Non linear evolution: revisiting the solution in the saturation region

TL;DR

This paper revisits the nonlinear evolution equations in the saturation region of QCD, deriving a refined solution that depends on a specific variable and extends to the full BFKL kernel across the entire kinematic range.

Contribution

It provides a detailed analysis of the solution form in the saturation domain and introduces a new solution for the full BFKL kernel consistent with initial conditions.

Findings

Derived the form of the solution in the saturation region.

Calculated the constant in the Levin-Tuchin solution.

Proposed a solution valid for the full BFKL kernel across all kinematic regions.

Abstract

In this paper we revisit the problem of the solution to Balitsky-Kovchegov equation deeply in the saturation domain. We find that solution has the form of Levin-Tuchin solution but it depends on variable $\bar{z} = \ln(r^2 Q^2_s) + \mbox{Const}$ and the value of $\mbox{Const}$ is calculated in this paper. We propose the solution for full BFKL kernel at large $z$ in the entire kinematic region that satisfies the McLerram-Venugopalan initial condition