Analytical solution of Balitsky-Kovchegov equation with homogeneous balance method
Xiaopeng Wang, Yirui Yang, Wei Kou, Rong Wang, Xurong Chen
Abstract
Nonlinear QCD evolution equations are essential tools in understanding the saturation of partons at small Bjorken ${x}_{\mathrm{B}}$, 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 ${Q}_{s}^{2}(x)$.