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
Highlights
We propose the solution for full BFKL kernel at large zin the entire kinematic region that satisfies the McLerran-Venugopalan-type [3,4,5,6,7] initial condition
This derivation shows two problems that have been mentioned above: we need to assume that the main contribution in eq (1.5) stems from the saturation region; and the answer has a geometric scaling behaviour that contradicts the initial condition for the DIS with nuclei
In this paper we show that at large z the solution to Balitsky-Kovchegov equation takes the following form
Summary
We re-write the Balitsky-Kovchegov equation of eq (1.1) in the momentum space introducing. First we find the geometrical scaling solution which depends only on z In this case eq (2.11) takes the form dM (z, b) κ. As has been mentioned we are not able to find the geometric scaling solution that satisfy both initial and boundary conditions given by eq (1.8) and eq (2.13). We replace eq (2.33) by the integral, i.e. The large Ybehaviour of eq (2.34) can be obtained using the transformation 2F1(α, β, γ, t) = (1 − t)γ−α−β2F1(γ − α, γ − β, γ, t) We replace eq (2.35) by the integral to estimate the large Y dependence of this term, i.e. Taking the integral by the steepest decent method in the same way as in eq (2.41) we obtain the equation for the saddle point tSP :.
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