Analytical solution of Balitsky-Kovchegov equation with homogeneous balance method

2020/09/30 by Xiaopeng Wang, Yirui Yang, Wei Kou +2
Mathematics · Physics and Astronomy · #Amplitude #Dipole #Gluon #High-Energy Particle Collisions Research #Mathematics #Particle physics #Particle physics theoretical and experimental studies #Parton #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum electrodynamics #Quantum mechanics #Saturation (graph theory) #Scaling #Scattering #Scattering amplitude #Statistical physics #Unitarity #hep-ph

paper · pdf · doi:10.1103/physrevd.103.056008

published as Phys. Rev. D 103, 056008 (2021) · 6 pages, 5 figures

openalex publication_date 2021/03/12 · arxiv created 2021/03/14 · arxiv updated 2021/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Nonlinear QCD evolution equations are essential tools in understanding the saturation of partons at small Bjorken x_B, as they are supposed to restore an upper bound of unitarity for the cross section of high-energy scattering. In this paper, we present an analytical solution of the Balitsky-Kovchegov equation using the homogeneous balance method. The obtained analytical solution is similar to the solution of a traveling wave. By matching the gluon distribution in the dilute region which is determined from the global analysis of experimental data (CT14 analysis), we get a definitive solution of the dipole-proton forward scattering amplitude in the momentum space. Based on the acquired scattering amplitude and the behavior of geometric scaling, we present also a new estimated saturation scale Q_s²(x).

Citations

• Diffusion into infrared and unitarization of the Balitskiĭ-Fadin-Kuraev-Lipatov Pomeron
• Statistical physics in QCD evolution towards high energies
• Universality and tree structure of high-energy QCD
• Infrared instability from nonlinear QCD evolution
• Traveling wave fronts and the transition to saturation
• The BFKL equation from the Wilson renormalization group
• Unitarity at small Bjorken x
• Impact parameter dipole saturation model
• γ*pcross section from the dipole model in momentum space
• Geometric Scaling as Traveling Waves
• Operator expansion for diffractive high-energy scattering
• Saturation effects in deep inelastic scattering at lowQ2and its implications on diffraction
• The Color Glass Condensate
• Effective field theory for the small-x evolution
• Modification of the saturation model: Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution
• Solitary wave solutions of FKPP equation using Homogeneous balance method(HB method)