Unintegrated gluon distributions from the color dipole cross section in the BGK saturation model

TL;DR

This paper derives the unintegrated gluon distribution from the color dipole model incorporating saturation and DGLAP evolution, and validates it against HERA data for the proton structure function.

Contribution

It presents a method to extract unintegrated gluon distributions directly from the dipole cross section with saturation effects and DGLAP evolution, matching high-momentum behavior to collinear gluons.

Findings

Good agreement with HERA data for F_L(x,Q^2)

Consistent matching at high transverse momentum

Effective incorporation of saturation effects

Abstract

We evaluate the unintegrated gluon distribution of the proton starting from a parametrization of the color dipole cross section including DGLAP evolution and saturation effects. To this end, we perform the Fourier-Bessel transform of $\sigma(x,r)/\alpha(r)$. At large transverse momentum of gluons we match the so-obtained distribution to the logarithmic derivative of the collinear gluon distribution. We check our approach by calculating the proton structure function $F_L(x,Q^2)$ finding good agreement with HERA data.