An Analytical Solution of the Balitsky-Kovchegov Equation with the Homogeneous Balance Method

TL;DR

This paper derives an analytical solution to the nonlinear Balitsky-Kovchegov equation using the homogeneous balance method, providing insights into gluon saturation and geometric scaling in high-energy QCD.

Contribution

It introduces a novel analytical solution to the BK equation via the homogeneous balance method, linking it with experimental data and saturation scale estimation.

Findings

Analytical solution resembles a traveling wave.

Derived a new estimate for the saturation scale Q_s^2(x).

Connected the solution with experimental gluon distribution data.

Abstract

Nonlinear QCD evolution equations are essential tools in understanding the saturation of partons at small Bjorken $x_{\rm B}$, 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 Balitsky-Kovchegov (BK) 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 $Q_s^2(x)$.