Can $1/N_c$ corrections be treated in the Pomeron calculus?

Abstract

The main goal of the paper is to show that we can treat the $1/N_c$ QCD corrections in the Pomeron calculus. We develop the one dimensional model which is a simplification of the QCD approach that includes $\pom \to 2 \pom$, $2 \pom \to \pom$ and $ 2 \pom \to 2 \pom$ vertices and gives the description of the high energy interaction, both in the framework of the parton cascade and in the Pomeron calculus. In this model we show that the scattering amplitude can be written as the sum of Green's function of $n$ Pomeron exchanges $G_{n \pom} \propto e^{ \omega_n \Y}$ with $\omega_n =\kappa\,n^2$ at $\kappa \ll 1$. This means that choosing $\kappa = 1/N^2_c$ we can reproduce the intercepts of QCD in $1/N_c$ order. The scattering amplitude is an asymptotic series that cannot be sum using Borel approach. We found a general way of summing such series. In addition to the positive eigenvalues we found the set of negative eigenvalues which corresponds to the partonic description of the scattering amplitude. Using Abramowsky, Gribov and Kancheli cutting rules we found the multiplicity distributions of the produced dipoles as well as their entropy $S_E$.