Can $1/N_c$ corrections destroy the saturation of dipole densities?

Abstract

In this paper we discuss a well known QCD result: the steep increase of Green's function for exchange of $n$ BFKL Pomerons $G_{n \pom}\Lb Y\Rb\propto \exp\Lb \frac{n^2}{N^2_c} \Delta_{\mbox{\tiny BFKL}} Y\Rb$ where $N_c $ is the number of colours ,Y is the rapidity and $\Delta_{\mbox{\tiny BFKL}}$ is the intercept of the BFKL Pomeron. We consider this problem in the framework of the simple Pomeon models in zero transverse dimensions, which have two advantages :(i) they allow to take into account all shadowing corrections, including the summation of the Pomeron loops and (ii) they have the same as in QCD striking increase of $G_{n \pom}\Lb Y\Rb $. We found that the strength of shadowing corrections is not enough to stop the increase of the scattering amplitude with energy in contradiction to the unitarity constraints. Hence, our answer to the question in the title is positive.We believe that we need to search an approach beyond of the BFKL Pomeron calculus to treat $1/N_c$ corrections in Colour Glass Condensate effective theory.