchegov equation at next-to-leading order
• Exclusive heavy vector meson production at next-to-leading order in the dipole picture
• Inclusive gauge boson production in the color dipole formalism
• Homotopy solution to non-linear evolution for heavy nuclei
• Modified homotopy approach for diffractive production in the saturation region
• A numerical implementation of the NLO DIS structure functions in the dipole picture
• Homotopy approach for scattering amplitude for running QCD coupling
• Improving the solver for the Balitsky-Kovchegov evolution equation with Automatic Differentiation
• High energy evolution for Gribov-Zwanziger confinement: solution to the equation
• Signatures of gluon saturation from structure-function measurements