Soft Pomeron in the Colour Glass Condensate approach

Abstract

In this paper we suggest a new approach to the structure of the soft Pomeron: based on the $t$-channel unitarity, we expressed the exchange of the soft Pomeron through the interaction of the dipole of small size of the order of $1/Q_s(Y)$ ($Q_s(Y)$ is the saturation momentum) with the hadrons. Therefore, it is shown that the typical distances in soft processes are small $r\sim 1/Q_s\text{Lb}\text{h}Y\text{Rb}$, where $Y=lns$. The saturation momentum, which determines the energy dependence of the scattering amplitude is proportional to $Q_s^2\text{Lb}\text{h}Y\text{Rb}\propto \exp \text{Lb}\text{h}\lambda Y\text{Rb}$, with $\lambda \approx 0.2$, and this behaviour is in perfect agreement with phenomenological Donnachie-Landshoff Pomeron. We demonstrate that the saturation models could describe the experimental data for ${\sigma }_{tot},{\sigma }_{el},{\sigma }_{diff}$ and $B_{el}$. Hence our approach is a good first approximation to start discussion of the soft processes in CGC approach on the solid theoretical basis.

Comments: 19pp 28 figures in pdf files