Evolution of the color dipole cross section

TL;DR

This paper develops an analytical method using Laplace transforms to describe the evolution of the color dipole cross section at low x, incorporating saturation and geometric scaling, and compares results with existing models.

Contribution

It introduces a Laplace transform-based evolution approach for the color dipole cross section at LO and NLO, including Sudakov effects, and provides analytical expressions for gluon distributions.

Findings

Saturation scale and geometric scaling are preserved during evolution.

Analytical expressions for gluon distribution functions are derived.

Results agree with existing parametrizations and models at small and large transverse momenta.

Abstract

Using Laplace transform techniques, we describe the evolution of the color dipole cross section, at the leading-order and next-to-leading order approximations, from the Bartels-Golec-Biernat-Kowalski model in a kinematical region of low values of the Bjorken variable $x$ and a wide range of transverse dipole size $r$. This evolution method shows that the saturation scale and geometric scaling are retained. We derived analytical results for the integrated and unintegrated color dipole gluon distribution functions and compared them with the CJ15 parametrization group and the unintegrated color dipole gluon distribution models respectively. The Sudakov form factor into the evolution of the unintegrated color dipole gluon distribution is incorporated and the results are considered at small and large values of $k_{t}^{2}$