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arXiv · 2009.13325

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

Xiaopeng Wang·Yirui Yang·Wei Kou·Rong Wang·Xurong Chen
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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 $Q_s^2(x)$.

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Xiaopeng Wang, Yirui Yang, Wei Kou, Rong Wang, Xurong Chen. 2020-09-28. An Analytical Solution of the Balitsky-Kovchegov Equation with the Homogeneous Balance Method. https://doi.org/10.1103/physrevd.103.056008

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