Impact Parameter Dependence in the Balitsky-Kovchegov Equation

Abstract

We study the impact parameter dependence of solutions to the Balitsky-Kovchegov (BK) equation. We argue that if the kernel of the BK integral equation is regulated to cutoff infrared singularities, then it can be approximated by an equation without diffusion in impact parameter. For some purposes, when momentum scales large compared to ${\Lambda }_{QCD}$ are probed, the kernel may be approximated as massless. In particular, we find that the Froissart bound limit is saturated for physical initial conditions and seem to be independent of the cutoff so long as the cutoff is sufficiently large compared to the momentum scale associated with the large distance falloff of the impact parameter distribution.

15 pages, 7 figures

References in corpus (30)

• Computing Quark and Gluon Distribution Functions for Very Large Nuclei
• Operator expansion for high-energy scattering
• Gluon Distribution Functions for Very Large Nuclei at Small Transverse Momentum
• Small-x F_2 Structure Function of a Nucleus Including Multiple Pomeron Exchanges
• Nonlinear Gluon Evolution in the Color Glass Condensate: I
• The Wilson renormalization group for low x physics: towards the high density regime
• Green's Functions in the Color Field of a Large Nucleus
• The BFKL Equation from the Wilson Renormalization Group
• Unitarization of the BFKL Pomeron on a Nucleus
• The Intrinsic Glue Distribution at Very Small x
• The Energy Dependence of the Saturation Momentum
• Geometric Scaling above the Saturation Scale
• Saturation and Universality in QCD at small x
• Structure function of the nucleus in the perturbative QCD with $N_c\to \infty$ (BFKL pomeron fan diagrams)
• The Energy Dependence of the Saturation Momentum from RG Improved BFKL Evolution
• Universal features of JIMWLK and BK evolution at small x
• On solutions of the Balitsky-Kovchegov equation with impact parameter
• Diffusion into infra-red and unitarization of the BFKL pomeron
• Numerical analysis of the Balitsky-Kovchegov equation with running coupling: dependence of the saturation scale on nuclear size and rapidity
• Parton densities and dipole cross-sections at small x in large nuclei
• Froissart Bound from Gluon Saturation
• Interactions of Reggeized Gluons in the Möbius Representation
• No Froissart Bound from Gluon Saturation
• Perturbative Saturation and the Soft Pomeron
• Towards a New Global QCD Analysis: Solution to the Non-Linear Equation at Arbitrary Impact Parameter
• QCD Saturation in the Semi-classical Approach
• Pomeron fan diagrams with an infrared cutoff and running coupling
• QCD Saturation Equations including Dipole-Dipole Correlation
• Describing F_2 through a finite sum of gluon ladders
• Would unitarity slow down the rise of $F_2(x,Q^2)$ at $x\to 0$?

Cited by in corpus (13)

• AdS black disk model for small-x DIS
• Confronting impact parameter dependent JIMWLK evolution with HERA data
• Saturation physics at HERA and RHIC: An unified description
• Wigner, Husimi and GTMD distributions in the Color Glass Condensate
• Could saturation effects be visible in a future electron-ion collider?
• A modified Balitsky-Kovchegov equation
• Gluon saturation and the Froissart bound: a simple approach
• 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
• Froissart bound and gluon number fluctuations
• On the High Energy Behaviour of The Total Cross Section in the QCD Dipole Model
• On the behaviour of single scale hard small $x$ processes in QCD near the black disc limit
• Cronin momentum behavior in saturation model for $p+A$, $d+A$, $A+A$ collisions