Color dipole cross-section from unifying the color dipole picture and improved saturation models

TL;DR

This paper unifies the color dipole picture with improved saturation models to analyze the gluon density at low-x, demonstrating good agreement with saturation effects and perturbative QCD across different dipole sizes.

Contribution

It introduces a unified approach combining the color dipole picture with an improved saturation model to better describe the dipole cross-section across various sizes.

Findings

Good description of dipole cross-section at large r confirming saturation

Matching perturbative QCD results at small r due to gluon distribution running

Transition between saturation and perturbative regimes depends on x and expansion point

Abstract

We present an analysis of the color-dipole picture (CDP) for determination of the gluon density at low-$x$ which is obtained from the Altarelli-Martinelli equation by expansion at distinct points of expansion. The dipole cross-sections with respect to the improved saturation model of Bartels-Golec-Biernat-Kowalski (BGK) are obtained in a wide range of transverse sizes $r$ and compared with the Golec-Biernat-W$\ddot{\mathrm{u}}$sthoff (GBW) model. We find that the model gives a good description of the dipole cross-section at large $r$ which confirms saturation and matches the perturbative QCD result at a small $r$ due to the significant role of the running of the gluon distribution. The transition between these regions occurs with decreasing transverse sizes with a decrease of Bjorken $x$ and dependence on the expansion point.