Soft Pomeron in the Colour Glass Condensate approach

TL;DR

This paper introduces a new approach to the soft Pomeron within the Colour Glass Condensate framework, linking soft process distances to saturation momentum and successfully describing various scattering cross sections.

Contribution

It presents a novel theoretical model connecting soft Pomeron exchange to small dipole interactions based on $t$-channel unitarity and saturation physics.

Findings

Saturation momentum grows exponentially with energy, matching phenomenological models.

The model describes experimental data for total, elastic, and diffractive cross sections.

Small dipole interactions effectively represent soft Pomeron exchange in the CGC 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\Lb \h Y \Rb $, where $Y \,=\,ln s$. The saturation momentum, which determines the energy dependence of the scattering amplitude is proportional to $ Q^2_s\Lb \h Y \Rb \propto\,\exp\Lb\h \lambda\,Y\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.