High energy amplitude in the dipole approach with Pomeron loops: asymptotic solution

Abstract

In this paper an analytical solution for the high energy scattering amplitude is suggested. This solution has several unexpected features:(i) the asymptotic amplitude is a function of dipole sizes and, therefore, this amplitude shows the gray disc structure at high energy, instead of black disc behaviour which was expected; (ii) the amplitude approaches the asymptotic limit in the same way as the solution to the Balitsky-Kovchegov equation does ($\propto \exp (-C{Y}^2)$), but the coefficient $C$ in eight times smaller than for the Balitsky-Kovchegov equation; (iii) the process of merging of two dipoles into one, only influences the high energy asymptotic behaviour by changing the initial condition from $Z(Y;[u_i=1])=1$ to $Z(Y;[u_i=1-{\hat{I}}_{0,i}^3])=1$. The value of ${\hat{I}}_0^3$ is determined by the process of merging of two dipoles into one. With this new initial condition the Balitsky-JIMWLK approach describes the high energy asymptotic behaviour of the scattering amplitude without any modifications recently suggested.

37 pages with 4 figures in eps format, this version will appear in Nucl.Phys.A, a couple of references is added as well as comments on physics of the solution