The unintegrated gluon distribution from the GBW and BGK models

TL;DR

This paper derives analytical expressions for the unintegrated gluon distribution from GBW and BGK models at low x, compares predictions with experimental data, and investigates parameter effects on the longitudinal structure function.

Contribution

It provides new analytical results for the unintegrated gluon distribution and compares model predictions with experimental data, enhancing understanding of gluon dynamics at low x.

Findings

Analytical expressions for unintegrated gluon distribution at small transverse momentum.

Good agreement of model predictions with HERA data for $F_L$.

Parameter effects, including charm contributions, on $F_L$ are significant.

Abstract

The gluon distribution is obtained from the Golec-Biernat-W$\ddot{\mathrm{u}}$sthoff (GBW) and Bartels, Golec-Biernat and Kowalski (BGK) models at low $x$. We derive analytical results for the unintegrated color dipole gluon distribution function at small transverse momentum, which provides useful information to constrain the $k_{t}$-shape of the unintegrated gluon distribution in comparison with the unintegrated gluon distribution (UGD) models. The longitudinal proton structure function $F_{L}(x,Q^2)$ from the $k_{t}$ factorization scheme, using the unintegrated gluon density is computed. We compare the predictions for the on-shell and twist-2 corrections with the HERA data and the CJ15 parametrization method for $F_{L}$. We show that this method is very well described the experimental data within the on-shell and twist-2 framework. Effects of parameters on $F_{L}$, where charm contribution is taken into account, are investigated. These results are in good agreement with the data at fixed $W$.