On the Analytic Solution of the Balitsky-Kovchegov Evolution Equation

TL;DR

This paper derives an analytic solution to the Balitsky-Kovchegov (BK) equation in momentum space, utilizing eigenfunctions of the BFKL equation, and demonstrates its accuracy in reproducing initial conditions and high-energy behavior.

Contribution

It introduces a novel analytic solution to the BK equation based on eigenfunctions of the BFKL equation with restored dual conformal symmetry.

Findings

Solution accurately reproduces initial conditions

Matches high energy asymptotics of scattering amplitudes

Utilizes eigenfunctions from the adjoint BFKL equation

Abstract

The study presents an analytic solution of the Balitsky-Kovchegov~(BK) equation in a particular kinematics. The solution is written in the momentum space and based on the eigenfunctions of the truncated Balitsky-Fadin-Kuraev-Lipatov~(BFKL) equation in the gauge adjoint representation, which was used for calculation of the Regge~(Mandelstam) cut contribution to the planar helicity amplitudes. We introduce an eigenfunction of the singlet BFKL equation constructed of the adjoint eigenfunction multiplied by a factor, which restores the dual conformal symmetry present in the adjoint and broken in the singlet BFKL equations. The proposed analytic BK solution correctly reproduces the initial condition and the high energy asymptotics of the scattering amplitude.