High energy amplitude in the dipole approach with pomeron loops: asymptotic solution Original Research Article

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 (∝exp(−CY2)), 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;[ui=1])=1 to Z(Y;[ui=1−γ0,i])=1. The value of γ0 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.